Dr. Farkhod Eshmatov, PhD, DSc

Professor

Department: Mathematics

Office: 253, Avicenna Hall

Email: f.eshmatov[at]akfauniversity.org

Resume

  • Professor of AU Engineering School, AKFA University, Tashkent, Uzbekistan, January 2021 – Present

  • Doctor of Science in Mathematics and Physics, Secondary Doctorate, Habilitation, Tashkent, Uzbekistan, January 2021

  • Professor, Capital Normal University, 2019-2020

  • Professor, Sichuan University, Department of Mathematics, 2012–2019

  • Visiting Scholar, University of San Paulo, Spring 2014

  • Visiting Scholar, Indiana University, Spring 2013

  • Visiting Scholar, IHES , 2012 (April)

  • Visiting Scholar, MPIM at Bonn 2011-2012

  • Assistant Professor, University of Michigan, Department of Mathematics, 2007–2011

  • Cornell University, Ph.D. in Mathematics, 2007

  • Cornell University, MS in Mathematics, 2003

  • SUNY at Binghamton, MA in Mathematics, 2000

  • Tashkent State University, BS in Mathematics, 1998

Research interests

  • Algebra

  • (Noncommutative) Algebraic Geometry

  • Integrable Systems

  • Infinite Dimensional Lie Algebras

  • Mathematical Physics

  • Algebraic geometry

  • Representation Theory

Work in progress:

  • Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras, submitted to Math. Z. (joint X. Chen, A. Eshmatov and L.Liu)

  • Van den Bergh’s functor and the moduli stack of Calabi-Yau categories, in preparation (joint with X. Chen, A. Eshmatov and J. Zeng)

  • On algebras Morita equivalent to generalized Weyl algebras in preparation (joint with X. Chen, A. Eshmatov and V.Futorny)


Teaching

  • Calculus 1 – AKFA University, Spring 2022

  • Linear Algebra – AKFA University, Fall 2021

  • Calculus 2 – AKFA University, Spring 2021

  • Group Representations, Commutative Algebra, Geometry and Topology, Calculus – Sichuan University, Fall 2012-2019

  • Math 116 (Calculus II), University of Michigan, Fall 2009

  • Math 215 (Calculus III), University of Michigan, Spring 2009

  • Math 217 (Linear Algebra), University of Michigan, Fall 2008

  • Math 216 (Differential Equations), University of Michigan, Summer 2008

  • Math 417 (Matrix Algebra I), University of Michigan, Spring 2008

  • Math 285 (Honors Multivariable Calculus), University of Michigan, Fall 2007

  • Math 112 (Calculus II), Cornell University, Fall 2005

  • Math 221 (Calculus I), SUNY (Binghamton), Spring 2000.

Selected Publications

  • “DG-models of projective modules and Nakajima quiver varieties”, Homology, Homotopy and Applications, 9:2 (2007), 177–208.

  • “Recollement of deformed preprojective algebras and the Calogero-Moser correspondence” with Yu. Berest and O. Chalykh, Mosc. Math. J., 8:1 (2008), 21–37.

  • “Heat Kernel Coefficients for Two-Dimensional Schrodinger Operators” with Y. Berest, T. Cramer, Commun. Math. Phys., 283:3 (2008), 853–860.

  • “Quantization of the Lie bialgebra of string topology” with X. Chen, and W. L. Gan, Commun. Math. Phys., 301 (2011), no. 1, 37–53.

  • “On subgroups of the Dixmier group and Calogero-Moser spaces” with Yu. Berest and A. Eshmatov, Electronic Research Announcements in Mathematical Sciences (18) 2011, pp. 12–21.

  • “Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras” with Yu. Berest, X. Chen, A. Ramadoss, Mathematical aspects of quantization, 219–246, Contemp. Math., 583, Amer. Math. Soc., Providence, RI, 2012.

  • “Multitransitivity of Calogero–Moser spaces” with Yu. Berest and A. Eshmatov, Transformation Groups, 21 (2016), no. 1, 35–50.

  • “Dixmier groups and Borel subgroups” with Yu. Berest and A. Eshmatov, Adv. in Math., 286 (2016) 387–429.

  • “Noncommutative Noether’s problem for complex reflection groups” with V. Futorny, S. Ovsienko and J. Schwarz, Proc. Amer. Math. Soc. 145 (2017), no. 12, 5043–5052.

  • “Derived non-commutative Poisson bracket on Koszul Calabi-Yau algebras” with X. Chen, A. Eshmatov and S. Yang, Journal of Noncommutative Geometry, 11 (2017), 111–160.

  • “Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebras” with X. Chen and L. Liu, J. Geom. Phys. 147 (2020) 103522.

  • “Calabi-Yau algebras and the shifted noncommutative symplectic structure” (joint with X. Chen), Adv. Math. 367 (2020) 107126.

  • “Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras” with X. Chen, Y. Chen and S. Yang, to be accepted by J. Noncomm. Geom.

  • “On transitive action on quiver varieties” with X. Chen, A. Eshmatov and A. Tikaradze, accepted in IMRN.


Organized Conferences

  • Conference on Lie and Jordan algebras, their representations and applications, January 6-11, 2020 Chengdu, China

  • First China-Central Asia Joint Meeting of Mathematicians, Sichuan University, Chengdu, China, 15-20 September, 2019

  • Program on Derived Algebraic Geometry, Institute of Mathematics of Toulouse and Sichuan University, October 7-25, 2019

  • CIMPA, Nonassociative algebras and application, Tashkent, Uzbekistan, 10/09/2018 to 21/09/2018

Grants

  • National Natural Science Foundation of China (No. 11271269) String topology and its applications to symplectic geometry and non-commutative geometry, Participant, 2013-2016.

  • 2. National Natural Science Foundation of China (No. 11671281) Some non-commutative geometric structures on Calabi-Yau categories, Participant, 2017-2020.