Research departments

The members of the algebra department study the structure, combinatorial properties, and representations of various algebraic structures (like groups, rings, semigroups).

The main reserach areas include low dimensional topology (knot theory, contact 3-manifolds, Heegaard Floer theory, Seiberg-Witten theory) and theory of complex algebraic/analytic varieties with a focus on invariants of their singularities (e.g. lattice homology).

Main research areas: approximation theory, extremal problems for polynomials of several variables, potential theory, Fourier analysis and its applications, fractal geometry.

The Erdős Center hosts summer schools, workshops, visiting professors and postdocs in the framework of Thematic Semesters, and additional Focused Workshops in July.

Our department’s primary research focus is on extremal problems concerning finite hypergraphs, partially ordered sets, vector spaces over finite fields, and graphs, namely the determination of the maximum or minimum size of structures subject to given constraints.

In our department we primarily study the properties of geometric shapes, bodies, and sets.

The department was formed in 2021 by dividing the former Discrete Mathematics department into three parts. Members of the department study various properties of graphs, such as colorings, extremal questions, Ramsey problems, planarity, and geometric graphs.

The Department of Set Theory, Logic and Topology brings together research in infinite combinatorics, set-theoretical topology, descriptive set theory, and mathematical logic, continuing Hungary’s strong traditions while advancing foundational studies of mathematics and physics.

In our department, we conduct research on both theoretical and application oriented topics related to combinatorics (graph limit theory, network theory, algorithms in random graphs, etc.) in projects funded by the EU and the Hungarian government.

Our department focuses on the mathematical foundations of machine learning. Our vision is to foster a research environment where theoretical studies in artificial intelligence and practical applications are closely interconnected, each mutually strengthening the other.

The Didactics Group focuses primarily on research into guided discovery and its potential applications. In addition, research into and implementation of talent nurturing plays a prominent role.

The Number Theory Department conducts research in the areas of additive combinatorics, classical analytic number theory and automorphic forms.

The department carries out research on probability and its applications. Focus areas are statistical physics and random algorithms.