Algebra and Number Theory
- Algebraic topology
- Arithmetic statistics
- Combinatorial and analytic number theory
Analysis, Calculus of Variations, PDE & Applications
- Diffusion, particle systems, stochastic partial differential equations
- Energy-driven systems
- Fluids and continuum mechanics
- Free and moving boundary problems
- Harmonic Analysis
- Multiscale problems
- Optimal transport
- Applications of these topics to
- Materials science
- Physical sciences
- Data science
- Image processing
Combinatorics
- Extremal combinatorics
- Probabilistic method
- Random Graphs and Randomized Algorithms
- Ramsey theory
- Topological methods in combinatorics
Computational Mathematics, Numerical Analysis, and Optimization
- Mathematics of machine learning
- Data-driven modeling
- Mathematics and computation in data sciences
- Nonsmooth and nonconvex optimization
- Numerical linear algebra
- Numerical methods for nonlinear partial differential equations and variational problems
Geometry
- Applied algebraic topology
- Convexity and polytopes
- Geometric and topological combinatorics
- Geometric functional analysis and concentration of measure
- The Abelian sandpile
- Tiling, packing, and covering problems
Logic
- Lambda-calculus and combinatory logic
- Model theory
- Semantics of programming languages
- Descriptive set theory
- Large cardinals, forcing and inner models
- Type theory
Mathematical Finance
- Martingale problems and Markov processes
- Equilibrium theory
- Stochastic control
- Stochastic differential equations
- Viscosity solutions of Hamilton-Jacobi-Bellman equations
Probability
- Discrete Random Structures
- Markov Chain Mixing Times
- Random Dynamics
- Stochastic Homogenization and Random Media
- Stochastic Partial Differential Equations
