# 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, Commutative homological algebra seminar*grants:*[GAČR] Homological and structural theory in geometric contexts (Jan Šťovíček), [Primus] Categorical Knörrer periodicity, cluster categories and tensor triangulated geometry (Sebastian Opper), [GAUK] Methods of homotopy theory in tilting theory (Chiara Sava)

#### 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)

#### Number theory

*contact person:*Víťa Kala, Pavlo Yatsyna*seminars:*Number Theory Seminar*grants:*[GAČR Junior Star] Universal quadratic forms and class numbers (Víťa Kala), [GAČR PIF] Arithmetic properties of Hopf-Galois extensions (Daniel Gil-Muňoz), [Primus] Statistical properties of totally real number fields (Pavlo Yatsyna)

#### Nonassociative algebraic structures

*contact persons:*Aleš Drápal, David Stanovský*seminars:*Seminar on combinatorial, algorithmic and finitary algebra*grants:*[GAUK] Universal algebraic and group theoretic methods in algebraic structures with unique division (Filippo Spaggiari)

#### 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

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)