Mathematical Physics, Geometry and Integrability

June 26—July 2, 2022

Description

Mathematical physics and geometry are among the most rapidly developing branches of pure and applied mathematics. Geometry has traditionally played a central role in the mathematical formalism of physics, the integrability traditionally associated with classical mechanics and reaching back to Newton and Euler. However, the work of Jacobi on geodesics on ellipsoid revealed deep connections with algebraic geometry and abelian functions, something that had a great impact on the development of these areas in the 19th century.

On the other hand, the striking discoveries made in soliton theory in the 1960s pushed overwhelming developments in the theory of integrability, and that notion is now considered an important ingredient in algebraic, differential, and enumerative geometry as well as mathematical physics. This conceptual breakthrough produced many new fantastically fruitful ideas in both mathematics and physics. The main feature of integrability, one might say, is to be a binding element between the seemingly unrelated areas of mathematics and theoretical physics — the integrability of complex and other geometric structures; the integrability of classical dynamical systems of particles, soliton dynamics, and hydrodynamical flows presented in geometrical form; the integrability in classical differential systems and Riemann–Hilbert correspondence as a part of complex analysis; integrable (holonomic) D-modules and quantum cohomology in singularity theory; instantons (Belavin and others); matrix and statistical models; “integrable sectors” in quantum field theory; Hitchin integrability of moduli space of “Higgs pairs”; Gromov–Witten invariants; and the mirror symmetry in algebraic geometry.

The universality of this concept is a particular and illuminating example of Manin’s famous “meta-theorem” on the unity of mathematics. In a broad sense, including due to modern traditions and rules, mathematical physics is a part of that.

All our keynote speakers are world-leading experts, each in all three branches of the triad. By way of reminder, Lomonosov Moscow State University scientists, albeit scattered all over the world, have traditionally been and remain among the leaders in these domains of research. The conference should manifest the continuity of these traditions.

One scope of the conference is to provide fruitful ground where students, early career researchers, and experienced scientists can unify and reinforce their interest and efforts in this exciting interdisciplinary area.

OBJECTIVES

The aim of the conference is to bring together specialists in this united triad to share their experience and knowledge about the most recent developments in all the related fields, domains, and components.

Thu Nov 18 2021 14:18:42 GMT+0300 (Moscow Standard Time)