Eshmatov Farxod Xasanovich

Farkhod Eshmatov is a Professor at the School of Engineering at New Uzbekistan University. With deep expertise in algebra and geometry, he has held various academic roles across the globe:

1. Professor, AKFA University, Uzbekistan (Sep 2021 – Present)
2. Professor, Capital Normal University, Beijing, China (Dec 2019 – Sep 2021)
3. Professor, Sichuan University, Chengdu, China (Sep 2012 – Dec 2019)
4. Visiting Professor, University of São Paulo, Brazil (Spring 2014)
5. Visiting Professor, Indiana University, USA (Spring 2013)
6. Visiting Professor, IHES, Paris, France (Spring 2012)
7. Visiting Professor, MPIM, Bonn, Germany (Sep 2011 – Mar 2012)
8. Assistant Professor, University of Michigan, Ann Arbor, USA (Sep 2007 – Aug 2011)

Research Interests

1. Representation Theory of Algebras
2. Homological Algebra
3. Algebraic Geometry
4. Mathematical Physics

Teaching Areas

1. Calculus (all levels)
2. Linear Algebra
3. Differential Equations & Partial Differential Equations
4. Abstract Algebra
5. Representation Theory
6. Algebraic & Differential Geometry
7. Topology & Algebraic Topology
8. Homological Algebra

X. Chen, A. Eshmatov, L. Liu, F. Eshmatov. Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras. Selecta Mathematica, 28(3), 2022, 1–33.

X. Chen, A. Eshmatov, A. Tikaradze, F. Eshmatov. On transitive action on quiver varieties. International Mathematics Research Notices, (10), 2022, 7694–7728.

X. Chen, Y. Chen, S. Yang, F. Eshmatov. Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras. Journal of Noncommutative Geometry, 15(3), 2021, 889–918.

X. Chen, F. Eshmatov. Calabi-Yau algebras and the shifted noncommutative symplectic structure. Advances in Mathematics, 367, 2020, 107126.

X. Chen, Y. Chen, S. Yang, F. Eshmatov. Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras. Journal of Noncommutative Geometry.

X. Chen, L. Liu, F. Eshmatov. Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebras. Journal of Geometry and Physics, 147, 2020, 103522.

X. Chen, A. Eshmatov, S. Yang, F. Eshmatov. Derived non-commutative Poisson bracket on Koszul Calabi-Yau algebras. Journal of Noncommutative Geometry, 11, 2017, 111–160.

V. Futorny, S. Ovsienko, J. Schwarz, F. Eshmatov. Noncommutative Noether's problem for complex reflection groups. Proceedings of the American Mathematical Society, 145(12), 2017, 5043–5052.

Yu. Berest, A. Eshmatov, F. Eshmatov. Dixmier groups and Borel subgroups. Advances in Mathematics, 286, 2016, 387–429.

Yu. Berest, A. Eshmatov, F. Eshmatov. Multitransitivity of Calogero–Moser spaces. Transformation Groups, 21(1), 2016, 35–50.

Yu. Berest, X. Chen, A. Ramadoss, F. Eshmatov. Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras. Contemp. Math., 583, AMS, 2012, 219–246.

Yu. Berest, A. Eshmatov, F. Eshmatov. On subgroups of the Dixmier group and Calogero-Moser spaces. Electronic Research Announcements in Mathematical Sciences, 18, 2011, 12–21.

X. Chen, W. L. Gan, F. Eshmatov. Quantization of the Lie bialgebra of string topology. Communications in Mathematical Physics, 301(1), 2011, 37–53.

Y. Berest, T. Cramer, F. Eshmatov. Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators. Communications in Mathematical Physics, 283, 2008, 853–860.

Yu. Berest, O. Chalykh, F. Eshmatov. Recollement of deformed preprojective algebras and the Calogero-Moser correspondence. Moscow Mathematical Journal, 8, 2008, 21–37.

F. Eshmatov. DG-models of projective modules and Nakajima quiver varieties. Homology, Homotopy and Applications, 9(2), 2007, 177–208.

1. Non-Associative Algebras and Related Topics II, University of Coimbra, Portugal, July 18–22, 2022
2. Visiting Professor roles across the USA, Brazil, France, and Germany (2011–2014)

National Natural Science Foundation of China – Project on String Topology and Noncommutative Geometry (2013–2016)

National Natural Science Foundation of China – Calabi-Yau Categories (2017–2020)

University of Michigan Fellowship (2009)

Eleanor Norton York Award, Cornell University (2003)

Presidential Scholarship for Graduate Study Abroad (1998–2000)

Tashkent State University Award for Top Mathematics Graduate (1998)