# 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] Symmetry, dualities and approximations in derived algebraic geometry and representation theory (Jan Šťovíček), [GAČR Junior] Cohen-Macaulay rings and their applications in higher algebra and topology (Liran Shaul)

#### Universal algebra, mathematical logic and computational complexity

*contact persons:*Libor Barto, Jan Krajíček*seminars:*Logic seminar, Seminar on combinatorial, algorithmic and finitary algebra*grants:*[ERC Consolidator] Symmetry in Computational Complexity (Libor Barto), [GAČR] Rozšíření záběru univerzální algebry (Michael Pinsker), [START] Klasifikace automatických formálních systémů (Barbora Hudcová)

#### Number theory

*contact person:*Víťa Kala*seminars:*Number Theory Seminar*grants:*[GAČR Junior Star] Universal quadratic forms and class numbers (Víťa Kala), [Primus] Universal quadratic forms: geometry and analysis (Víťa Kala), [GAUK] Number systems in lattices and number field orders (Jakub Krásenský)

#### Nonassociative algebraic structures

*contact persons:*Aleš Drápal, David Stanovský*seminars:*Seminar on combinatorial, algorithmic and finitary algebra*grants:*[INTER-EXCELLENCE] Commutators, quasigroups and the Yang-Baxter equation (Aleš Drápal)

#### 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:*[GAČR] Formalization of combinatorics on words (Štěpán Holub), [GAČR] Cryptography based on finite fields (Faruk Göloglu), [Primus] Algebraic methods in discrete geometry and topology (Zuzana Patáková)

The Department of Algebra participates on several institutional projects: UNCE for young researchers (Jan Krajíček), SVV for doctoral students (Jan Žemlička), Progres Q-49 for the development of the school of mathematics (Vít Dolejší).