Algebra and Number Theory
- Algebraic topology
- Arithmetic statistics
- Combinatorial and analytic number theory
![Algebra and Number Theory](../assets/imgs/aoe_algebra.jpg)
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
![Pure and Applied Analysis, Calculus of Variations, PDE and Applications](../assets/imgs/aoe_calculus.jpg)
Combinatorics
- Extremal combinatorics
- Probabilistic method
- Random Graphs and Randomized Algorithms
- Ramsey theory
- Topological methods in combinatorics
![Combinatorics](../assets/imgs/aoe_combinatorics.png)
Computational Mathematics, Numerical Analysis, and Optimization
- 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
![Computational Mathematics, Numerical Analysis, and Optimization](../assets/imgs/aoe_cna.jpg)
Faculty
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
![Discrete and Convex Geometry](../assets/imgs/aoe_discrete.png)
Logic
- Lambda-calculus and combinatory logic
- Model theory
- Semantics of programming languages
- Descriptive set theory
- Large cardinals, forcing and inner models
- Type theory
![Logic](../assets/imgs/aoe_logic.png)
Mathematical Finance
- Martingale problems and Markov processes
- Equilibrium theory
- Stochastic control
- Stochastic differential equations
- Viscosity solutions of Hamilton-Jacobi-Bellman equations
![Mathematical Finance](../assets/imgs/aoe_cmumathfinance.jpg)
Faculty
William J. Hrusa
Dmitry Kramkov
Martin Larsson
Steven E. Shreve (Emeritus)
Johannes Wiesel
Probability
- Discrete Random Structures
- Markov Chain Mixing Times
- Random Dynamics
- Stochastic Homogenization and Random Media
- Stochastic Partial Differential Equations
![Probability](../assets/imgs/aoe_probability.png)