# Research Areas

Mathematical research at YMSC spans a broad range in pure mathematics, applied mathematics, computational mathematics and related disciplines and engineering. The following are its five main research groups:

## Representation theory, algebraic geometry and number theory

This group focuses on research in algebraic and geometric representation theory, category theory, I-adic cohomology and applications, moduli spaces, Hodge theory, singularity theory, arithmetic geometry.

## Geometry and topology

Research of this group covers a broad range of research including differential geometry, geometric analysis, Teichmüller theory, topology in higher and lower dimensions, complex geometry, and etc.

## Analysis, partial differential equation (PDE) and dynamical systems

This group study the evolution of both finite dimensional and infinite dimensional phase spaces of ordinary or partial differential equations originated from dynamical systems, general relativity, hydrodynamics, and etc.

## Probability theory and applied mathematics

This group is interested in mathematical problems from real world, including rigorous understanding of statistical models, PDEs with random coefficients, modeling of self-organization in biology, mathematical methods in imaging science, and other numerical methods.

## Mathematical physics

Mathematical physics group are devoted to the interdisciplinary study between mathematics and physics, including superstring theory, gauge/gravity duality, supersymmetric theories and their applications in geometry, category theory and topological order in condensed matter physics, machine learning in mathematical physics, and etc.