Research
The research at our department covers various topics in algebra, mathematical logic, number theory and their applications in computer science. Below, there is a list our major research topics, including contact persons, grant projects and links to specialized seminars. Contacts and specializations of our staff can be found in section People.
Homological algebra and representation theory
- contact persons: Jan Trlifaj, Jan Šťovíček, Liran Shaul
- seminars: Algebra seminar
- grants: [GAČR] Homological and model-theoretic methods in algebra and geometry (Jan Šťovíček), [Primus] Categorical Knörrer periodicity, cluster categories and tensor triangulated geometry (Sebastian Opper), [GAUK] Methods of set theory and module theory in the theory of representations (Kateřina Fuková), [GAUK] Representation theoretic and homological properties of tame algebras (Anna Olšáková)
Universal algebra, mathematical logic and computational complexity
- contact persons: Libor Barto, Jan Krajíček
- seminars: Logic seminar
- grants: [ERC Synergy] POCOCOP: Polynomial-time computation – opening the blackboxes in constraint problems (Libor Barto), [Primus] The subpower membership problem for algebras with cube term (Michael Kompatscher), [GAUK] Models of bounded arithmetics and complexity theory (Mykyta Narusevych), [GAČR] Modern Czech logic in philosophy of mathematics (co-PI Štěpán Holub)
Number theory
- contact persons: Víťa Kala, Pavlo Yatsyna, Siu Hang Man
- seminars: Number Theory Seminar
- grants: [GAČR] Sailing to criterion sets for quadratic forms (Víťa Kala), [Primus] Statistical properties of totally real number fields (Pavlo Yatsyna), [Primus] Automorphic forms for symplectic groups via trace formulas (Siu Hang Man), [Návraty na UK] Aperiodic sequences in number theory (Kateřina Kalová), [GAUK] Universality of generalized higher degree forms over number fields (Om Prakash)
Nonassociative algebraic structures
- contact persons: Aleš Drápal, David Stanovský
- seminars: Seminar on combinatorial, algorithmic and finitary algebra
Computational aspects of algebra and geometry
- contact persons: Štěpán Holub (words, formalization), Faruk Göloglu (cryptography), Zuzaná Patáková (computational geometry)
- seminars: Seminar on combinatorial, algorithmic and finitary algebra
- grants: [ERC Advanced – secondary beneficiary] NextReason: Next Generation Computer Assisted Reasoning (Josef Urban, local team: David Stanovský)
The Department of Algebra participates on several institutional projects: Cooperatio SCI-Mathematics for the development of the school of mathematics (Vít Dolejší), UNCE Intersections of algebra, geometry, and informatics for young researchers (Libor Barto), and an SVV project for doctoral students (Jan Žemlička).
Selected older projects:
- [ERC Consolidator] Symmetry in Computational Complexity (CoCoSym) (Libor Barto, 2018–2023)
- 2nd wave of UNCE projects (Jan Krajíček, 2018–2023)
