Here you find a brief description of the research areas and some subareas in which our faculty members are active. Keep in mind that we are often interested in related areas as well.

Combinatorics

Combinatorics can be simply defined as the art of counting, enumerating, ordering, constructing, and analyzing discrete mathematical objects. However, it is much more than that, being a branch of mathematics with applications in both computer science and various other fields of mathematics. It is a set of techniques and strategies for handling discrete structures. Furthermore, a fundamental characteristic of Combinatorics is its focus on problems that are easy to formulate (often self-contained) but challenging to solve.

• Extremal combinatorics
• Probabilistic combinatorics
• Graph theory

Combinatorial Optimization

Combinatorial optimization deals with problems where the aim is to find the best solution from a finite set of possible solutions. These problems often involve optimizing an objective function over discrete structures such as graphs, integers, or permutations. Common applications include scheduling, network design, and resource allocation. Techniques used in combinatorial optimization include greedy algorithms, dynamic programming, and branch-and-bound methods. This field is fundamental in both theoretical computer science and practical operations research.

• Linear and integer programming
• Semidefinite optimization
• Approximation algorithms

Theory of computing

The theory of computing is a branch of computer science that focuses on understanding the fundamental principles and limits of computation. It encompasses the study of algorithms, computational complexity, automata theory, and formal languages. It involves questions about what can be computed, how efficiently it can be done, and the inherent difficulty of computational problems. This theoretical framework is essential in software development, cryptography, and artificial intelligence, shaping the capabilities and boundaries of modern computing systems.

• Algorithms and data structures
• Computational complexity
• Quantum computing