"Simplicity is a great virtue but it requires hard work to achieve it and education to appreciate it. And to make matters worse: complexity sells better." - E. W. Dijkstra
Members of our department are focused on the more foundational aspects of Theoretical Computer Science and their work can be classified into three main areas: Combinatorics, Computational Complexity, and Mathematical Logic. In all these areas, we strive not only to achieve new results but to broaden the repertoire of approaches that are considered standard. In particular we pursue three main aims:
Combinatorics: to study the recent challenging problems of extremal graph theory and discrete random structures, and thus contribute to these central topics in combinatorics which are crucial e.g. for our understanding of very large networks.
Mathematical Logic: to develop and apply non-classical logics for reasoning, in both natural and artificial scenarios, with real-life information, which is often uncertain, graded, or even contradictory, and changing over time.
Computational Complexity: to deepen our knowledge of relations among complexity classes via standard and non-standard computational models considering both the usual complexity measures like time or space and new ones relevant in neurocomputing and knowledge compilation.
Combinatorics: Extremal Graph Theory, Regularity Method, Probabilistic Method, Limits of Graphs, Random Graphs, Discrete Structures, Computational Geometry, Combinatorial and Algebraic Methods in Number Theory.
Mathematical Logic: Logic and Reasoning, Graded Notions, Vagueness, Uncertainty, Mathematical Fuzzy Logic, Substructural Logics, Paraconsistent Logic, Dynamic and Non-Monotonic Logic, Modal Logic, Abstract Algebraic Logic, Complexity of Non-Classical Logics, Philosophy of Mathematics.
Computational Complexity: Branching Programs, Neural Networks, Boolean Functions, Preprocessing Instances for SAT Problem, Knowledge Compilation, Logical Descriptions of Computation, Non-Standard Positional Numeral Systems.
Combinatorial group:
a group dedicated to study of extremal graph theory, discrete structures, graph limits, and computational geometry. We organize a combinatorial seminar.
Hladký Jan; Komlós J; Piguet Diana; Simonovits Miklos; Stein Maya; Szemeredi Endre. The approximate Loebl-Komlós-Sós conjecture I, II, III, IV. SIAM Journal on Discrete Mathematics, 2017
