Currently, the areas of active research in the Department of Combinatorics and Optimization are:
- Algebraic and Enumerative Combinatorics. Classical and bijective methods; additive number theory, asymptotic analysis; combinatorial aspects of algebraic geometry, finite reflection groups, symmetric functions; random matrix models.
- Continuous Optimization. Linear and quadratic programming, convex analysis, duality theory, optimization in abstract spaces, matrix eigenvalue problems, interior-point methods, semi-definite programming problems; applications in finance, combinatorial optimization and many engineering disciplines.
- Cryptography. Finite fields, elliptic curves, design and analysis of public key systems.
- Discrete Optimization. Polyhedral combinatorics, approximation algorithms for NP-hard problems, semi-definite relaxations, extensions of matching and network flow theory, and matroids and generalizations.
- Graph Theory. Algebraic graph theory (association schemes, knot polynomials, eigenvalues), algorithmic graph theory, asymptotic enumeration of graphs, random graph theory, probabilistic methods, topological graph theory, extremal graph theory, matching theory, minimax theorems, and Ramsey theory.
- Quantum Information. Quantum computer algorithms and implementations, quantum cryptography, discrete logarithms.