• 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

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

• Algebra
• Geometry & topology
• Integrable systems & mathematical physics

List by: Type | Date

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

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), or directly through the school. 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

• 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)

Master Students

• Quinton Aboud, University of Arizona, degree awarded in 2021
• Konstantin Aleshkin, Moscow State University, degree awarded in 2015

Current teaching:

• Math 1 (Head of Core Skills)
• Math 2C

I co-ogranize the following seminars:

• University of Glasgow Integrable Systems and Mathematical Physics Seminar
• Edinburgh-Glasgow Joint Integrability Seminar
• Hamiltonian Systems Seminar (Online)