School of Mathematics & Statistics

Dr Anton Izosimov

  • Reader (Mathematics)

Biography

  • 2025 - Present: Reader of Mathematics, University of Glasgow
  • 2018 - 2025: Assistant and Associate Professor of Mathematics, University of Arizona
  • 2014 - 2017: Postdoctoral Fellow, University of Toronto
  • 2013 - 2014: Associate Professor, National Research University Higher School of Economics
  • 2012 - 2014: Assistant Professor, Moscow State University
  • 2008 - 2012: PhD in Mathematics, Loughborough University
  • 2008 - 2011: PhD in Mathematics, Moscow State University
  • 2003 - 2008: MSc in Mathematics, Moscow State University

Here is my complete CV: https://aizosimov.github.io/izosimov_cv.pdf

Research interests

My work lies at the crossroads of algebra, geometry, and mathematical physics. Among other things, I am interested in:

  • integrable systems and Poisson geometry, along with their connections to Lie theory, theory of cluster algebras, algebraic combinatorics, etc.;
  • geometric and group-theoretic methods in fluid dynamics.

For a complete list of my publications with links see https://aizosimov.github.io/papers.html

Research groups

Publications

List by: Type | Date

Prior publications

Article

Anton Izosimov (2026) Folding of quadrilaterals and Arnold-Liouville integrability Arnold Mathematical Journal Anton Izosimov. ISSN 2199-6806 (doi: 10.56994/armj.011.004.005)

Anton Izosimov, Boris Khesin, Ilia Kirillov (2025) Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces Journal of Symplectic Geometry Anton Izosimov. ISSN 1540-2347 (doi: 10.4310/jsg.250403020521)

Izosimov, A., Khesin, B. (2024) Geometry of generalized fluid flows Calculus of Variations and Partial Differential Equations Scopus - Elsevier. ISSN 14320835 09442669 (doi: 10.1007/s00526-023-02612-5)

Izosimov, A. (2023) Change of Polytope Volumes Under Möbius Transformations and the Circumcenter Of Mass Discrete and Computational Geometry Scopus - Elsevier. ISSN 14320444 01795376 (doi: 10.1007/s00454-022-00481-x)

Izosimov, A., Khesin, B. (2023) Long-diagonal pentagram maps Bulletin of the London Mathematical Society Scopus - Elsevier. ISSN 14692120 00246093 (doi: 10.1112/blms.12792)

Izosimov, A. (2023) Polygon recutting as a cluster integrable system Selecta Mathematica, New Series Scopus - Elsevier. ISSN 14209020 10221824 (doi: 10.1007/s00029-023-00826-1)

Izosimov, A., Beffa, G.M. (2023) What is a Lattice W-Algebra? International Mathematics Research Notices Scopus - Elsevier. ISSN 16870247 10737928 (doi: 10.1093/imrn/rnad151)

Izosimov, A. (2022) Dimers, networks, and cluster integrable systems Geometric and Functional Analysis Scopus - Elsevier. ISSN 14208970 1016443X (doi: 10.1007/s00039-022-00605-8)

Izosimov, A. (2022) INTERSECTING the SIDES of A POLYGON Proceedings of the American Mathematical Society Scopus - Elsevier. ISSN 10886826 00029939 (doi: 10.1090/proc/15698)

Izosimov, A. (2022) Pentagram maps and refactorization in Poisson-Lie groups Advances in Mathematics Scopus - Elsevier. ISSN 10902082 00018708 (doi: 10.1016/j.aim.2022.108476)

Aboud, Q., Izosimov, A. (2022) The Limit Point of the Pentagram Map and Infinitesimal Monodromy International Mathematics Research Notices Scopus - Elsevier. ISSN 16870247 10737928 (doi: 10.1093/imrn/rnaa258)

Izosimov, A. (2022) The pentagram map, Poncelet polygons, and commuting difference operators Compositio Mathematica Scopus - Elsevier. ISSN 0010437X (doi: 10.1112/S0010437X22007345)

Bolsinov, A., Izosimov, A., Kozlov, I. (2021) JORDAN–KRONECKER INVARIANTS OF LIE ALGEBRA REPRESENTATIONS AND DEGREES OF INVARIANT POLYNOMIALS Transformation Groups Scopus - Elsevier. ISSN 1531586X 10834362 (doi: 10.1007/s00031-021-09661-0)

Bolsinov, A., Izosimov, A. (2019) Smooth invariants of focus-focus singularities and obstructions to product decomposition Journal of Symplectic Geometry Scopus - Elsevier. ISSN 15402347 15275256 (doi: 10.4310/JSG.2019.v17.n6.a2)

Izosimov, A., Khesin, B. (2018) Vortex sheets and diffeomorphism groupoids Advances in Mathematics Scopus - Elsevier. ISSN 10902082 00018708 (doi: 10.1016/j.aim.2018.09.015)

Izosimov, A., Khesin, B. (2017) Characterization of steady solutions to the 2D Euler equation International Mathematics Research Notices Scopus - Elsevier. ISSN 16870247 10737928 (doi: 10.1093/imrn/rnw230)

Izosimov, A., Khesin, B. (2017) Classification of casimirs in 2D hydrodynamics Moscow Mathematical Journal Scopus - Elsevier. ISSN 16094514 16093321 (doi: 10.17323/1609-4514-2017-17-4-699-716)

Bolsinov, A.V., Izosimov, A.M., Tsonev, D.M. (2017) Finite-dimensional integrable systems: A collection of research problems Journal of Geometry and Physics Scopus - Elsevier. ISSN 03930440 (doi: 10.1016/j.geomphys.2016.11.003)

Izosimov, A. (2017) Singularities of Integrable Systems and Algebraic Curves International Mathematics Research Notices Scopus - Elsevier. ISSN 16870247 10737928 (doi: 10.1093/imrn/rnw168)

Izosimov, A., Khesin, B., Mousavi, M. (2016) Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics Annales de l'Institut Fourier Scopus - Elsevier. ISSN 03730956 (doi: 10.5802/aif.3066)

Izosimov, A. (2016) Flat Bi-Hamiltonian Structures and Invariant Densities Letters in Mathematical Physics Scopus - Elsevier. ISSN 15730530 03779017 (doi: 10.1007/s11005-016-0875-1)

Izosimov, A. (2016) Pentagrams, inscribed polygons, and prym varieties Electronic Research Announcements in Mathematical Sciences Scopus - Elsevier. ISSN 19359179 (doi: 10.3934/era.2016.23.004)

Izosimov, A. (2015) Algebraic geometry and stability for integrable systems Physica D: Nonlinear Phenomena Scopus - Elsevier. ISSN 01672789 (doi: 10.1016/j.physd.2014.10.006)

Bolsinov, A., Izosimov, A. (2014) Singularities of Bi-Hamiltonian Systems Communications in Mathematical Physics Scopus - Elsevier. ISSN 14320916 00103616 (doi: 10.1007/s00220-014-2048-3)

Izosimov, A. (2014) Stability of relative equilibria of multidimensional rigid body Nonlinearity Scopus - Elsevier. ISSN 13616544 09517715 (doi: 10.1088/0951-7715/27/6/1419)

Izosimov, A. (2014) The derived algebra of a stabilizer, families of coadjoint orbits, and sheets Journal of Lie Theory Scopus - Elsevier. ISSN 09495932

Izosimov, A. (2013) Curvature of Poisson pencils in dimension three Differential Geometry and its Application Scopus - Elsevier. ISSN 09262245 (doi: 10.1016/j.difgeo.2013.05.011)

Izosimov, A.M. (2013) Stability of stationary rotations of multidimensional rigid body Moscow University Mathematics Bulletin Scopus - Elsevier. ISSN 00271322 19348444 (doi: 10.3103/S002713221301018X)

Izosimov, A. (2012) A note on relative equilibria of a free multidimensional rigid body Journal of Physics A: Mathematical and Theoretical Scopus - Elsevier. ISSN 17518113 17518121 (doi: 10.1088/1751-8113/45/32/325203)

Izosimov, A. (2012) Stability in bihamiltonian systems and multidimensional rigid body Journal of Geometry and Physics Scopus - Elsevier. ISSN 03930440 (doi: 10.1016/j.geomphys.2012.09.006)

Izosimov, A.M. (2011) Classification of almost toric singularities of Lagrangian foliations Sbornik Mathematics Scopus - Elsevier. ISSN 14684802 10645616 (doi: 10.1070/SM2011v202n07ABEH004175)

Izosimov, A.M. (2011) Smooth invariants of focus-focus singularities Moscow University Mathematics Bulletin Scopus - Elsevier. ISSN 00271322 19348444 (doi: 10.3103/S0027132211040103)

Grants

  • Simons Foundation Travel Support for Mathematicians, 2024 - 2025, $42000
  • National Science Foundation Research Grant, 2020 - 2024, $217000

Supervision

I welcome enquiries to supervise PhD students with interests in algebra, geometry, and/or mathematical physics. There are two routes to apply: through the EPSRC Centre for Doctoral Training in Algebra, Geometry and Quantum Fields (CDT AGQ, deadline: 19 December 2025), or directly through the school (review of applications for scholarships will begin on 1 January 2026). The CDT route is more competitive, so if you choose that, it is recommended that you also apply through the school.

Potential PhD projects include the following:

  •  Integrable systems and cluster algebras. Integrable systems are nonlinear dynamics systems which exhibit unexpectedly organized long-term behavior. Such systems usually come with rich underlying algebraic and/or geometric structures. The aim of the project is to investigate integrable systems in the realm of cluster algebras, a remarkable class of algebras which were discovered just over twenty years ago but already found applications all over mathematics. The study of integrable systems in the framework of cluster algebras involves connections with Lie theory, graph theory, low-dimensional topology, and numerous other topics.
  •  Geometric methods in fluid dynamics. In his seminal 1966 paper, Vladimir Arnold showed that the Euler equation of incompressible fluid dynamics can be viewed as an equation of geodesics (shortest curves) on the infinite-dimensional Lie group of volume-preserving diffeomorphisms. Quite recently, it was shown that other hydrodynamical settings (such as fluids with a discontinuity of the velocity profile) lead to more general algebraic and geometric structures, such as Lie groupoids. The goal of the project is to investigate various group and groupoid-like structures in a range of fluid-dynamical applications.

 

Past PhD Students

  • Quinton Aboud, University of Arizona, degree awarded in 2026
  • Abigayle Dirdak, University of Arizona, degree awarded in 2024
  • Ilia Kirillov, University of Toronto, degree awarded in 2024 (joint supervision with B. Khesin)
  • Leaha Hand, University of Arizona, degree awarded in 2024
  • Daniel Fusca, University of Toronto, degree awarded in 2018 (joint supervision with B. Khesin)

 

Teaching

Current teaching:

  • Mathematics 1 (Head of Core Skills)

  • Mathematics 2C: Introduction To Real Analysis

  • Mathematics 4H: Galois Theory

Additional information

I co-ogranize the following seminars: