Carnegie Mellon University

Calculus of Variations, Partial Differential Equations, and Applications

  • Diffusion, particle systems, stochastic partial differential equations
  • Energy-driven systems
  • Fluids and continuum mechanics
  • Free and moving boundary problems
  • Multiscale problems
  • Optimal transport
  • Applications of these topics to
    • Materials science
    • Physical sciences
    • Data science
    • Image processing

CNA

Calculus of Variations, Partial Differential Equations, and Applications

Faculty

Irene Fonseca
William J. Hrusa
Gautam Iyer
David Kinderlehrer
Giovanni Leoni
Robert Pego
Hayden Schaeffer
Dejan Slepčev
Ian Tice
Noel J. Walkington
Franziska Weber

Combinatorics

  • Extremal combinatorics
  • Probabilistic method
  • Random Graphs and Randomized Algorithms
  • Ramsey theory
  • Topological methods in combinatorics

ACO

Combinatorics

Faculty

Tom Bohman
Boris Bukh
Gerard Cornuejols
Florian Frick
Alan Frieze
Po-Shen Loh
Wesley Pegden

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

CNA

Computational Mathematics, Numerical Analysis, and Optimization

Faculty

Hayden Schaeffer
Dejan Slepčev
Noel J. Walkington
Franziska Weber

Discrete and Convex 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

Faculty

Boris Bukh
Florian Frick
Wesley Pegden
Tomasz Tkocz

Logic

  • Lambda-calculus and combinatory logic
  • Model theory
  • Semantics of programming languages
  • Descriptive set theory
  • Large cardinals, forcing and inner models
  • Type theory
Logic

Faculty

Clinton Conley
James Cummings
Rami Grossberg
Ernest Schimmerling
Richard Statman

Mathematical Finance

  • Martingale problems and Markov processes
  • Equilibrium theory
  • Stochastic control
  • Stochastic differential equations
  • Viscosity solutions of Hamilton-Jacobi-Bellman equations

BSCF MSCF

Mathematical Finance

Faculty

William J. Hrusa
Dmitry Kramkov
Martin Larsson
John P. Lehoczky

Probability

  • Discrete Random Structures
  • Markov Chain Mixing Times
  • Random Dynamics
  • Stochastic Homogenization and Random Media
  • Stochastic Partial Differential Equations
Probability

Faculty

Alan Frieze
Gautam Iyer
Dmitry Kramkov
Martin Larsson
Wesley Pegden
Agoston Pisztora
Tomasz Tkocz