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Eshmatov Farkhod

Eshmatov Farkhod

Professor, Vice-Dean

Department of Mathematics, New Uzbekistan University

Biography

Farkhod Eshmatov works in noncommutative algebraic geometry and representation theory. His research centres on Calabi–Yau algebras and categories, noncommutative Poisson and symplectic structures, Calogero–Moser spaces and quiver varieties, and the Dixmier group of automorphisms of the Weyl algebra.

He took his PhD at Cornell University in 2007 and holds a Doctor of Science degree in physics and mathematics (2021). Before returning to Tashkent he was Assistant Professor at the University of Michigan and Professor at Sichuan University and at Capital Normal University in Beijing, with visiting positions at the Max Planck Institute for Mathematics in Bonn, IHES, Indiana University and the University of São Paulo. At New Uzbekistan University he is a Professor in the Department of Mathematics and Deputy Dean for Academic Affairs, and he has been on the organising committee of every conference and summer school the department has held.

Research Interests

  • Representation theory of algebras
  • Noncommutative algebraic geometry
  • Homological algebra
  • Algebraic geometry
  • Integrable systems
  • Infinite dimensional Lie algebras
  • Mathematical physics

Education

Doctor of Science (DSc) in Physics and Mathematics — Tashkent, Uzbekistan (2021).

PhD in Mathematics — Cornell University, USA (2007).

MS in Mathematics — Cornell University, USA (2003).

MA in Mathematics — SUNY at Binghamton, USA (2000).

BS in Mathematics — Tashkent State University, Uzbekistan (1998).

Academic Positions

  • Present — Professor and Deputy Dean for Academic Affairs, New Uzbekistan University, Tashkent.
  • From 2021 — Professor, Central Asian University (formerly AKFA University), Tashkent.
  • 2019–2021 — Professor, Capital Normal University, Beijing, China.
  • 2012–2019 — Professor, Department of Mathematics, Sichuan University, Chengdu, China.
  • 2007–2011 — Assistant Professor, Department of Mathematics, University of Michigan, Ann Arbor, USA.
  • Spring 2014 — Visiting Professor, University of São Paulo, Brazil.
  • Spring 2013 — Visiting Professor, Indiana University, USA.
  • Spring 2012 — Visiting Professor, Institut des Hautes Études Scientifiques (IHES), France.
  • 2011–2012 — Visiting Professor, Max Planck Institute for Mathematics, Bonn, Germany.

Publications

  1. X. Chen, F. Eshmatov and M. Huang, Algebraic K-theory, cohomotopy K-groups, and Koszul duality, preprint (2026). arXiv:2605.05128
  2. X. Chen, F. Eshmatov and M. Huang, Deformation and quantization of the Loday–Quillen–Tsygan isomorphism for Calabi–Yau categories, preprint (2025). arXiv:2505.09378
  3. F. Eshmatov, X. García-Martínez and R. Turdibaev, Noncommutative Poisson structure and invariants of matrices, Advances in Mathematics 469 (2025), Paper No. 110212. doi
  4. F. Eshmatov, X. García-Martínez, Z. Normatov and R. Turdibaev, On the coordinate rings of Calogero–Moser spaces and the invariant commuting variety of a pair of matrices, Results in Mathematics 80 (2025), no. 3, Paper No. 68. doi
  5. X. Chen, A. Eshmatov, F. Eshmatov and L. Liu, Twisted bi-symplectic structure on Koszul twisted Calabi–Yau algebras, Selecta Mathematica (N.S.) 28 (2022), no. 3, Paper No. 62. doi
  6. X. Chen, A. Eshmatov, F. Eshmatov and A. Tikaradze, On transitive action on quiver varieties, International Mathematics Research Notices 2022, no. 10, 7694–7728. doi
  7. X. Chen, Y. Chen, F. Eshmatov and S. Yang, Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras, Journal of Noncommutative Geometry 15 (2021), no. 3, 889–918. doi
  8. X. Chen, Y. Chen, A. Eshmatov and F. Eshmatov, The shifted Poisson structure on derived representation schemes of Koszul Calabi–Yau algebras, Acta Scientiarum Naturalium Universitatis Sunyatseni 59 (2020), no. 5, 1–18.
  9. X. Chen and F. Eshmatov, Calabi–Yau algebras and the shifted noncommutative symplectic structure, Advances in Mathematics 367 (2020), 107126. doi
  10. X. Chen, F. Eshmatov and L. Liu, Gravity algebra structure on the negative cyclic homology of Calabi–Yau algebras, Journal of Geometry and Physics 147 (2020), 103522. doi
  11. X. Chen, A. Eshmatov, F. Eshmatov and S. Yang, The derived non-commutative Poisson bracket on Koszul Calabi–Yau algebras, Journal of Noncommutative Geometry 11 (2017), no. 1, 111–160. doi
  12. F. Eshmatov, V. Futorny, S. Ovsienko and J. F. Schwarz, Noncommutative Noether's problem for complex reflection groups, Proceedings of the American Mathematical Society 145 (2017), no. 12, 5043–5052. doi
  13. Yu. Berest, A. Eshmatov and F. Eshmatov, Dixmier groups and Borel subgroups, Advances in Mathematics 286 (2016), 387–429. doi
  14. Yu. Berest, A. Eshmatov and F. Eshmatov, Multitransitivity of Calogero–Moser spaces, Transformation Groups 21 (2016), no. 1, 35–50. doi
  15. Yu. Berest, X. Chen, F. Eshmatov and A. Ramadoss, Noncommutative Poisson structures, derived representation schemes and Calabi–Yau algebras, Mathematical Aspects of Quantization, Contemporary Mathematics 583, American Mathematical Society (2012), 219–246. doi
  16. Yu. Berest, A. Eshmatov and F. Eshmatov, On subgroups of the Dixmier group and Calogero–Moser spaces, Electronic Research Announcements in Mathematical Sciences 18 (2011), 12–21. doi
  17. X. Chen, F. Eshmatov and W. L. Gan, Quantization of the Lie bialgebra of string topology, Communications in Mathematical Physics 301 (2011), no. 1, 37–53. doi
  18. Yu. Berest, T. Cramer and F. Eshmatov, Heat kernel coefficients for two-dimensional Schrödinger operators, Communications in Mathematical Physics 283 (2008), no. 3, 853–860. doi
  19. Yu. Berest, O. Chalykh and F. Eshmatov, Recollement of deformed preprojective algebras and the Calogero–Moser correspondence, Moscow Mathematical Journal 8 (2008), no. 1, 21–37. doi
  20. F. Eshmatov, DG-models of projective modules and Nakajima quiver varieties, Homology, Homotopy and Applications 9 (2007), no. 2, 177–208. doi

Organized Conferences

At New Uzbekistan University:

Earlier:

  • Conference on Lie and Jordan Algebras, their Representations and Applications, Chengdu, China, 6–11 January 2020.
  • Program on Derived Algebraic Geometry, Institute of Mathematics of Toulouse and Sichuan University, Chengdu, China, 7–25 October 2019.
  • First China–Central Asia Joint Meeting of Mathematicians, Sichuan University, Chengdu, China, 15–20 September 2019.
  • CIMPA School on Nonassociative Algebras and Applications, Tashkent, Uzbekistan, 10–21 September 2018.

Grants and Awards

  • 2017–2020 — National Natural Science Foundation of China, grant no. 11671281, Some noncommutative geometric structures on Calabi–Yau categories.
  • 2013–2016 — National Natural Science Foundation of China, grant no. 11271269, String topology and its applications to symplectic geometry and noncommutative geometry.
  • 2009 — University of Michigan Fellowship.
  • 2003 — Eleanor Norton York Award, Cornell University.
  • 1998–2000 — Presidential Scholarship for Graduate Study Abroad, Uzbekistan.
  • 1998 — Tashkent State University Award for the top mathematics graduate.

Department publications for 2025 and 2026 are collected on the Archive page.