Program Overview

Doctoral Program in Mathematical Sciences

The Doctoral Program in Mathematical Sciences offers a comprehensive curriculum that encompasses various fields of mathematics. The program is designed to provide students with a deep understanding of mathematical concepts and techniques, as well as the opportunity to engage in cutting-edge research.

Research Areas

The curriculum in Mathematics includes:

• Algebra
• Geometry
• Mathematical Analysis
• Mathematical Logic
• Mathematical Physics Research within these subjects may concern:
  • Additive and triangulated Categories
  • Representation and Group theory, Lie theory
  • Asymptotic and probabilistic Group theory
  • Calculus of variations, Geometric measure theory, Geometric Analysis, Sub-Riemannian geometry
  • Deterministic and Stochastic Control theory and Differential Games
  • Partial Differential Equations, linear (spectral theory) and nonlinear (motivated either by geometry or by control problems)
  • Algebraic and Complex Analysis
  • Celestial Mechanics and KAM theory
  • Hamiltonian systems
  • Algebraic Geometry, arithmetic of elliptic curves and modular forms
  • Number Theory
  • Foundations of Logic

The curriculum in Computational Mathematics includes:

• Mathematical Finance
• Numerical Analysis
• Optimization
• Probability Research within these subjects may concern:
  • Stochastic methods for Finance
  • Stochastic models in Statistical Physics
  • Integer programming and combinatorial optimization, Nonlinear programming and mixed integer nonlinear programming, methods for large dimensional problems
  • Models for the optimal management of limited resources
  • Methods of numerical approximation for differential and integral equations, extrapolation methods
  • Numerical methods for image processing
  • Numerical linear and nonlinear algebra and applications, numerical software

Program Structure

The program is structured to provide students with a broad foundation in mathematical sciences, as well as specialized knowledge in their chosen area of research. The curriculum is designed to be flexible, allowing students to tailor their course of study to their individual interests and goals.