Moduli spaces of local systems and higher Teichmüller theory

Fock, Vladimir; Goncharov, Alexander

doi:10.1007/s10240-006-0039-4

Fock, Vladimir ; Goncharov, Alexander

Publications Mathématiques de l'IHÉS, Tome 103 (2006), pp. 1-211.

Résumé

Let G be a split semisimple algebraic group over $𝐐$ with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to $G (𝐑)$ , construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmüller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil-Petersson form for one of these spaces. It is related to the motivic dilogarithm.

MR Zbl | 9 citations dans Numdam

DOI : 10.1007/s10240-006-0039-4

@article{PMIHES_2006__103__1_0,
     author = {Fock, Vladimir and Goncharov, Alexander},
     title = {Moduli spaces of local systems and higher {Teichm\"uller} theory},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--211},
     publisher = {Springer},
     volume = {103},
     year = {2006},
     doi = {10.1007/s10240-006-0039-4},
     mrnumber = {2233852},
     zbl = {1099.14025},
     language = {en},
     url = {https://www.numdam.org/articles/10.1007/s10240-006-0039-4/}
}

TY  - JOUR
AU  - Fock, Vladimir
AU  - Goncharov, Alexander
TI  - Moduli spaces of local systems and higher Teichmüller theory
JO  - Publications Mathématiques de l'IHÉS
PY  - 2006
SP  - 1
EP  - 211
VL  - 103
PB  - Springer
UR  - https://www.numdam.org/articles/10.1007/s10240-006-0039-4/
DO  - 10.1007/s10240-006-0039-4
LA  - en
ID  - PMIHES_2006__103__1_0
ER  -

%0 Journal Article
%A Fock, Vladimir
%A Goncharov, Alexander
%T Moduli spaces of local systems and higher Teichmüller theory
%J Publications Mathématiques de l'IHÉS
%D 2006
%P 1-211
%V 103
%I Springer
%U https://www.numdam.org/articles/10.1007/s10240-006-0039-4/
%R 10.1007/s10240-006-0039-4
%G en
%F PMIHES_2006__103__1_0

Fock, Vladimir; Goncharov, Alexander. Moduli spaces of local systems and higher Teichmüller theory. Publications Mathématiques de l'IHÉS, Tome 103 (2006), pp. 1-211. doi : 10.1007/s10240-006-0039-4. https://www.numdam.org/articles/10.1007/s10240-006-0039-4/

Bibliographie
Cité par

1. I. Biswas, P. Ares-Gastesi and S. Govindarajan, Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces, Trans. Amer. Math. Soc., 349 (1997), no. 4, 1551-1560, alg-geom/9510011. | MR | Zbl

2. A. A. Beilinson and V. G. Drinfeld, Opers, math.AG/0501398.

3. A. Berenstein and D. Kazhdan, Geometric and unipotent crystals, Geom. Funct. Anal., Special volume, part II (2000), 188-236. | MR | Zbl

4. A. Berenstein and A. Zelevinsky, Tensor product multiplicities, canonical bases and totally positive algebras, Invent. Math., 143 (2001), no. 1, 77-128, math.RT/9912012. | MR | Zbl

5. A. Berenstein, S. Fomin and A. Zelevinsky, Parametrizations of canonical bases and totally positive matrices, Adv. Math., 122 (1996), no. 1, 49-149. | MR | Zbl

6. A. Berenstein, S. Fomin and A. Zelevinsky, Cluster algebras. III: Upper bounds and double Bruhat cells, Duke Math. J., 126 (2005), no. 1, 1-52, math.RT/0305434. | MR

7. L. Bers, Universal Teichmüller space, Analytic Methods in Mathematical Physics (Sympos., Indiana Univ., Bloomington, Ind., 1968), pp. 65-83, Gordon and Breach (1970). | MR | Zbl

8. L. Bers, On the boundaries of Teichmüller spaces and on Kleinian groups, Ann. Math., 91 (1970), 670-600. | MR | Zbl

9. F. Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math., 92 (1988), no. 1, 139-162. | MR | Zbl

10. N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, translated from the 1968 French original by A. Pressley, Elements of Mathematics (Berlin), Springer, Berlin (2002). | MR | Zbl

11. M. Borovoi, Abelianization of the second nonabelian Galois cohomology, Duke Math. J., 72 (1993), 217-239. | MR | Zbl

12. J.-J Brylinsky and P. Deligne, Central extensions of reductive groups by K2, Publ. Math., Inst. Hautes Étud. Sci., 94 (2001), 5-85. | Numdam | MR | Zbl

13. N. Chriss and V. Ginzburg, Representation Theory and Complex Geometry, Birkhäuser Boston, Inc., Boston, MA (1997). | MR | Zbl

14. L. O. Chekhov and V. V. Fock, Quantum Teichmüller spaces, Teor. Mat. Fiz., 120 (1999), no. 3, 511-528, math.QA/9908165. | MR | Zbl

15. K. Corlette, Flat G-bundles with canonical metrics, J. Differ. Geom., 28 (1988), 361-382. | MR | Zbl

16. P. Deligne, Équations différentielles à points singuliers réguliers, Springer Lect. Notes Math., vol. 163 (1970). | MR | Zbl

17. V. G. Drinfeld and V. V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, Curr. Probl. Math., 24 (1984), 81-180, in Russian. | MR | Zbl

18. S. Donaldson, Twisted harmonic maps and the self-duality equations, Proc. Lond. Math. Soc., 55 (1987), 127-131. | MR | Zbl

19. H. Esnault, B. Kahn, M. Levine and E. Viehweg, The Arason invariant and mod 2 algebraic cycles, J. Amer. Math. Soc., 11 (1998), no. 1, 73-118. | MR | Zbl

20. V. V. Fock, Dual Teichmüller spaces, dg-ga/9702018.

21. V. V. Fock and A. A. Rosly, Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix, Transl., Ser. 2, Amer. Math. Soc., 191 (1999), 67-86, math.QA/9802054. | MR | Zbl

22. V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm, math.AG/0311245.

23. V. V. Fock and A. B. Goncharov, Moduli spaces of convex projective structures on surfaces, to appear in Adv. Math. (2006), math.AG/0405348. | MR | Zbl

24. V. V. Fock and A. B. Goncharov, Dual Teichmüller and lamination spaces, to appear in the Handbook on Teichmüller theory, math.AG/0510312. | MR

25. V. V. Fock and A. B. Goncharov, Cluster $𝒳$ -Varieties, Amalganations, and Poisson-Lie Groups, Progr. Math., Birkhäuser, volume dedicated to V. G. Drinfeld, math.RT/0508408. | MR

26. V. V. Fock and A. B. Goncharov, to appear.

27. S. Fomin and A. Zelevinsky, Double Bruhat cells and total positivity, J. Amer. Math. Soc., 12 (1999), no. 2, 335-380, math.RA/9912128. | MR | Zbl

28. S. Fomin and A. Zelevinsky, Cluster algebras, I, J. Amer. Math. Soc., 15 (2002), no. 2, 497-529, math.RT/0104151. | MR | Zbl

29. S. Fomin and A. Zelevinsky, Cluster algebras, II: Finite type classification, Invent. Math., 154 (2003), no. 1, 63-121, math.RA/0208229. | MR | Zbl

30. S. Fomin and A. Zelevinsky, The Laurent phenomenon. Adv. Appl. Math., 28 (2002), no. 2, 119-144, math.CO/0104241. | MR | Zbl

31. A. M. Gabrielov, I. M. Gelfand and M. V. Losik, Combinatorial computation of characteristic classes, I, II. (Russian), Funkts. Anal. Prilozh., 9 (1975), no. 2, 12-28; no. 3, 5-26. | MR | Zbl

32. F. R. Gantmacher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, revised edition of the 1941 Russian original. | Zbl

33. F. R. Gantmacher, M. G. Krein, Sur les Matrices Oscillatores, C.R. Acad. Sci. Paris, 201 (1935), AMS Chelsea Publ., Providence, RI (2002).

34. M. Gekhtman, M. Shapiro and A. Vainshtein, Cluster algebras and Poisson geometry, Mosc. Math. J., 3 (2003), no. 3, 899-934, math.QA/0208033. | MR | Zbl

35. M. Gekhtman, M. Shapiro and A. Vainshtein, Cluster algebras and Weil-Petersson forms, Duke Math. J., 127 (2005), no. 2, 291-311, math.QA/0309138. | MR | Zbl

36. O. Guichard, Sur les répresentations de groupes de surface, preprint.

37. W. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math., 54 (1984), no. 2, 200-225. | MR | Zbl

38. W. Goldman, Convex real projective structures on compact surfaces, J. Differ. Geom., 31 (1990), 126-159. | MR | Zbl

39. A. B. Goncharov, Geometry of configurations, polylogarithms, and motivic cohomology, Adv. Math., 114 (1995), no. 2, 197-318. | MR | Zbl

40. A. B. Goncharov, Polylogarithms and motivic Galois groups, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, part 2, pp. 43-96, Amer. Math. Soc., Providence, RI (1994). | MR | Zbl

41. A. B. Goncharov, Explicit Construction of Characteristic Classes, I, M. Gelfand Seminar, Adv. Soviet Math., vol. 16, part 1, pp. 169-210, Amer. Math. Soc., Providence, RI (1993). | MR | Zbl

42. A. B. Goncharov, Deninger's conjecture of L-functions of elliptic curves at s=3. Algebraic geometry, 4. J. Math. Sci., 81 (1996), no. 3, 2631-2656, alg-geom/9512016. | Zbl

43. A. B. Goncharov, Polylogarithms, regulators and Arakelov motivic complexes, J. Amer. Math. Soc., 18 (2005), no. 1, 1-6; math.AG/0207036. | MR | Zbl

44. A. B. Goncharov and Yu. I. Manin, Multiple ζ-motives and moduli spaces ℳ0,n , Compos. Math., 140 (2004), no. 1, 1-14, math.AG/0204102. | Zbl

45. J. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math., 84 (1986), no. 1, 157-176. | MR | Zbl

46. N. J. Hitchin, Lie groups and Teichmüller space, Topology, 31 (1992), no. 3, 449-473. | MR | Zbl

47. N. J. Hitchin, The self-duality equation on a Riemann surface, Proc. Lond. Math. Soc., 55 (1987), 59-126. | MR | Zbl

48. R. M. Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys., 43 (1998), no. 2, 105-115. | MR | Zbl

49. I. Kra, Deformation spaces, A Crash Course on Kleinian Groups (Lectures at a Special Session, Annual Winter Meeting, Amer. Math. Soc., San Francisco, Calif., 1974), Lect. Notes Math., vol. 400, pp. 48-70, Springer, Berlin (1974). | MR | Zbl

50. M. Kontsevich, Formal (non)commutative symplectic geometry, The Gelfand Mathematical Seminars 1990-1992, Birkhäuser Boston, Boston, MA (1993), 173-187. | MR | Zbl

51. F. Labourie, Anosov flows, surface groups and curves in projective spaces, preprint, Dec. 8 (2003). | MR | Zbl

52. G. Lusztig, Total positivity in reductive groups, Lie Theory and Geometry, Progr. Math., vol. 123, pp. 531-568, Birkhäuser Boston, Boston, MA (1994). | MR | Zbl

53. G. Lusztig, Total positivity and canonical bases, Algebraic Groups and Lie Groups, Austral. Math. Soc. Lect. Ser., vol. 9, pp. 281-295, Cambridge Univ. Press, Cambridge (1997). | MR | Zbl

54. C. Mcmullen, Iteration on Teichmüller space, Invent. Math., 99 (1990), no. 2, 425-454. | MR | Zbl

55. J. Milnor, Introduction to algebraic K-theory, Annals of Mathematics Studies, no. 72. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo (1971). | MR | Zbl

56. I. Nikolaev and E. Zhuzhoma, Flows on 2-dimensional manifolds, Springer Lect. Notes Math., vol. 1705 (1999). | MR | Zbl

57. R. C. Penner, The decorated Teichmüller space of punctured surfaces, Commun. Math. Phys., 113 (1987), no. 2, 299-339. | MR | Zbl

58. R. C. Penner, Weil-Petersson volumes, J. Differ. Geom., 35 (1992), no. 3, 559-608. | MR | Zbl

59. R. C. Penner, Universal constructions in Teichmüller theory, Adv. Math., 98 (1993), no. 2, 143-215. | MR | Zbl

60. R. C. Penner, The universal Ptolemy group and its completions, Geometric Galois Actions, 2, 293-312, Lond. Math. Soc. Lect. Note Ser., 243, Cambridge Univ. Press (1997). | MR | Zbl

61. R. C. Penner and J. L. Harer, Combinatorics of train tracks, Ann. Math. Studies, 125, Princeton University Press, Princeton, NJ (1992). | MR | Zbl

62. I. J. Schoenberg, Convex domains and linear combinations of continuous functions, Bull. Amer. Math. Soc., 39 (1933), 273-280. | MR | Zbl

63. I. J. Schoenberg, Über variationsvermindernde lineare Transformationen, Math. Z., 32 (1930), 321-322. | JFM | MR

64. C. Simpson, Constructing variations of Hodge structures using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc., 1 (1988), 867-918. | MR | Zbl

65. J.-P. Serre, Cohomologie Galoisienne (French), with a contribution by J.-L. Verdier, Lect. Notes Math., no. 5, 3rd edn., v+212pp., Springer, Berlin, New York (1965). | MR | Zbl

66. K. Strebel, Quadratic Differentials, Springer, Berlin, Heidelberg, New York (1984). | MR | Zbl

67. P. Sherman and A. Zelevinsky, Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Mosc. Math. J., 4 (2004), no. 4, 947-974, math.RT/0307082. | MR | Zbl

68. A. A. Suslin, Homology of GLn , characteristic classes and Milnor K-theory, Algebraic Geometry and its Applications, Tr. Mat. Inst. Steklova, 165 (1984), 188-204. | MR | Zbl

69. W. Thurston, The geometry and topology of three-manifolds, Princeton University Notes, http://www.msri.org/publications/books/gt3m.

70. A. M. Whitney, A reduction theorem for totally positive matrices, J. Anal. Math., 2 (1952), 88-92. | MR | Zbl

71. S. Wolpert, Geometry of the Weil-Petersson completion of the Teichmüller space, Surv. Differ. Geom., Suppl. J. Differ. Geom., VIII (2002), 357-393. | MR | Zbl

Rungi, Nicholas; Tamburelli, Andrea A semi-pseudo-Kähler structure on the SL(3,R)-Hitchin component and the Goldman symplectic form, Advances in Mathematics, Volume 461 (2025), p. 110066 | DOI:10.1016/j.aim.2024.110066
Bridgeland, Tom Joyce structures and their twistor spaces, Advances in Mathematics, Volume 462 (2025), p. 110089 | DOI:10.1016/j.aim.2024.110089
Evans, Parker Geometric structures for the G2′-Hitchin component, Advances in Mathematics, Volume 462 (2025), p. 110091 | DOI:10.1016/j.aim.2024.110091
Ishibashi, Tsukasa; Yuasa, Wataru Skein and cluster algebras of unpunctured surfaces for sp4, Advances in Mathematics, Volume 465 (2025), p. 110149 | DOI:10.1016/j.aim.2025.110149
Mathews, Daniel V. Spinors and horospheres, Advances in Mathematics, Volume 468 (2025), p. 110200 | DOI:10.1016/j.aim.2025.110200
Douglas, Daniel C.; Sun, Zhe Tropical Fock–Goncharov coordinates for SL 3 -webs on surfaces II: naturality, Algebraic Combinatorics, Volume 8 (2025) no. 1, p. 101 | DOI:10.5802/alco.408
Fei, JiaRui On the General Ranks of QP Representations, Algebras and Representation Theory, Volume 28 (2025) no. 1, p. 47 | DOI:10.1007/s10468-024-10306-5
Coman, Ioana; Longhi, Pietro; Teschner, Jörg From Quantum Curves to Topological String Partition Functions II, Annales Henri Poincaré (2025) | DOI:10.1007/s00023-025-01538-2
Jordan, David Quantum Character Varieties, Encyclopedia of Mathematical Physics (2025), p. 635 | DOI:10.1016/b978-0-323-95703-8.00015-x
Barman, Pabitra; Gupta, Subhojoy Dominating surface-group representations via Fock–Goncharov coordinates, Geometriae Dedicata, Volume 219 (2025) no. 1 | DOI:10.1007/s10711-024-00974-4
Dey, Subhadip On Borel Anosov subgroups of SL(d, ℝ), Geometry Topology, Volume 29 (2025) no. 1, p. 171 | DOI:10.2140/gt.2025.29.171
Ishibashi, Tsukasa; Kano, Shunsuke; Yuasa, Wataru Skein and Cluster Algebras with Coefficients for Unpunctured Surfaces, International Mathematics Research Notices, Volume 2025 (2025) no. 4 | DOI:10.1093/imrn/rnaf024
Beyer, James; Muller, Greg Deep Points of Cluster Algebras, International Mathematics Research Notices, Volume 2025 (2025) no. 4 | DOI:10.1093/imrn/rnaf027
Guichard, Olivier; Wienhard, Anna Generalizing Lusztig’s total positivity, Inventiones mathematicae, Volume 239 (2025) no. 3, p. 707 | DOI:10.1007/s00222-024-01303-y
Kantarcı Oğuz, Ezgi; Yıldırım, Emine Cluster expansions: T-walks, labeled posets and matrix calculations, Journal of Algebra, Volume 669 (2025), p. 183 | DOI:10.1016/j.jalgebra.2025.01.024
Baba, Shinpei Neck‐pinching of CP1 $C P^{1}$ ‐structures in the PSL2C ${P S L}_{2} C$ ‐character variety, Journal of Topology, Volume 18 (2025) no. 1 | DOI:10.1112/topo.70010
Çanakçı, İlke; Kalck, Martin; Pressland, Matthew Cluster categories for completed infinity‐gons I: Categorifying triangulations, Journal of the London Mathematical Society, Volume 111 (2025) no. 2 | DOI:10.1112/jlms.70092
Kineider, Clarence; Rogozinnikov, Eugen On partial abelianization of framed local systems, Mathematische Annalen (2025) | DOI:10.1007/s00208-025-03093-x
Bossinger, Lara; Cheung, Man-Wai; Magee, Timothy; Nájera Chávez, Alfredo Newton–Okounkov bodies and minimal models for cluster varieties, Advances in Mathematics, Volume 447 (2024), p. 109680 | DOI:10.1016/j.aim.2024.109680
Chen, Qiyue; Mandel, Travis; Qin, Fan Stability scattering diagrams and quiver coverings, Advances in Mathematics, Volume 459 (2024), p. 110019 | DOI:10.1016/j.aim.2024.110019
Douglas, Daniel C Points of quantum SLn coming from quantum snakes, Algebraic Geometric Topology, Volume 24 (2024) no. 5, p. 2537 | DOI:10.2140/agt.2024.24.2537
Martone, Giuseppe; Ouyang, Charles; Tamburelli, Andrea A closed ball compactification of a maximal component via cores of trees, Algebraic Geometric Topology, Volume 24 (2024) no. 7, p. 3693 | DOI:10.2140/agt.2024.24.3693
Goncharov, Alexander; Kontsevich, Maxim Spectral Description of Non-Commutative Local Systems on Surfaces and Non-Commutative Cluster Varieties, Arithmetic and Algebraic Geometry (2024), p. 109 | DOI:10.1007/978-3-031-74134-0_5
Ip, Ivan Chi-Ho; Man, Ryuichi Positive Representations with Zero Casimirs, Communications in Mathematical Physics, Volume 405 (2024) no. 4 | DOI:10.1007/s00220-024-04955-2
Kim, Hyun Kyu; Scarinci, Carlos A Quantization of Moduli Spaces of 3-Dimensional Gravity, Communications in Mathematical Physics, Volume 405 (2024) no. 6 | DOI:10.1007/s00220-024-05012-8
Dumas, David; Neitzke, Andrew Opers and Non-Abelian Hodge: Numerical Studies, Experimental Mathematics, Volume 33 (2024) no. 1, p. 27 | DOI:10.1080/10586458.2021.1988006
Douglas, Daniel C.; Sun, Zhe Tropical Fock–Goncharov coordinates for -webs on surfaces I: construction, Forum of Mathematics, Sigma, Volume 12 (2024) | DOI:10.1017/fms.2023.120
Hamenstädt, Ursula; Jäckel, Frieder Rigidity of geometric structures, Geometriae Dedicata, Volume 218 (2024) no. 1 | DOI:10.1007/s10711-023-00861-4
Lee, Gye-Seon; Zhang, Tengren Cusped Borel Anosov representations with positivity, Geometriae Dedicata, Volume 218 (2024) no. 2 | DOI:10.1007/s10711-024-00895-2
Gao, Honghao; Shen, Linhui; Weng, Daping Augmentations, Fillings, and Clusters, Geometric and Functional Analysis, Volume 34 (2024) no. 3, p. 798 | DOI:10.1007/s00039-024-00673-y
Loray, Frank The Riemann-Hilbert Correspondence for Rank 2 Meromorphic Connections on Curves, Handbook of Geometry and Topology of Singularities VI: Foliations (2024), p. 267 | DOI:10.1007/978-3-031-54172-8_8
Pan, Huiping; Su, Weixu The Geometry of the Thurston Metric: A Survey, In the Tradition of Thurston III (2024), p. 7 | DOI:10.1007/978-3-031-43502-7_2
Simpson, Carlos T. Twistor space for local systems on an open curve, International Journal of Mathematics, Volume 35 (2024) no. 09 | DOI:10.1142/s0129167x24410131
Inoue, Rei; Kuniba, Atsuo; Terashima, Yuji Quantum Cluster Algebras and 3D Integrability: Tetrahedron and 3D Reflection Equations, International Mathematics Research Notices, Volume 2024 (2024) no. 16, p. 11549 | DOI:10.1093/imrn/rnae128
Suen, Yat-Hin Toric Vector Bundles, Non-abelianization, and Spectral Networks, International Mathematics Research Notices, Volume 2024 (2024) no. 24, p. 14576 | DOI:10.1093/imrn/rnae250
Asaka, Takeru; Ishibashi, Tsukasa; Kano, Shunsuke Earthquake Theorem for Cluster Algebras of Finite Type, International Mathematics Research Notices, Volume 2024 (2024) no. 8, p. 7129 | DOI:10.1093/imrn/rnae027
Dey, Subhadip; Kapovich, Michael Klein–Maskit combination theorem for Anosov subgroups: Amalgams, Journal für die reine und angewandte Mathematik (Crelles Journal) (2024) | DOI:10.1515/crelle-2024-0080
Yurikusa, Toshiya Denominator vectors and dimension vectors from triangulated surfaces, Journal of Algebra, Volume 641 (2024), p. 620 | DOI:10.1016/j.jalgebra.2023.12.002
Lüdenbach, Teresa Ideal polytopes for representations of GLn(C), Journal of Algebra, Volume 658 (2024), p. 90 | DOI:10.1016/j.jalgebra.2024.05.055
Kaufman, Dani Mutation invariant functions on cluster ensembles, Journal of Pure and Applied Algebra, Volume 228 (2024) no. 2, p. 107495 | DOI:10.1016/j.jpaa.2023.107495
Douglas, Daniel C. Quantum traces for SLn(C): The case n = 3, Journal of Pure and Applied Algebra, Volume 228 (2024) no. 7, p. 107652 | DOI:10.1016/j.jpaa.2024.107652
Beyrer, Jonas; Pozzetti, Beatrice Degenerations of k $k$ ‐positive surface group representations, Journal of Topology, Volume 17 (2024) no. 3 | DOI:10.1112/topo.12352
Lê, Thang T. Q.; Sikora, Adam S. Stated SL(n $n$ )‐skein modules and algebras, Journal of Topology, Volume 17 (2024) no. 3 | DOI:10.1112/topo.12350
Casals, Roger; Gorsky, Eugene; Gorsky, Mikhail; Le, Ian; Shen, Linhui; Simental, José Cluster structures on braid varieties, Journal of the American Mathematical Society, Volume 38 (2024) no. 2, p. 369 | DOI:10.1090/jams/1048
Przytycki, Józef H.; Bakshi, Rhea Palak; Ibarra, Dionne; Montoya-Vega, Gabriel; Weeks, Deborah The Kauffman Bracket Skein Module and Algebra of Surface I-Bundles, Lectures in Knot Theory (2024), p. 249 | DOI:10.1007/978-3-031-40044-5_13
Przytycki, Józef H.; Bakshi, Rhea Palak; Ibarra, Dionne; Montoya-Vega, Gabriel; Weeks, Deborah Multiplicative Structure of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt, Lectures in Knot Theory (2024), p. 265 | DOI:10.1007/978-3-031-40044-5_14
Aamand, Nanna; Kaufman, Dani A Wilson line realization of quantum groups, Letters in Mathematical Physics, Volume 114 (2024) no. 1 | DOI:10.1007/s11005-023-01756-x
Di Francesco, Philippe; Kedem, Rinat; Khoroshkin, Sergey; Schrader, Gus; Shapiro, Alexander Ruijsenaars wavefunctions as modular group matrix coefficients, Letters in Mathematical Physics, Volume 114 (2024) no. 6 | DOI:10.1007/s11005-024-01881-1
Allegretti, Dylan G. L. Stability conditions and Teichmüller space, Mathematische Annalen, Volume 390 (2024) no. 3, p. 3827 | DOI:10.1007/s00208-024-02852-6
Yoon, Seokbeom The twisted 1-loop invariant and the Jacobian of Ptolemy varieties, Mathematische Zeitschrift, Volume 307 (2024) no. 1 | DOI:10.1007/s00209-024-03491-y
Alessandrini, Daniele; Guichard, Olivier; Rogozinnikov, Eugen; Wienhard, Anna Noncommutative Coordinates for Symplectic Representations, Memoirs of the American Mathematical Society, Volume 300 (2024) no. 1504 | DOI:10.1090/memo/1504
Kenyon, R. Some combinatorial problems arising in the dimer model, Open Problems in Algebraic Combinatorics, Volume 110 (2024), p. 39 | DOI:10.1090/pspum/110/02012
Berestycki, Nathanaël; Laslier, Benoît; Ray, Gourab Dimers on Riemann surfaces, II: Conformal invariance and scaling limit, Probability and Mathematical Physics, Volume 5 (2024) no. 4, p. 961 | DOI:10.2140/pmp.2024.5.961
Song, Jinfeng Cluster realisations of ıquantum $ı q u a n t u m$ groups of type AI, Proceedings of the London Mathematical Society, Volume 129 (2024) no. 4 | DOI:10.1112/plms.12636
Argüz, Hülya; Bousseau, Pierrick Quivers and curves in higher dimension, Transactions of the American Mathematical Society (2024) | DOI:10.1090/tran/9232
Mondello, Gabriele; Panov, Dmitri On decorated representation spaces associated to spherical surfaces, Transactions of the American Mathematical Society (2024) | DOI:10.1090/tran/9112
Fraser, Chris; Pylyavskyy, Pavlo Tensor diagrams and cluster combinatorics at punctures, Advances in Mathematics, Volume 412 (2023), p. 108796 | DOI:10.1016/j.aim.2022.108796
Ishibashi, Tsukasa; Oya, Hironori; Shen, Linhui A=U for cluster algebras from moduli spaces of G-local systems, Advances in Mathematics, Volume 431 (2023), p. 109256 | DOI:10.1016/j.aim.2023.109256
Bray, Harrison; Canary, Richard; Kao, Lien-Yung; Martone, Giuseppe Pressure metrics for cusped Hitchin components, Advances in Mathematics, Volume 435 (2023), p. 109352 | DOI:10.1016/j.aim.2023.109352
Kim, Hyun Kyu; Lê, Thang T Q; Son, Miri SL2 quantum trace in quantum Teichmüller theory via writhe, Algebraic Geometric Topology, Volume 23 (2023) no. 1, p. 339 | DOI:10.2140/agt.2023.23.339
Boden, Hans U; Karimi, Homayun; Sikora, Adam S Adequate links in thickened surfaces and the generalized Tait conjectures, Algebraic Geometric Topology, Volume 23 (2023) no. 5, p. 2271 | DOI:10.2140/agt.2023.23.2271
Williams, Nicholas J. Quiver combinatorics and triangulations of cyclic polytopes, Algebraic Combinatorics, Volume 6 (2023) no. 3, p. 639 | DOI:10.5802/alco.280
Inoue, Rei; Yamazaki, Takao Invariants of Weyl Group Action and q-characters of Quantum Affine Algebras, Algebras and Representation Theory, Volume 26 (2023) no. 6, p. 3167 | DOI:10.1007/s10468-023-10205-1
Bousseau, Pierrick Strong Positivity for the Skein Algebras of the 4-Punctured Sphere and of the 1-Punctured Torus, Communications in Mathematical Physics, Volume 398 (2023) no. 1, p. 1 | DOI:10.1007/s00220-022-04512-9
Schulz, Sebastian Nilpotent Higgs Bundles and Families of Flat Connections, Communications in Mathematical Physics, Volume 403 (2023) no. 2, p. 877 | DOI:10.1007/s00220-023-04811-9
DAI, XIAN; MARTONE, GIUSEPPE Correlation of the renormalized Hilbert length for convex projective surfaces, Ergodic Theory and Dynamical Systems, Volume 43 (2023) no. 9, p. 2938 | DOI:10.1017/etds.2022.56
Casals, Roger; Zaslow, Eric Legendrian weaves : N–graph calculus, flag moduli and applications, Geometry Topology, Volume 26 (2023) no. 8, p. 3589 | DOI:10.2140/gt.2022.26.3589
Edwards, Samuel; Lee, Minju; Oh, Hee Anosov groups: local mixing, counting and equidistribution, Geometry Topology, Volume 27 (2023) no. 2, p. 513 | DOI:10.2140/gt.2023.27.513
Howie, Joshua A.; Mathews, Daniel V.; Purcell, Jessica S.; Thompson, Em K. A-polynomials of fillings of the Whitehead sister, International Journal of Mathematics, Volume 34 (2023) no. 13 | DOI:10.1142/s0129167x23500854
Chekhov, Leonid O; Shapiro, Michael Log-Canonical Coordinates for Symplectic Groupoid and Cluster Algebras, International Mathematics Research Notices, Volume 2023 (2023) no. 11, p. 9565 | DOI:10.1093/imrn/rnac101
Le, Ian; Luo, Sammy Generalized Minors and Tensor Invariants, International Mathematics Research Notices, Volume 2023 (2023) no. 16, p. 13658 | DOI:10.1093/imrn/rnac200
Lee, Minju; Oh, Hee Invariant Measures for Horospherical Actions and Anosov Groups, International Mathematics Research Notices, Volume 2023 (2023) no. 19, p. 16226 | DOI:10.1093/imrn/rnac262
Pushkar, Petya; Temkin, Misha Enhanced Bruhat Decomposition and Morse Theory, International Mathematics Research Notices, Volume 2023 (2023) no. 19, p. 16837 | DOI:10.1093/imrn/rnac326
Allegretti, Dylan G L On the Wall-Crossing Formula for Quadratic Differentials, International Mathematics Research Notices, Volume 2023 (2023) no. 9, p. 8033 | DOI:10.1093/imrn/rnac071
Bazier-Matte, Véronique; Huang, Ruiyan; Luo, Hanyi Number of triangulations of a Möbius strip, Involve, a Journal of Mathematics, Volume 16 (2023) no. 4, p. 547 | DOI:10.2140/involve.2023.16.547
Argüz, Hülya; Bousseau, Pierrick Fock–Goncharov dual cluster varieties and Gross–Siebert mirrors, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 0 (2023) no. 0 | DOI:10.1515/crelle-2023-0043
Holm, Thorsten; Skowroński, Andrzej; Skowyrski, Adam Virtual mutations of weighted surface algebras, Journal of Algebra, Volume 619 (2023), p. 822 | DOI:10.1016/j.jalgebra.2022.11.026
Dechant, Pierre-Philippe; He, Yang-Hui; Heyes, Elli; Hirst, Edward Cluster algebras: Network science and machine learning, Journal of Computational Algebra, Volume 8 (2023), p. 100008 | DOI:10.1016/j.jaca.2023.100008
Musiker, Gregg; Ovenhouse, Nicholas; Zhang, Sylvester W. Matrix formulae for decorated super Teichmüller spaces, Journal of Geometry and Physics, Volume 189 (2023), p. 104828 | DOI:10.1016/j.geomphys.2023.104828
Zhao, Peng; Zou, Hao Remarks on 2d unframed quiver gauge theories, Journal of High Energy Physics, Volume 2023 (2023) no. 5 | DOI:10.1007/jhep05(2023)121
Kim, Hyuk; Kim, Seonhwa; Yoon, Seokbeom Octahedral developing of knot complement II: Ptolemy coordinates and applications, Journal of Knot Theory and Its Ramifications, Volume 32 (2023) no. 09 | DOI:10.1142/s0218216523500578
Fei, Jiarui Tropical F $F$ ‐polynomials and general presentations, Journal of the London Mathematical Society, Volume 107 (2023) no. 6, p. 2079 | DOI:10.1112/jlms.12734
Bridgeland, Tom; Masoero, Davide On the monodromy of the deformed cubic oscillator, Mathematische Annalen, Volume 385 (2023) no. 1-2, p. 193 | DOI:10.1007/s00208-021-02337-w
Ishibashi, Tsukasa; Yuasa, Wataru Skein and cluster algebras of unpunctured surfaces for ${sl}_{3}$ , Mathematische Zeitschrift, Volume 303 (2023) no. 3 | DOI:10.1007/s00209-023-03208-7
Ishibashi, Tsukasa; Oya, Hironori Wilson lines and their Laurent positivity, Mathematische Zeitschrift, Volume 305 (2023) no. 2 | DOI:10.1007/s00209-023-03355-x
Huang, Yi; Sun, Zhe McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential, Memoirs of the American Mathematical Society, Volume 286 (2023) no. 1422 | DOI:10.1090/memo/1422
Fock, Vladimir; Tatitscheff, Valdo; Thomas, Alexander Topological quantum field theories from Hecke algebras, Representation Theory of the American Mathematical Society, Volume 27 (2023) no. 9, p. 248 | DOI:10.1090/ert/640
Zuevsky, A. Reduction cohomology of Riemann surfaces, Reviews in Mathematical Physics, Volume 35 (2023) no. 07 | DOI:10.1142/s0129055x23300054
Del Monte, Fabrizio; Longhi, Pietro The threefold way to quantum periods: WKB, TBA equations and q-Painlevé, SciPost Physics, Volume 15 (2023) no. 3 | DOI:10.21468/scipostphys.15.3.112
Goncharov, Alexander B.; Kislinskyi, Oleksii Cluster construction of the second motivic Chern class, Selecta Mathematica, Volume 29 (2023) no. 4 | DOI:10.1007/s00029-023-00854-x
Szabó, Szilárd Hitchin WKB-problem andP = Wconjecture in lowest degree for rank 2 over the 5-punctured sphere, The Quarterly Journal of Mathematics, Volume 74 (2023) no. 2, p. 687 | DOI:10.1093/qmath/haac037
Chekhov, L. O. Cluster variables for affine Lie–Poisson systems, Theoretical and Mathematical Physics, Volume 217 (2023) no. 3, p. 1987 | DOI:10.1134/s0040577923120140
Schwarz, Albert S.; Zeitlin, Anton M. Super Riemann Surfaces and Fatgraphs, Universe, Volume 9 (2023) no. 9, p. 384 | DOI:10.3390/universe9090384
Bertola, Marco; Korotkin, Dmitry; del Monte, Fabrizio Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion, Zurnal matematiceskoj fiziki, analiza, geometrii, Volume 19 (2023) no. 2, p. 301 | DOI:10.15407/mag19.02.301
Gupta, Subhojoy; Su, Weixu Dominating surface-group representations into ${PSL}_{2} (C)$ in the relative representation variety, manuscripta mathematica, Volume 172 (2023) no. 3-4, p. 1169 | DOI:10.1007/s00229-022-01443-6
Canary, Richard; Zhang, Tengren; Zimmer, Andrew Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups, Advances in Mathematics, Volume 404 (2022), p. 108439 | DOI:10.1016/j.aim.2022.108439
Williams, Nicholas J. New interpretations of the higher Stasheff–Tamari orders, Advances in Mathematics, Volume 407 (2022), p. 108552 | DOI:10.1016/j.aim.2022.108552
Kim, Sungwoon; Tan, Ser Peow; Zhang, Tengren Weakly positive and directed Anosov representations, Advances in Mathematics, Volume 408 (2022), p. 108611 | DOI:10.1016/j.aim.2022.108611
Lam, Thomas; Speyer, David E. Cohomology of cluster varieties, I: Locally acyclic case, Algebra Number Theory, Volume 16 (2022) no. 1, p. 179 | DOI:10.2140/ant.2022.16.179
Bertola, M.; Tarricone, S. Stokes Manifolds and Cluster Algebras, Communications in Mathematical Physics, Volume 390 (2022) no. 3, p. 1413 | DOI:10.1007/s00220-021-04293-7
Schaffhauser, Florent Symmetric Differentials and the Dimension of Hitchin Components for Orbi-Curves, Current Trends in Analysis, its Applications and Computation (2022), p. 129 | DOI:10.1007/978-3-030-87502-2_13
Christ, Merlin Ginzburg algebras of triangulated surfaces and perverse schobers, Forum of Mathematics, Sigma, Volume 10 (2022) | DOI:10.1017/fms.2022.1
Kydonakis, Georgios From Hyperbolic Dehn Filling to Surgeries in Representation Varieties, In the Tradition of Thurston II (2022), p. 201 | DOI:10.1007/978-3-030-97560-9_6
Zuevsky, A. Schottky vertex operator cluster algebras, International Journal of Modern Physics A, Volume 37 (2022) no. 17 | DOI:10.1142/s0217751x22501111
Cheung, Man-Wai; Magee, Timothy; Nájera Chávez, Alfredo Compactifications of Cluster Varieties and Convexity, International Mathematics Research Notices, Volume 2022 (2022) no. 14, p. 10858 | DOI:10.1093/imrn/rnab030
Shen, Linhui Duals of Semisimple Poisson–Lie Groups and Cluster Theory of Moduli Spaces of G-local Systems, International Mathematics Research Notices, Volume 2022 (2022) no. 18, p. 14295 | DOI:10.1093/imrn/rnab094
Bray, Harrison; Canary, Richard; Kao, Lien-Yung; Martone, Giuseppe Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2022 (2022) no. 791, p. 1 | DOI:10.1515/crelle-2022-0035
Musiker, Gregg; Ovenhouse, Nicholas; Zhang, Sylvester W. Double dimer covers on snake graphs from super cluster expansions, Journal of Algebra, Volume 608 (2022), p. 325 | DOI:10.1016/j.jalgebra.2022.05.033
Casals, Roger Lagrangian skeleta and plane curve singularities, Journal of Fixed Point Theory and Applications, Volume 24 (2022) no. 2 | DOI:10.1007/s11784-022-00939-8
Łukowski, Tomasz; Moerman, Robert; Stalknecht, Jonah Pushforwards via scattering equations with applications to positive geometries, Journal of High Energy Physics, Volume 2022 (2022) no. 10 | DOI:10.1007/jhep10(2022)003
Semenyakin, M. Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux, Journal of High Energy Physics, Volume 2022 (2022) no. 10 | DOI:10.1007/jhep10(2022)198
Kruthoff, Jorrit Higher spin JT gravity and a matrix model dual, Journal of High Energy Physics, Volume 2022 (2022) no. 9 | DOI:10.1007/jhep09(2022)017
Neitzke, Andrew; Yan, Fei The quantum UV-IR map for line defects in $gl$ (3)-type class S theories, Journal of High Energy Physics, Volume 2022 (2022) no. 9 | DOI:10.1007/jhep09(2022)081
Labourie, François Entropy and affine actions for surface groups, Journal of Topology, Volume 15 (2022) no. 3, p. 1017 | DOI:10.1112/topo.12243
Gekhtman, Misha; Shapiro, Michael; Vainshtein, Alek Generalized cluster structures related to the Drinfeld double of GLn $G L_{n}$ , Journal of the London Mathematical Society, Volume 105 (2022) no. 3, p. 1601 | DOI:10.1112/jlms.12542
Stecker, Florian; Treib, Nicolaus Domains of discontinuity in oriented flag manifolds, Journal of the London Mathematical Society, Volume 106 (2022) no. 2, p. 1380 | DOI:10.1112/jlms.12602
Abenda, Simonetta; Grinevich, Petr G. Real regular KP divisors on $M$ -curves and totally non-negative Grassmannians, Letters in Mathematical Physics, Volume 112 (2022) no. 6 | DOI:10.1007/s11005-022-01609-z
Ishibashi, Tsukasa Wilson Lines and Their Laurent Positivity, Lie Theory and Its Applications in Physics, Volume 396 (2022), p. 457 | DOI:10.1007/978-981-19-4751-3_42
Burelle, Jean-Philippe; Treib, Nicolaus Schottky presentations of positive representations, Mathematische Annalen, Volume 382 (2022) no. 3-4, p. 1705 | DOI:10.1007/s00208-021-02326-z
Finski, Siarhei Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion, Mathematische Zeitschrift, Volume 301 (2022) no. 4, p. 3285 | DOI:10.1007/s00209-022-03020-9
Bertola, M.; Korotkin, D. On the tau function of the hypergeometric equation, Physica D: Nonlinear Phenomena, Volume 439 (2022), p. 133381 | DOI:10.1016/j.physd.2022.133381
Simpson, Carlos The twistor geometry of parabolic structures in rank two, Proceedings - Mathematical Sciences, Volume 132 (2022) no. 2 | DOI:10.1007/s12044-022-00696-1
Chekhov, Leonid Olegovich; Shapiro, Michael Zalmanovich; Shibo, Huang Roots of the characteristic equation for the symplectic groupoid, Russian Mathematical Surveys, Volume 77 (2022) no. 3, p. 552 | DOI:10.1070/rm9999
Lê, Thang T. Q.; Yu, Tao Quantum traces and embeddings of stated skein algebras into quantum tori, Selecta Mathematica, Volume 28 (2022) no. 4 | DOI:10.1007/s00029-022-00781-3
Allegretti, Dylan G. L. Quantization of canonical bases and the quantum symplectic double, manuscripta mathematica, Volume 167 (2022) no. 3-4, p. 613 | DOI:10.1007/s00229-021-01276-9
Collier, Brian; Sanders, Andrew (G,P)-Opers and global Slodowy slices, Advances in Mathematics, Volume 377 (2021), p. 107490 | DOI:10.1016/j.aim.2020.107490
Allegretti, Dylan G.L. Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces, Advances in Mathematics, Volume 380 (2021), p. 107610 | DOI:10.1016/j.aim.2021.107610
Gupta, Subhojoy; Mj, Mahan Meromorphic projective structures, grafting and the monodromy map, Advances in Mathematics, Volume 383 (2021), p. 107673 | DOI:10.1016/j.aim.2021.107673
Weng, Daping Donaldson-Thomas transformation of Grassmannian, Advances in Mathematics, Volume 383 (2021), p. 107721 | DOI:10.1016/j.aim.2021.107721
Pappas, Georgios Volume and symplectic structure for ℓ-adic local systems, Advances in Mathematics, Volume 387 (2021), p. 107836 | DOI:10.1016/j.aim.2021.107836
Bao, Huanchen; He, Xuhua Flag manifolds over semifields, Algebra Number Theory, Volume 15 (2021) no. 8, p. 2037 | DOI:10.2140/ant.2021.15.2037
Le, Ian Intersection Pairings for Higher Laminations, Algebraic Combinatorics, Volume 4 (2021) no. 5, p. 823 | DOI:10.5802/alco.182
Arthamonov, S.; Reshetikhin, N. Superintegrable Systems on Moduli Spaces of Flat Connections, Communications in Mathematical Physics, Volume 386 (2021) no. 3, p. 1337 | DOI:10.1007/s00220-021-04128-5
Bertola, M.; Korotkin, D. Tau-Functions and Monodromy Symplectomorphisms, Communications in Mathematical Physics, Volume 388 (2021) no. 1, p. 245 | DOI:10.1007/s00220-021-04224-6
Savini, A. Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups, Geometriae Dedicata, Volume 213 (2021) no. 1, p. 375 | DOI:10.1007/s10711-020-00587-7
Zeybek, Hatice Shearing deformations of Hitchin representations and the Atiyah–Bott–Goldman symplectic form, Geometriae Dedicata, Volume 213 (2021) no. 1, p. 401 | DOI:10.1007/s10711-020-00588-6
Brunswic, Léo Cauchy-compact flat spacetimes with extreme BTZ, Geometriae Dedicata, Volume 214 (2021) no. 1, p. 571 | DOI:10.1007/s10711-021-00629-8
Ballas, Samuel A.; Casella, Alex Gluing equations for real projective structures on 3-manifolds, Geometriae Dedicata, Volume 215 (2021) no. 1, p. 69 | DOI:10.1007/s10711-021-00641-y
Dumas, David; Sanders, Andrew Uniformization of compact complex manifolds by Anosov homomorphisms, Geometric and Functional Analysis, Volume 31 (2021) no. 4, p. 815 | DOI:10.1007/s00039-021-00572-6
Lam, Wai Yeung Quadratic differentials and circle patterns on complex projective tori, Geometry Topology, Volume 25 (2021) no. 2, p. 961 | DOI:10.2140/gt.2021.25.961
Fock, Vladimir; Thomas, Alexander Higher Complex Structures, International Mathematics Research Notices, Volume 2021 (2021) no. 20, p. 15873 | DOI:10.1093/imrn/rnz283
Lê, Thang T Q; Thurston, Dylan P; Yu, Tao Lower and Upper Bounds for Positive Bases of Skein Algebras, International Mathematics Research Notices, Volume 2021 (2021) no. 4, p. 3186 | DOI:10.1093/imrn/rnaa082
Swoboda, Jan Moduli Spaces of Higgs Bundles – Old and New, Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 123 (2021) no. 2, p. 65 | DOI:10.1365/s13291-021-00229-1
Pozzetti, Maria Beatrice; Sambarino, Andrés; Wienhard, Anna Conformality for a robust class of non-conformal attractors, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2021 (2021) no. 774, p. 1 | DOI:10.1515/crelle-2020-0029
Kim, Hyun Kyu Irreducible self-adjoint representations of quantum Teichmüller space and the phase constants, Journal of Geometry and Physics, Volume 162 (2021), p. 104103 | DOI:10.1016/j.geomphys.2021.104103
Damgaard, David; Ferro, Livia; Łukowski, Tomasz; Moerman, Robert Momentum amplituhedron meets kinematic associahedron, Journal of High Energy Physics, Volume 2021 (2021) no. 2 | DOI:10.1007/jhep02(2021)041
Cirafici, Michele A note on discrete dynamical systems in theories of class S, Journal of High Energy Physics, Volume 2021 (2021) no. 5 | DOI:10.1007/jhep05(2021)224
Stern, Walker H. 2-Segal objects and algebras in spans, Journal of Homotopy and Related Structures, Volume 16 (2021) no. 2, p. 297 | DOI:10.1007/s40062-021-00282-8
Gupta, Subhojoy Monodromy groups of CP1‐structures on punctured surfaces, Journal of Topology, Volume 14 (2021) no. 2, p. 538 | DOI:10.1112/topo.12189
Galashin, Pavel; Karp, Steven; Lam, Thomas Regularity theorem for totally nonnegative flag varieties, Journal of the American Mathematical Society, Volume 35 (2021) no. 2, p. 513 | DOI:10.1090/jams/983
Loftin, John; Zhang, Tengren Coordinates on the augmented moduli space of convex RP2 structures, Journal of the London Mathematical Society, Volume 104 (2021) no. 4, p. 1930 | DOI:10.1112/jlms.12488
Inoue, Rei Cluster realization of Weyl groups and q-characters of quantum affine algebras, Letters in Mathematical Physics, Volume 111 (2021) no. 1 | DOI:10.1007/s11005-020-01347-0
Ip, Ivan C. H. On tensor product decomposition of positive representations of $U_{q \tilde{q}} (sl (2, R))$ , Letters in Mathematical Physics, Volume 111 (2021) no. 2 | DOI:10.1007/s11005-021-01381-6
Sun, Zhe Rank n swapping algebra for ${PGL}_{n}$ Fock–Goncharov $X$ moduli space, Mathematische Annalen, Volume 380 (2021) no. 3-4, p. 1311 | DOI:10.1007/s00208-020-02025-1
Kim, Inkang; Kim, Sungwoon Primitive stable representations in higher rank semisimple Lie groups, Revista Matemática Complutense, Volume 34 (2021) no. 3, p. 715 | DOI:10.1007/s13163-020-00372-w
Inoue, Rei; Ishibashi, Tsukasa; Oya, Hironori Cluster realizations of Weyl groups and higher Teichmüller theory, Selecta Mathematica, Volume 27 (2021) no. 3 | DOI:10.1007/s00029-021-00630-9
Beyrer, Jonas; Pozzetti, Beatrice A collar lemma for partially hyperconvex surface group representations, Transactions of the American Mathematical Society (2021) | DOI:10.1090/tran/8453
Bridgeman, Martin; Canary, Richard; Labourie, François Simple length rigidity for Hitchin representations, Advances in Mathematics, Volume 360 (2020), p. 106901 | DOI:10.1016/j.aim.2019.106901
Ovenhouse, Nicholas Non-commutative integrability of the Grassmann pentagram map, Advances in Mathematics, Volume 373 (2020), p. 107309 | DOI:10.1016/j.aim.2020.107309
Gyoda, Yasuaki; Yurikusa, Toshiya F-Matrices of Cluster Algebras from Triangulated Surfaces, Annals of Combinatorics, Volume 24 (2020) no. 4, p. 649 | DOI:10.1007/s00026-020-00507-2
Erdmann, Karin; Skowroński, Andrzej Higher spherical algebras, Archiv der Mathematik, Volume 114 (2020) no. 1, p. 25 | DOI:10.1007/s00013-019-01365-y
Cho, So Young; Kim, Hyuna; Kim, Hyun Kyu; Oh, Doeun Laurent Positivity of Quantized Canonical Bases for Quantum Cluster Varieties from Surfaces, Communications in Mathematical Physics, Volume 373 (2020) no. 2, p. 655 | DOI:10.1007/s00220-019-03411-w
Coman, Ioana; Pomoni, Elli; Teschner, Jörg Toda Conformal Blocks, Quantum Groups, and Flat Connections, Communications in Mathematical Physics, Volume 375 (2020) no. 2, p. 1117 | DOI:10.1007/s00220-019-03617-y
Hollands, Lotte; Neitzke, Andrew Exact WKB and Abelianization for the $T_{3}$ Equation, Communications in Mathematical Physics, Volume 380 (2020) no. 1, p. 131 | DOI:10.1007/s00220-020-03875-1
Bossinger, Lara; Frías-Medina, Bosco; Magee, Timothy; Nájera Chávez, Alfredo Toric degenerations of cluster varieties and cluster duality, Compositio Mathematica, Volume 156 (2020) no. 10, p. 2149 | DOI:10.1112/s0010437x2000740x
Whang, Junho Peter Global geometry on moduli of local systems for surfaces with boundary, Compositio Mathematica, Volume 156 (2020) no. 8, p. 1517 | DOI:10.1112/s0010437x20007241
Çanakçı, İlke; Schiffler, Ralf Snake graphs and continued fractions, European Journal of Combinatorics, Volume 86 (2020), p. 103081 | DOI:10.1016/j.ejc.2020.103081
Sun, Zhe; Wienhard, Anna; Zhang, Tengren Flows on the $PGL (V)$ -Hitchin Component, Geometric and Functional Analysis, Volume 30 (2020) no. 2, p. 588 | DOI:10.1007/s00039-020-00534-4
Dumas, David; Sanders, Andrew Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations, Geometry Topology, Volume 24 (2020) no. 4, p. 1615 | DOI:10.2140/gt.2020.24.1615
Ohshika, Ken’ichi; Papadopoulos, Athanase A Glimpse into Thurston’s Work, In the Tradition of Thurston (2020), p. 1 | DOI:10.1007/978-3-030-55928-1_1
Yurikusa, Toshiya Density ofg-Vector Cones From Triangulated Surfaces, International Mathematics Research Notices, Volume 2020 (2020) no. 21, p. 8081 | DOI:10.1093/imrn/rnaa008
Danciger, Jeffrey; Maloni, Sara; Schlenker, Jean-Marc Polyhedra inscribed in a quadric, Inventiones mathematicae, Volume 221 (2020) no. 1, p. 237 | DOI:10.1007/s00222-020-00948-9
Çanakçı, İlke; Lampe, Philipp An expansion formula for type A and Kronecker quantum cluster algebras, Journal of Combinatorial Theory, Series A, Volume 171 (2020), p. 105132 | DOI:10.1016/j.jcta.2019.105132
Neitzke, Andrew; Yan, Fei q-nonabelianization for line defects, Journal of High Energy Physics, Volume 2020 (2020) no. 9 | DOI:10.1007/jhep09(2020)153
Zickert, Christian K. Fock-Goncharov coordinates for rank two Lie groups, Mathematische Zeitschrift, Volume 294 (2020) no. 1-2, p. 251 | DOI:10.1007/s00209-019-02307-8
ERDMANN, KARIN; SKOWROŃSKI, ANDRZEJ ALGEBRAS OF GENERALIZED DIHEDRAL TYPE, Nagoya Mathematical Journal, Volume 240 (2020), p. 181 | DOI:10.1017/nmj.2019.1
Gupta, Subhojoy; Mj, Mahan Monodromy representations of meromorphic projective structures, Proceedings of the American Mathematical Society, Volume 148 (2020) no. 5, p. 2069 | DOI:10.1090/proc/14866
Magee, Timothy Littlewood–Richardson coefficients via mirror symmetry for cluster varieties, Proceedings of the London Mathematical Society, Volume 121 (2020) no. 3, p. 463 | DOI:10.1112/plms.12329
Chekhov, L. O. Fenchel–Nielsen coordinates and Goldman brackets, Russian Mathematical Surveys, Volume 75 (2020) no. 5, p. 929 | DOI:10.1070/rm9972
Fraser, Chris Braid group symmetries of Grassmannian cluster algebras, Selecta Mathematica, Volume 26 (2020) no. 2 | DOI:10.1007/s00029-020-0542-3
Lu, Jiang-Hua; Yu, Shizhuo Bott–Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces, Selecta Mathematica, Volume 26 (2020) no. 5 | DOI:10.1007/s00029-020-00595-1
Allegretti, Dylan; Bridgeland, Tom The monodromy of meromorphic projective structures, Transactions of the American Mathematical Society, Volume 373 (2020) no. 9, p. 6321 | DOI:10.1090/tran/8093
Amiot, Claire Cluster algebras and cluster categories associated with triangulated surfaces: an introduction, Winter Braids Lecture Notes, Volume 5 (2020), p. 1 | DOI:10.5802/wbln.21
Chekhov, Leonid Olegovich Симплектические структуры на пространствах Тейхмюллера $T_{g, s, n}$ и кластерные алгебры, Труды Математического института имени В. А. Стеклова, Volume 309 (2020), p. 99 | DOI:10.4213/tm4082
Chekhov, Leonid Olegovich Координаты Фенхеля-Нильсена и скобки Голдмана, Успехи математических наук, Volume 75 (2020) no. 5(455), p. 153 | DOI:10.4213/rm9972
Fei, Jiarui Cluster algebras, invariant theory, and Kronecker coefficients II, Advances in Mathematics, Volume 341 (2019), p. 536 | DOI:10.1016/j.aim.2018.10.042
Paquette, Charles; Schiffler, Ralf Group actions on cluster algebras and cluster categories, Advances in Mathematics, Volume 345 (2019), p. 161 | DOI:10.1016/j.aim.2019.01.009
Çanakçı, İlke; Felikson, Anna Infinite rank surface cluster algebras, Advances in Mathematics, Volume 352 (2019), p. 862 | DOI:10.1016/j.aim.2019.06.008
Ishibashi, Tsukasa On a Nielsen–Thurston classification theory for cluster modular groups, Annales de l'Institut Fourier, Volume 69 (2019) no. 2, p. 515 | DOI:10.5802/aif.3250
Felikson, Anna; Tumarkin, Pavel Geometry of Mutation Classes of Rank 3 Quivers, Arnold Mathematical Journal, Volume 5 (2019) no. 1, p. 37 | DOI:10.1007/s40598-019-00101-2
CASELLA, ALEX BRANCHED CAUCHY–RIEMANN STRUCTURES ON ONCE-PUNCTURED TORUS BUNDLES, Bulletin of the Australian Mathematical Society, Volume 100 (2019) no. 1, p. 173 | DOI:10.1017/s0004972719000455
Shende, Vivek; Treumann, David; Williams, Harold; Zaslow, Eric Cluster varieties from Legendrian knots, Duke Mathematical Journal, Volume 168 (2019) no. 15 | DOI:10.1215/00127094-2019-0027
Rietsch, K.; Williams, L. Newton–Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, Duke Mathematical Journal, Volume 168 (2019) no. 18 | DOI:10.1215/00127094-2019-0028
Haraway,, Robert C.; Tillmann, Stephan Tessellating the Moduli Space of Strictly Convex Projective Structures on the Once-Punctured Torus, Experimental Mathematics, Volume 28 (2019) no. 3, p. 369 | DOI:10.1080/10586458.2017.1409671
LE, IAN CLUSTER STRUCTURES ON HIGHER TEICHMULLER SPACES FOR CLASSICAL GROUPS, Forum of Mathematics, Sigma, Volume 7 (2019) | DOI:10.1017/fms.2019.5
Allegretti, Dylan G. L. Laminations from the symplectic double, Geometriae Dedicata, Volume 199 (2019) no. 1, p. 27 | DOI:10.1007/s10711-018-0339-0
Danciger, Jeffrey; Zhang, Tengren Affine actions with Hitchin linear part, Geometric and Functional Analysis, Volume 29 (2019) no. 5, p. 1369 | DOI:10.1007/s00039-019-00511-6
Dyckerhoff, Tobias; Kapranov, Mikhail Discrete 2-Segal Spaces, Higher Segal Spaces, Volume 2244 (2019), p. 31 | DOI:10.1007/978-3-030-27124-4_3
Parreau, Anne On triples of ideal chambers in A2-buildings, Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial, Volume 17 (2019) no. 2, p. 109 | DOI:10.2140/iig.2019.17.109
Le, Ian An Approach to Higher Teichmüller Spaces for General Groups, International Mathematics Research Notices, Volume 2019 (2019) no. 16, p. 4899 | DOI:10.1093/imrn/rnx249
Çanakçı, İlke; Schiffler, Ralf Snake Graph Calculus and Cluster Algebras from Surfaces III: Band Graphs and Snake Rings, International Mathematics Research Notices, Volume 2019 (2019) no. 4, p. 1145 | DOI:10.1093/imrn/rnx157
Schrader, Gus; Shapiro, Alexander A cluster realization of $U_{q} ({sl}_{n})$ U q ( sl n ) from quantum character varieties, Inventiones mathematicae, Volume 216 (2019) no. 3, p. 799 | DOI:10.1007/s00222-019-00857-6
Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; García-Prada, Oscar; Gothen, Peter B.; Oliveira, André $SO (p, q)$ -Higgs bundles and Higher Teichmüller components, Inventiones mathematicae, Volume 218 (2019) no. 1, p. 197 | DOI:10.1007/s00222-019-00885-2
Blommaert, Andreas; Mertens, Thomas G.; Verschelde, Henri Fine structure of Jackiw-Teitelboim quantum gravity, Journal of High Energy Physics, Volume 2019 (2019) no. 9 | DOI:10.1007/jhep09(2019)066
Kim, Hyun Kyu Finite dimensional quantum Teichmüller space from the quantum torus at root of unity, Journal of Pure and Applied Algebra, Volume 223 (2019) no. 3, p. 1337 | DOI:10.1016/j.jpaa.2018.08.011
Allegretti, Dylan G. L. Voros symbols as cluster coordinates, Journal of Topology, Volume 12 (2019) no. 4, p. 1031 | DOI:10.1112/topo.12106
Martone, Giuseppe Positive configurations of flags in a building and limits of positive representations, Mathematische Zeitschrift, Volume 293 (2019) no. 3-4, p. 1337 | DOI:10.1007/s00209-019-02286-w
NAGAO, KENTARO; TERASHIMA, YUJI; YAMAZAKI, MASAHITO HYPERBOLIC 3-MANIFOLDS AND CLUSTER ALGEBRAS, Nagoya Mathematical Journal, Volume 235 (2019), p. 1 | DOI:10.1017/nmj.2017.39
Abenda, Simonetta; Grinevich, Petr G. Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons, Selecta Mathematica, Volume 25 (2019) no. 3 | DOI:10.1007/s00029-019-0488-5
Le, Ian; Fraser, Chris Tropicalization of positive Grassmannians, Selecta Mathematica, Volume 25 (2019) no. 5 | DOI:10.1007/s00029-019-0514-7
Allegretti, Dylan G. L. Categorified canonical bases and framed BPS states, Selecta Mathematica, Volume 25 (2019) no. 5 | DOI:10.1007/s00029-019-0518-3
Mandel, Travis Cluster algebras are Cox rings, manuscripta mathematica, Volume 160 (2019) no. 1-2, p. 153 | DOI:10.1007/s00229-018-1054-8
Goncharov, Alexander; Shen, Linhui Donaldson–Thomas transformations of moduli spaces of G-local systems, Advances in Mathematics, Volume 327 (2018), p. 225 | DOI:10.1016/j.aim.2017.06.017
Berenstein, Arkady; Retakh, Vladimir Noncommutative marked surfaces, Advances in Mathematics, Volume 328 (2018), p. 1010 | DOI:10.1016/j.aim.2018.02.014
Allegretti, Dylan G.L. Stability conditions and cluster varieties from quivers of type A, Advances in Mathematics, Volume 337 (2018), p. 260 | DOI:10.1016/j.aim.2018.08.017
Barnard, Emily; Meehan, Emily; Reading, Nathan; Viel, Shira Universal Geometric Coefficients for the Four-Punctured Sphere, Annals of Combinatorics, Volume 22 (2018) no. 1, p. 1 | DOI:10.1007/s00026-018-0378-0
Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; García-Prada, Oscar; Gothen, Peter B.; Oliveira, André Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars, Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, p. 666 | DOI:10.1016/j.crma.2018.04.024
BRIDGEMAN, MARTIN; CANARY, RICHARD; SAMBARINO, ANDRÉS An introduction to pressure metrics for higher Teichmüller spaces, Ergodic Theory and Dynamical Systems, Volume 38 (2018) no. 6, p. 2001 | DOI:10.1017/etds.2016.111
Wienhard, Anna; Zhang, Tengren Deforming convex real projective structures, Geometriae Dedicata, Volume 192 (2018) no. 1, p. 327 | DOI:10.1007/s10711-017-0243-z
Bonahon, Francis; Kim, Inkang The Goldman and Fock-Goncharov coordinates for convex projective structures on surfaces, Geometriae Dedicata, Volume 192 (2018) no. 1, p. 43 | DOI:10.1007/s10711-017-0233-1
Danciger, Jeffrey; Guéritaud, François; Kassel, Fanny Convex cocompactness in pseudo-Riemannian hyperbolic spaces, Geometriae Dedicata, Volume 192 (2018) no. 1, p. 87 | DOI:10.1007/s10711-017-0294-1
Burelle, Jean-Philippe; Treib, Nicolaus Schottky groups and maximal representations, Geometriae Dedicata, Volume 195 (2018) no. 1, p. 215 | DOI:10.1007/s10711-017-0285-2
Labourie, François Goldman algebra, opers and the swapping algebra, Geometry Topology, Volume 22 (2018) no. 3, p. 1267 | DOI:10.2140/gt.2018.22.1267
Schiffler, Ralf Cluster Algebras from Surfaces, Homological Methods, Representation Theory, and Cluster Algebras (2018), p. 65 | DOI:10.1007/978-3-319-74585-5_3
Bucher, Eric; Mills, Matthew R. Maximal green sequences for cluster algebras associated with the n-torus with arbitrary punctures, Journal of Algebraic Combinatorics, Volume 47 (2018) no. 3, p. 345 | DOI:10.1007/s10801-017-0778-y
Mikhaylov, Victor Teichmüller TQFT vs. Chern-Simons theory, Journal of High Energy Physics, Volume 2018 (2018) no. 4 | DOI:10.1007/jhep04(2018)085
Yamazaki, Masahito Quantum trilogy: discrete Toda, Y-system and chaos, Journal of Physics A: Mathematical and Theoretical, Volume 51 (2018) no. 5, p. 053002 | DOI:10.1088/1751-8121/aaa08e
Bucher, Eric; Yakimov, Milen Recovering the topology of surfaces from cluster algebras, Mathematische Zeitschrift, Volume 288 (2018) no. 1-2, p. 565 | DOI:10.1007/s00209-017-1901-4
Chekhov, Leonid; Mazzocco, Marta Colliding holes in Riemann surfaces and quantum cluster algebras, Nonlinearity, Volume 31 (2018) no. 1, p. 54 | DOI:10.1088/1361-6544/aa9729
Reading, Nathan; Stella, Salvatore Initial-seed recursions and dualities for d-vectors, Pacific Journal of Mathematics, Volume 293 (2018) no. 1, p. 179 | DOI:10.2140/pjm.2018.293.179
Franco, Sebastián; Musiker, Gregg Higher cluster categories and QFT dualities, Physical Review D, Volume 98 (2018) no. 4 | DOI:10.1103/physrevd.98.046021
Ip, Ivan C. H. Cluster realization of $U_{q} (g)$ U q ( g ) and factorizations of the universal R-matrix, Selecta Mathematica, Volume 24 (2018) no. 5, p. 4461 | DOI:10.1007/s00029-018-0432-0
Allegretti, Dylan G.L.; Kim, Hyun Kyu A duality map for quantum cluster varieties from surfaces, Advances in Mathematics, Volume 306 (2017), p. 1164 | DOI:10.1016/j.aim.2016.11.007
Canakci, Ilke; Schroll, Sibylle Extensions in Jacobian algebras and cluster categories of marked surfaces, Advances in Mathematics, Volume 313 (2017), p. 1 | DOI:10.1016/j.aim.2017.03.016
Felikson, Anna; Tumarkin, Pavel Bases for cluster algebras from orbifolds, Advances in Mathematics, Volume 318 (2017), p. 191 | DOI:10.1016/j.aim.2017.07.025
Labourie, François Cyclic surfaces and Hitchin components in rank 2, Annals of Mathematics, Volume 185 (2017) no. 1 | DOI:10.4007/annals.2017.185.1.1
Romo, Mauricio Cluster partition function and invariants of 3-manifolds, Chinese Annals of Mathematics, Series B, Volume 38 (2017) no. 4, p. 937 | DOI:10.1007/s11401-017-1105-6
Gabella, Maxime Quantum Holonomies from Spectral Networks and Framed BPS States, Communications in Mathematical Physics, Volume 351 (2017) no. 2, p. 563 | DOI:10.1007/s00220-016-2729-1
Lai, Tri; Musiker, Gregg Beyond Aztec Castles: Toric Cascades in the dP 3 Quiver, Communications in Mathematical Physics, Volume 356 (2017) no. 3, p. 823 | DOI:10.1007/s00220-017-2993-8
Qiu, Yu; Zhou, Yu Cluster categories for marked surfaces: punctured case, Compositio Mathematica, Volume 153 (2017) no. 9, p. 1779 | DOI:10.1112/s0010437x17007229
Qin, Fan Triangular bases in quantum cluster algebras and monoidal categorification conjectures, Duke Mathematical Journal, Volume 166 (2017) no. 12 | DOI:10.1215/00127094-2017-0006
Guéritaud, François; Guichard, Olivier; Kassel, Fanny; Wienhard, Anna Anosov representations and proper actions, Geometry Topology, Volume 21 (2017) no. 1, p. 485 | DOI:10.2140/gt.2017.21.485
Zuevsky, Alexander Clusterization of Correlation Functions, Groups, Modules, and Model Theory - Surveys and Recent Developments (2017), p. 459 | DOI:10.1007/978-3-319-51718-6_28
Sun, Zhe RanknSwapping Algebra for the PSL(n, ℝ) Hitchin Component, International Mathematics Research Notices, Volume 2017 (2017) no. 2, p. 583 | DOI:10.1093/imrn/rnw064
Cheung, Man Wai; Gross, Mark; Muller, Greg; Musiker, Gregg; Rupel, Dylan; Stella, Salvatore; Williams, Harold The greedy basis equals the theta basis: A rank two haiku, Journal of Combinatorial Theory, Series A, Volume 145 (2017), p. 150 | DOI:10.1016/j.jcta.2016.08.004
Fleury, Thiago; Komatsu, Shota Hexagonalization of correlation functions, Journal of High Energy Physics, Volume 2017 (2017) no. 1 | DOI:10.1007/jhep01(2017)130
Neitzke, Andrew; Yan, Fei Line defect Schur indices, Verlinde algebras and U(1)r fixed points, Journal of High Energy Physics, Volume 2017 (2017) no. 11 | DOI:10.1007/jhep11(2017)035
Gabella, Maxime; Longhi, Pietro; Park, Chan Y.; Yamazaki, Masahito BPS graphs: from spectral networks to BPS quivers, Journal of High Energy Physics, Volume 2017 (2017) no. 7 | DOI:10.1007/jhep07(2017)032
Gross, Mark; Hacking, Paul; Keel, Sean; Kontsevich, Maxim Canonical bases for cluster algebras, Journal of the American Mathematical Society, Volume 31 (2017) no. 2, p. 497 | DOI:10.1090/jams/890
Fei, Jiarui Cluster algebras and semi-invariant rings II: projections, Mathematische Zeitschrift, Volume 285 (2017) no. 3-4, p. 939 | DOI:10.1007/s00209-016-1733-7
Guichard, Olivier; Guéritaud, François; Kassel, Fanny; Wienhard, Anna Compactification of certain Clifford-Klein forms of reductive homogeneous spaces, Michigan Mathematical Journal, Volume 66 (2017) no. 1 | DOI:10.1307/mmj/1488510025
Muller, Greg; Speyer, David E. The twist for positroid varieties, Proceedings of the London Mathematical Society, Volume 115 (2017) no. 5, p. 1014 | DOI:10.1112/plms.12056
Glick, Max; Rupel, Dylan Introduction to Cluster Algebras, Symmetries and Integrability of Difference Equations (2017), p. 325 | DOI:10.1007/978-3-319-56666-5_7
Kassel, Adrien; Kenyon, Richard Random curves on surfaces induced from the Laplacian determinant, The Annals of Probability, Volume 45 (2017) no. 2 | DOI:10.1214/15-aop1078
Fraser, Chris Quasi-homomorphisms of cluster algebras, Advances in Applied Mathematics, Volume 81 (2016), p. 40 | DOI:10.1016/j.aam.2016.06.005
Safronov, Pavel Quasi-Hamiltonian reduction via classical Chern–Simons theory, Advances in Mathematics, Volume 287 (2016), p. 733 | DOI:10.1016/j.aim.2015.09.031
Kim, Hyun Kyu The dilogarithmic central extension of the Ptolemy–Thompson group via the Kashaev quantization, Advances in Mathematics, Volume 293 (2016), p. 529 | DOI:10.1016/j.aim.2016.02.016
Leclerc, B. Cluster structures on strata of flag varieties, Advances in Mathematics, Volume 300 (2016), p. 190 | DOI:10.1016/j.aim.2016.03.018
Fock, V.V.; Goncharov, A.B. Symplectic double for moduli spaces of G-local systems on surfaces, Advances in Mathematics, Volume 300 (2016), p. 505 | DOI:10.1016/j.aim.2016.03.026
Bezrukavnikov, Roman; Kapranov, Mikhail Microlocal sheaves and quiver varieties, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 25 (2016) no. 2-3, p. 473 | DOI:10.5802/afst.1502
Goncharov, A. B. Exponential complexes, period morphisms, and characteristic classes, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 25 (2016) no. 2-3, p. 619 | DOI:10.5802/afst.1507
Bucher, Eric Maximal Green Sequences for Cluster Algebras Associated to Orientable Surfaces with Empty Boundary, Arnold Mathematical Journal, Volume 2 (2016) no. 4, p. 487 | DOI:10.1007/s40598-016-0057-3
Penner, R. Moduli spaces and macromolecules, Bulletin of the American Mathematical Society, Volume 53 (2016) no. 2, p. 217 | DOI:10.1090/bull/1524
Ip, Ivan C. H. Positive Casimir and Central Characters of Split Real Quantum Groups, Communications in Mathematical Physics, Volume 344 (2016) no. 3, p. 857 | DOI:10.1007/s00220-016-2639-2
Le, Ian Higher laminations and affine buildings, Geometry Topology, Volume 20 (2016) no. 3, p. 1673 | DOI:10.2140/gt.2016.20.1673
Heusener, Michael; Muñoz, Vicente; Porti, Joan The $S L (3, C)$ -character variety of the figure eight knot, Illinois Journal of Mathematics, Volume 60 (2016) no. 1 | DOI:10.1215/ijm/1498032024
Zuevsky, Alexander Cluster algebras based on vertex operator algebras, International Journal of Modern Physics B, Volume 30 (2016) no. 28n29, p. 1640030 | DOI:10.1142/s0217979216400300
Lê, Thang T. Q. On Positivity of Kauffman Bracket Skein Algebras of Surfaces, International Mathematics Research Notices (2016), p. rnw280 | DOI:10.1093/imrn/rnw280
Iwaki, Kohei; Nakanishi, Tomoki Exact WKB Analysis and Cluster Algebras II: Simple Poles, Orbifold Points, and Generalized Cluster Algebras, International Mathematics Research Notices, Volume 2016 (2016) no. 14, p. 4375 | DOI:10.1093/imrn/rnv270
Lampe, Philipp Diophantine equations via cluster transformations, Journal of Algebra, Volume 462 (2016), p. 320 | DOI:10.1016/j.jalgebra.2016.04.033
Xu, Binbin Central extension of mapping class group via Chekhov–Fock quantization, Journal of Geometry and Physics, Volume 110 (2016), p. 9 | DOI:10.1016/j.geomphys.2016.07.002
Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B. K-decompositions and 3d gauge theories, Journal of High Energy Physics, Volume 2016 (2016) no. 11 | DOI:10.1007/jhep11(2016)151
Hollands, Lotte; Neitzke, Andrew Spectral Networks and Fenchel–Nielsen Coordinates, Letters in Mathematical Physics, Volume 106 (2016) no. 6, p. 811 | DOI:10.1007/s11005-016-0842-x
Kim, Hyun Kyu Ratio coordinates for higher Teichmüller spaces, Mathematische Zeitschrift, Volume 283 (2016) no. 1-2, p. 469 | DOI:10.1007/s00209-015-1607-4
Zickert, Christian K. Ptolemy coordinates, Dehn invariant and the A-polynomial, Mathematische Zeitschrift, Volume 283 (2016) no. 1-2, p. 515 | DOI:10.1007/s00209-015-1608-3
Dimofte, Tudor 3d Superconformal Theories from Three-Manifolds, New Dualities of Supersymmetric Gauge Theories (2016), p. 339 | DOI:10.1007/978-3-319-18769-3_11
Teschner, Jörg Supersymmetric Gauge Theories, Quantization of $M_{flat}$ , and Conformal Field Theory, New Dualities of Supersymmetric Gauge Theories (2016), p. 375 | DOI:10.1007/978-3-319-18769-3_12
Neitzke, Andrew Hitchin Systems in $N = 2$ Field Theory, New Dualities of Supersymmetric Gauge Theories (2016), p. 53 | DOI:10.1007/978-3-319-18769-3_3
Morozov, A. A. The properties of conformal blocks, the AGT hypothesis, and knot polynomials, Physics of Particles and Nuclei, Volume 47 (2016) no. 5, p. 775 | DOI:10.1134/s106377961605004x
Mandel, Travis Tropical theta functions and log Calabi–Yau surfaces, Selecta Mathematica, Volume 22 (2016) no. 3, p. 1289 | DOI:10.1007/s00029-015-0221-y
Fock, V. V.; Goncharov, A. B. Cluster Poisson varieties at infinity, Selecta Mathematica, Volume 22 (2016) no. 4, p. 2569 | DOI:10.1007/s00029-016-0282-6
Hong, Jiuzu; Shen, Linhui Tensor invariants, saturation problems, and Dynkin automorphisms, Advances in Mathematics, Volume 285 (2015), p. 629 | DOI:10.1016/j.aim.2015.08.015
Garoufalidis, Stavros; Goerner, Matthias; Zickert, Christian The Ptolemy field of 3–manifold representations, Algebraic Geometric Topology, Volume 15 (2015) no. 1, p. 371 | DOI:10.2140/agt.2015.15.371
Garoufalidis, Stavros; Goerner, Matthias; Zickert, Christian Gluing equations for PGL(n,ℂ)–representations of 3–manifolds, Algebraic Geometric Topology, Volume 15 (2015) no. 1, p. 565 | DOI:10.2140/agt.2015.15.565
Lee, Kyungyong; Schiffler, Ralf Positivity for cluster algebras, Annals of Mathematics (2015), p. 73 | DOI:10.4007/annals.2015.182.1.2
Dimofte, Tudor Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence, Communications in Mathematical Physics, Volume 339 (2015) no. 2, p. 619 | DOI:10.1007/s00220-015-2401-1
Benini, Francesco; Park, Daniel S.; Zhao, Peng Cluster Algebras from Dualities of 2d $N$ N = (2, 2) Quiver Gauge Theories, Communications in Mathematical Physics, Volume 340 (2015) no. 1, p. 47 | DOI:10.1007/s00220-015-2452-3
Gross, Mark; Hacking, Paul; Keel, Sean Moduli of surfaces with an anti-canonical cycle, Compositio Mathematica, Volume 151 (2015) no. 2, p. 265 | DOI:10.1112/s0010437x14007611
Wolpert, Scott A. Products of twists, geodesic lengths and Thurston shears, Compositio Mathematica, Volume 151 (2015) no. 2, p. 313 | DOI:10.1112/s0010437x1400757x
Garoufalidis, Stavros; Thurston, Dylan P.; Zickert, Christian K. The complex volume of SL(n,C)-representations of 3-manifolds, Duke Mathematical Journal, Volume 164 (2015) no. 11 | DOI:10.1215/00127094-3121185
Kitayama, Takahiro; Terashima, Yuji Torsion functions on moduli spaces in view of the cluster algebra, Geometriae Dedicata, Volume 175 (2015) no. 1, p. 125 | DOI:10.1007/s10711-014-0032-x
Strubel, Tobias Fenchel–Nielsen coordinates for maximal representations, Geometriae Dedicata, Volume 176 (2015) no. 1, p. 45 | DOI:10.1007/s10711-014-9959-1
Manon, Christopher Compactifications of character varieties and skein relations on conformal blocks, Geometriae Dedicata, Volume 179 (2015) no. 1, p. 335 | DOI:10.1007/s10711-015-0084-6
Zhang, Tengren Degeneration of Hitchin representations along internal sequences, Geometric and Functional Analysis, Volume 25 (2015) no. 5, p. 1588 | DOI:10.1007/s00039-015-0342-7
Goncharov, Alexander; Shen, Linhui Geometry of canonical bases and mirror symmetry, Inventiones mathematicae, Volume 202 (2015) no. 2, p. 487 | DOI:10.1007/s00222-014-0568-2
Dupont, Grégoire; Palesi, Frédéric Quasi-cluster algebras from non-orientable surfaces, Journal of Algebraic Combinatorics, Volume 42 (2015) no. 2, p. 429 | DOI:10.1007/s10801-015-0586-1
Galakhov, D.; Mironov, A.; Morozov, A. Wall-crossing invariants: from quantum mechanics to knots, Journal of Experimental and Theoretical Physics, Volume 120 (2015) no. 3, p. 549 | DOI:10.1134/s1063776115030206
Coman, Ioana; Gabella, Maxime; Teschner, Jörg Line operators in theories of class S $S$ , quantized moduli space of flat connections, and Toda field theory, Journal of High Energy Physics, Volume 2015 (2015) no. 10 | DOI:10.1007/jhep10(2015)143
Brüstle, Thomas; Qiu, Yu Tagged mapping class groups: Auslander–Reiten translation, Mathematische Zeitschrift, Volume 279 (2015) no. 3-4, p. 1103 | DOI:10.1007/s00209-015-1405-z
Canakci, Ilke; Schiffler, Ralf Snake graph calculus and cluster algebras from surfaces II: self-crossing snake graphs, Mathematische Zeitschrift, Volume 281 (2015) no. 1-2, p. 55 | DOI:10.1007/s00209-015-1475-y
Canakci, Ilke; Lee, Kyungyong; Schiffler, Ralf On cluster algebras from unpunctured surfaces with one marked point, Proceedings of the American Mathematical Society, Series B, Volume 2 (2015) no. 3, p. 35 | DOI:10.1090/bproc/21
Heusener, Michael Some recent results about the SL n (ℂ)–representation spaces of knot groups, Séminaire de théorie spectrale et géométrie, Volume 32 (2015), p. 137 | DOI:10.5802/tsg.307
Williams, H. Cluster characters and the combinatorics of Toda systems, Theoretical and Mathematical Physics, Volume 185 (2015) no. 3, p. 1789 | DOI:10.1007/s11232-015-0379-7
Manon, Christopher Newton-Okounkov polyhedra for character varieties and configuration spaces, Transactions of the American Mathematical Society, Volume 368 (2015) no. 8, p. 5979 | DOI:10.1090/tran/6698
Williams, Harold Характеры кластеров и комбинаторика систем Тоды, Теоретическая и математическая физика, Volume 185 (2015) no. 3, p. 495 | DOI:10.4213/tmf8892
Funar, Louis; Kashaev, Rinat M. Centrally extended mapping class groups from quantum Teichmüller theory, Advances in Mathematics, Volume 252 (2014), p. 260 | DOI:10.1016/j.aim.2013.10.015
Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Spectral Networks and Snakes, Annales Henri Poincaré, Volume 15 (2014) no. 1, p. 61 | DOI:10.1007/s00023-013-0238-8
Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei Gauge Theories Labelled by Three-Manifolds, Communications in Mathematical Physics, Volume 325 (2014) no. 2, p. 367 | DOI:10.1007/s00220-013-1863-2
Kenyon, Richard Conformal Invariance of Loops in the Double-Dimer Model, Communications in Mathematical Physics, Volume 326 (2014) no. 2, p. 477 | DOI:10.1007/s00220-013-1881-0
Bonahon, Francis; Dreyer, Guillaume Parameterizing Hitchin components, Duke Mathematical Journal, Volume 163 (2014) no. 15 | DOI:10.1215/0012794-2838654
Biswas, Indranil; Florentino, Carlos; Lawton, Sean; Logares, Marina The topology of parabolic character varieties of free groups, Geometriae Dedicata, Volume 168 (2014) no. 1, p. 143 | DOI:10.1007/s10711-012-9822-1
Bergeron, Nicolas; Falbel, Elisha; Guilloux, Antonin Tetrahedra of flags, volume and homology of SL(3), Geometry Topology, Volume 18 (2014) no. 4, p. 1911 | DOI:10.2140/gt.2014.18.1911
Neitzke, Andrew Notes on a New Construction of Hyperkahler Metrics, Homological Mirror Symmetry and Tropical Geometry, Volume 15 (2014), p. 351 | DOI:10.1007/978-3-319-06514-4_8
Matherne, J. P.; Muller, G. Computing Upper Cluster Algebras, International Mathematics Research Notices (2014) | DOI:10.1093/imrn/rnu027
Balasubramanian, Aswin The Euler anomaly and scale factors in Liouville/Toda CFTs, Journal of High Energy Physics, Volume 2014 (2014) no. 4 | DOI:10.1007/jhep04(2014)127
Galakhov, D.; Mironov, A.; Morozov, A. S-duality and modular transformation as a non-perturbative deformation of the ordinary pq-duality, Journal of High Energy Physics, Volume 2014 (2014) no. 6 | DOI:10.1007/jhep06(2014)050
Anokhina, A.; Morozov, A. Towards ℛ-matrix construction of Khovanov-Rozansky polynomials I. Primary T-deformation of HOMFLY, Journal of High Energy Physics, Volume 2014 (2014) no. 7 | DOI:10.1007/jhep07(2014)063
Kim, Joonho; Lee, Sangmin Positroid stratification of orthogonal Grassmannian and ABJM amplitudes, Journal of High Energy Physics, Volume 2014 (2014) no. 9 | DOI:10.1007/jhep09(2014)085
Córdova, Clay; Neitzke, Andrew Line defects, tropicalization, and multi-centered quiver quantum mechanics, Journal of High Energy Physics, Volume 2014 (2014) no. 9 | DOI:10.1007/jhep09(2014)099
HIKAMI, KAZUHIRO; INOUE, REI CLUSTER ALGEBRA AND COMPLEX VOLUME OF ONCE-PUNCTURED TORUS BUNDLES AND 2-BRIDGE LINKS, Journal of Knot Theory and Its Ramifications, Volume 23 (2014) no. 01, p. 1450006 | DOI:10.1142/s0218216514500060
Iwaki, Kohei; Nakanishi, Tomoki Exact WKB analysis and cluster algebras, Journal of Physics A: Mathematical and Theoretical, Volume 47 (2014) no. 47, p. 474009 | DOI:10.1088/1751-8113/47/47/474009
Leoni, Megan; Musiker, Gregg; Neel, Seth; Turner, Paxton Aztec castles and the dP3 quiver, Journal of Physics A: Mathematical and Theoretical, Volume 47 (2014) no. 47, p. 474011 | DOI:10.1088/1751-8113/47/47/474011
Kenyon, Richard; Wilson, David Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs, Journal of the American Mathematical Society, Volume 28 (2014) no. 4, p. 985 | DOI:10.1090/s0894-0347-2014-00819-5
Gothen, Peter B. Representations of surface groups and Higgs bundles, Moduli Spaces (2014), p. 151 | DOI:10.1017/cbo9781107279544.004
Mironov, Andrei; Morozov, Alexei; Sleptsov, Alexei; Smirnov, Andrey On genus expansion of superpolynomials, Nuclear Physics B, Volume 889 (2014), p. 757 | DOI:10.1016/j.nuclphysb.2014.11.003
Leclerc, Bernard; Williams, Lauren K. Cluster algebras, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 27, p. 9676 | DOI:10.1073/pnas.1410635111
Fomin, Sergey; Pylyavskyy, Pavlo Webs on surfaces, rings of invariants, and clusters, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 27, p. 9680 | DOI:10.1073/pnas.1313068111
Goodearl, Kenneth R.; Yakimov, Milen T. Quantum cluster algebras and quantum nilpotent algebras, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 27, p. 9696 | DOI:10.1073/pnas.1313071111
Neitzke, Andrew Cluster-like coordinates in supersymmetric quantum field theory, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 27, p. 9717 | DOI:10.1073/pnas.1313073111
Thurston, Dylan Paul Positive basis for surface skein algebras, Proceedings of the National Academy of Sciences, Volume 111 (2014) no. 27, p. 9725 | DOI:10.1073/pnas.1313070111
Terashima, Y.; Yamazaki, M. N = 2 theories from cluster algebras, Progress of Theoretical and Experimental Physics, Volume 2014 (2014) no. 2, p. 23B01 | DOI:10.1093/ptep/ptt115
Nekrasov, N. A.; Rosly, A. A.; Shatashvili, S. L. Darboux coordinates, Yang-Yang functional, and gauge theory, Theoretical and Mathematical Physics, Volume 181 (2014) no. 1, p. 1206 | DOI:10.1007/s11232-014-0209-3
Некрасов, Никита Александрович; Nekrasov, Nikita Alexandrovich; Рослый, Алексей Андреевич; Roslyi, Aleksei Andreevich; Шаташвили, Самсон Лулиевич; Shatashvili, Samson Lulievich Координаты Дарбу, функционал Янга - Янга и калибровочная теория, Теоретическая и математическая физика, Volume 181 (2014) no. 1, p. 86 | DOI:10.4213/tmf8648
Muller, Greg Locally acyclic cluster algebras, Advances in Mathematics, Volume 233 (2013) no. 1, p. 207 | DOI:10.1016/j.aim.2012.10.002
Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Wall-crossing, Hitchin systems, and the WKB approximation, Advances in Mathematics, Volume 234 (2013), p. 239 | DOI:10.1016/j.aim.2012.09.027
Dreyer, Guillaume Length functions of Hitchin representations, Algebraic Geometric Topology, Volume 13 (2013) no. 6, p. 3153 | DOI:10.2140/agt.2013.13.3153
Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew Spectral Networks, Annales Henri Poincaré, Volume 14 (2013) no. 7, p. 1643 | DOI:10.1007/s00023-013-0239-7
Chekhov, Leonid; Mazzocco, Marta Poisson Algebras of Block-Upper-Triangular Bilinear Forms and Braid Group Action, Communications in Mathematical Physics, Volume 322 (2013) no. 1, p. 49 | DOI:10.1007/s00220-013-1757-3
Fontaine, Bruce; Kamnitzer, Joel; Kuperberg, Greg Buildings, spiders, and geometric Satake, Compositio Mathematica, Volume 149 (2013) no. 11, p. 1871 | DOI:10.1112/s0010437x13007136
Musiker, Gregg; Schiffler, Ralf; Williams, Lauren Bases for cluster algebras from surfaces, Compositio Mathematica, Volume 149 (2013) no. 2, p. 217 | DOI:10.1112/s0010437x12000450
BARCELO, HÉLÈNE; SEVERS, CHRISTOPHER; WHITE, JACOB A. THE DISCRETE FUNDAMENTAL GROUP OF THE ASSOCIAHEDRON, AND THE EXCHANGE MODULE, International Journal of Algebra and Computation, Volume 23 (2013) no. 04, p. 745 | DOI:10.1142/s0218196713400079
Musiker, Gregg; Williams, Lauren Matrix Formulae and Skein Relations for Cluster Algebras from Surfaces, International Mathematics Research Notices, Volume 2013 (2013) no. 13, p. 2891 | DOI:10.1093/imrn/rns118
Canakci, Ilke; Schiffler, Ralf Snake graph calculus and cluster algebras from surfaces, Journal of Algebra, Volume 382 (2013), p. 240 | DOI:10.1016/j.jalgebra.2013.02.018
Marshakov, A. Lie groups, cluster variables and integrable systems, Journal of Geometry and Physics, Volume 67 (2013), p. 16 | DOI:10.1016/j.geomphys.2012.12.003
Nie, Xin The quasi-Poisson Goldman formula, Journal of Geometry and Physics, Volume 74 (2013), p. 1 | DOI:10.1016/j.geomphys.2013.06.010
Cirafici, Michele Line defects and (framed) BPS quivers, Journal of High Energy Physics, Volume 2013 (2013) no. 11 | DOI:10.1007/jhep11(2013)141
Dimofte, Tudor; Gukov, Sergei Chern-Simons theory and S-duality, Journal of High Energy Physics, Volume 2013 (2013) no. 5 | DOI:10.1007/jhep05(2013)109
Barot, M.; Geiss, Ch.; Jasso, G. Tubular cluster algebras II: Exponential growth, Journal of Pure and Applied Algebra, Volume 217 (2013) no. 10, p. 1825 | DOI:10.1016/j.jpaa.2012.12.012
Marché, Julien; Will, Pierre Configurations of flags and representations of surface groups in complex hyperbolic geometry, Geometriae Dedicata, Volume 156 (2012) no. 1, p. 49 | DOI:10.1007/s10711-011-9589-9
Muller, Greg The Weil–Petersson Form on an Acyclic Cluster Variety, International Mathematics Research Notices, Volume 2012 (2012) no. 16, p. 3680 | DOI:10.1093/imrn/rnr155
Guichard, Olivier; Wienhard, Anna Anosov representations: domains of discontinuity and applications, Inventiones mathematicae, Volume 190 (2012) no. 2, p. 357 | DOI:10.1007/s00222-012-0382-7
Xie, Dan; Yamazaki, Masahito Network and Seiberg duality, Journal of High Energy Physics, Volume 2012 (2012) no. 9 | DOI:10.1007/jhep09(2012)036
Галахов, Д В; Galakhov, D V; Галахов, Д В; Galakhov, D V; Миронов, Андрей Дмитриевич; Mironov, Andrei Dmitrievich; Миронов, Андрей Дмитриевич; Mironov, Andrei Dmitrievich; Морозов, Алексей Юрьевич; Morozov, Aleksei Yur'evich; Смирнов, Андрей Валерьевич; Smirnov, Andrei Valer'evich О трехмерном обобщении соответствия Алдая - Гайотто - Тачикавы, Теоретическая и математическая физика, Volume 172 (2012) no. 1, p. 73 | DOI:10.4213/tmf6930
Морозов, Алексей Юрьевич; Morozov, Aleksei Yur'evich Загадки $β$ -деформации, Теоретическая и математическая физика, Volume 173 (2012) no. 1, p. 104 | DOI:10.4213/tmf6967
Musiker, Gregg; Schiffler, Ralf; Williams, Lauren Positivity for cluster algebras from surfaces, Advances in Mathematics, Volume 227 (2011) no. 6, p. 2241 | DOI:10.1016/j.aim.2011.04.018
Terashima, Yuji; Yamazaki, Masahito $SL (2, R)$ Chern-Simons, Liouville, and gauge theory on duality walls, Journal of High Energy Physics, Volume 2011 (2011) no. 8 | DOI:10.1007/jhep08(2011)135
Nekrasov, N.; Rosly, A.; Shatashvili, S. Darboux coordinates, Yang-Yang functional, and gauge theory, Nuclear Physics B - Proceedings Supplements, Volume 216 (2011) no. 1, p. 69 | DOI:10.1016/j.nuclphysbps.2011.04.150
Kenyon, Richard Spanning forests and the vector bundle Laplacian, The Annals of Probability, Volume 39 (2011) no. 5 | DOI:10.1214/10-aop596
Henriques, Andre; Speyer, David E. The multidimensional cube recurrence, Advances in Mathematics, Volume 223 (2010) no. 3, p. 1107 | DOI:10.1016/j.aim.2009.09.004
Schiffler, Ralf On cluster algebras arising from unpunctured surfaces II, Advances in Mathematics, Volume 223 (2010) no. 6, p. 1885 | DOI:10.1016/j.aim.2009.10.015
Burger, Marc; Iozzi, Alessandra; Wienhard, Anna Surface group representations with maximal Toledo invariant, Annals of Mathematics, Volume 172 (2010) no. 1, p. 517 | DOI:10.4007/annals.2010.172.517
Labourie, François An algebra of observables for cross ratios, Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, p. 503 | DOI:10.1016/j.crma.2010.03.012
Lampe, P. A Quantum Cluster Algebra of Kronecker Type and the Dual Canonical Basis, International Mathematics Research Notices (2010) | DOI:10.1093/imrn/rnq162
Musiker, Gregg; Schiffler, Ralf Cluster expansion formulas and perfect matchings, Journal of Algebraic Combinatorics, Volume 32 (2010) no. 2, p. 187 | DOI:10.1007/s10801-009-0210-3
Drukker, Nadav; Gomis, Jaume; Okuda, Takuya; Teschner, Jörg Gauge theory loop operators and Liouville theory, Journal of High Energy Physics, Volume 2010 (2010) no. 2 | DOI:10.1007/jhep02(2010)057
Hatsuda, Yasuyuki; Ito, Katsushi; Sakai, Kazuhiro; Satoh, Yuji Thermodynamic Bethe ansatz equations for minimal surfaces in AdS 3, Journal of High Energy Physics, Volume 2010 (2010) no. 4 | DOI:10.1007/jhep04(2010)108
Funar, Louis; Sergiescu, Vlad Central extensions of the Ptolemy-Thompson group and quantized Teichmüller theory, Journal of Topology, Volume 3 (2010) no. 1, p. 29 | DOI:10.1112/jtopol/jtp033
Danilov, Vladimir I; Karzanov, Aleksander V; Koshevoy, Gleb A Separated set-systems and their geometric models, Russian Mathematical Surveys, Volume 65 (2010) no. 4, p. 659 | DOI:10.1070/rm2010v065n04abeh004692
Данилов, Владимир Иванович; Danilov, Vladimir Ivanovich; Карзанов, Александр Викторович; Karzanov, Aleksander Viktorovich; Кошевой, Глеб Алексеевич; Koshevoy, Gleb Alekseevich Системы разделенных множеств и их геометрические модели, Успехи математических наук, Volume 65 (2010) no. 4, p. 67 | DOI:10.4213/rm9364
Fock, V. V.; Goncharov, A. B. Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner, Algebra, Arithmetic, and Geometry, Volume 269 (2009), p. 655 | DOI:10.1007/978-0-8176-4745-2_15
Guichard, Olivier; Wienhard, Anna Domains of discontinuity for surface groups, Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, p. 1057 | DOI:10.1016/j.crma.2009.06.013
Labourie, François; McShane, Gregory Cross ratios and identities for higher Teichmüller-Thurston theory, Duke Mathematical Journal, Volume 149 (2009) no. 2 | DOI:10.1215/00127094-2009-040
Schiffler, R.; Thomas, H. On Cluster Algebras Arising from Unpunctured Surfaces, International Mathematics Research Notices (2009) | DOI:10.1093/imrn/rnp047
Fock, V.V.; Goncharov, A.B. The quantum dilogarithm and representations of quantum cluster varieties, Inventiones mathematicae, Volume 175 (2009) no. 2, p. 223 | DOI:10.1007/s00222-008-0149-3
Kontsevich, Maxim Holonomic -modules and positive characteristic, Japanese Journal of Mathematics, Volume 4 (2009) no. 1, p. 1 | DOI:10.1007/s11537-009-0852-x
McMullen, Curtis T. Ribbon ℝ-trees and holomorphic dynamics on the unit disk, Journal of Topology, Volume 2 (2009) no. 1, p. 23 | DOI:10.1112/jtopol/jtn032
Teschner, Jörg Nonrational Conformal Field Theory, New Trends in Mathematical Physics (2009), p. 697 | DOI:10.1007/978-90-481-2810-5_46
Fomin, Sergey; Shapiro, Michael; Thurston, Dylan Cluster algebras and triangulated surfaces. Part I: Cluster complexes, Acta Mathematica, Volume 201 (2008) no. 1, p. 83 | DOI:10.1007/s11511-008-0030-7
Guichard, Olivier; Wienhard, Anna Convex foliated projective structures and the Hitchin component for PSL4(R), Duke Mathematical Journal, Volume 144 (2008) no. 3 | DOI:10.1215/00127094-2008-040
Bonahon, Francis; Liu, Xiaobo Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geometry Topology, Volume 11 (2007) no. 2, p. 889 | DOI:10.2140/gt.2007.11.889
Baur, Karin; Marsh, Bethany Rose A Geometric Description of them-cluster Categories of TypeDn, International Mathematics Research Notices, Volume 2007 (2007) | DOI:10.1093/imrn/rnm011
Labourie, François Cross ratios, surface groups, PSL(n,ℝ) and diffeomorphisms of the circle, Publications mathématiques de l'IHÉS, Volume 106 (2007) no. 1, p. 139 | DOI:10.1007/s10240-007-0009-5

Cité par 382 documents. Sources : Crossref