Research activities at the Department encompass several main branches of pure and applied mathematics; namely algebra, geometry, mathematical analysis, history of mathematics and mathematical education, and statistics and mathematical modelling.

The Department provides teaching of professional mathematics (scholarly mathematics), mathematics aimed to finances and economy, and teaching of mathematics for future teachers in secondary schools. Our department also provides courses of mathematics for other branches at the Faculty of Science, such as physics, chemistry, biology, and geography. Furthermore, our members teach all main mathematical courses at the Faculty of Informatics and some mathematical courses at the Faculty of Economics and Administration. Our department has accreditation for the doctoral program of mathematics in

• algebra, number theory, and mathematical logic,
• geometry, topology, and global analysis,
• mathematical analysis,
• history of mathematics and mathematical education,
• probability, statistics, and mathematical modelling.

In cooperation with the university our department publishes the mathematical journal Archivum Mathematicum (http://emis.muni.cz/journals/AM/). Moreover, the Editorial Office of the journal Differential Geometry and its Applications (http://dga.math.muni.cz/) published by Elsevier is located at the department. Both journals are indexed in the international databases Mathematical Reviews, Zentralblatt für Mathematik, and in Scopus.

The following working groups are currently active at the department. The contact information for the employees is here, including the link to the publications, grant projects, and teaching activities.

ALGEBRA

„Categories and ordered sets“ (Jiří Rosický, David Kruml, Josef Niederle, Jan Paseka). Our research in category theory is mainly oriented to accessible categories and their applications to algebra, algebraic topology, model theory and theoretical computer science. Topics like Quillen model categories, homotopy coherent category theory and triangulated categories are included. Quantales are studied from the point of their structure theory but also in connection with C*-algebras and non-commutative geometry. Concerning ordered sets, we are interested in their lattice-like and fix points properties, including lattice effect algebras.

„Number theory“ (Radan Kučera, Michal Bulant, Ladislav Skula). The research activity of the team is focused on algebraic number theory, especially on abelian fields. The main aim of this research is investigation of algebraic structures having connection to the class group of these fields (like circular units or Stickelberger ideal). Our team also contains several doctoral students.

„Semigroups and their applications“ (Libor Polák, Jiří Kaďourek, Ondřej Klíma, Michal Kunc). The current research of our team is mainly devoted to the algebraic theory of formal languages, in particular, to classification of regular languages, language equations and inequalities. Concerning semigroup theory, we focus on varieties and pseudovarieties of semigroups and idempotent semirings. We also continue in the study of complexity issues of combinatorial problems in semigroup theory and other applications of semigroup theory to theoretical computer science.

GEOMETRY

„Algebraic techniques in geometry and analysis“ (Jan Slovák, Martin Čadek, Martin Kolář, Josef Šilhan, Lukáš Vokřínek). Our team is mainly active in the following areas: (i) differential geometry and geometric analysis (applications of Lie theory to geometric structures; geometric analysis of conformal, CR, quaternionic and other geometries modeled by means of semisimple Lie groups; invariant operators and related functional analysis), (ii) geometric complex analysis (normal forms and invariants of domains in complex spaces), (iii) algebraic topology (topology of vector bundles, string topology, Vassiliev homotopy principle).

„Natural operators and general geometric structures“ (Josef Janyška, Ivan Kolář). The main field of interest of the group is general theory of fibred spaces (jet bundles, Weil bundles and natural and gauge-natural bundles) and applications of geometrical methods in theoretical physics, namely in covariant classical and quantum theory over a curved spacetime.

MATHEMATICAL ANALYSIS

„Functional differential equations“ (Alexander Lomtatidze, Bedřich Půža). Our group explores problems on the existence and uniqueness of a solution of various functional differential equations. The main attention is paid to the case of non-Volterra's type equations and asymptotic properties of solutions.

„Ordinary differential and difference equations“ (Ondřej Došlý, Ladislav Adamec, Miroslav Bartušek, Zuzana Došlá, Josef Kalas, Zdeněk Pospíšil, Roman Šimon Hilscher). Our group explores qualitative theory of differential and difference equations. We pay particular attention to the following topics: (i) oscillation and asymptotic theory of half-linear and quasilinear differential and difference equations, (ii) asymptotic and stability theory of various nonlinear differential equations, (iii) oscillation, transformation, and spectral theory of Hamiltonian and symplectic differential and difference systems with applications in the calculus of variations and optimal control theory, (iv) qualitative theory of various dynamic equations and systems on time scales.

HISTORY OF MATHEMATICS AND MATHEMATICAL EDUCATION

„History of mathematics“ (Eduard Fuchs, Pavel Šišma). We investigate history of geometry, combinatorics and graph theory. We are also interested in history of the education of mathematics at technical universities in the Austro-Hungarian monarchy and Czechoslovakia during 19th and 20th centuries, especially at the German Technical University in Brno. Our future activities will include preparation of biographies of the most important mathematicians at the Masaryk University in Brno.

„Mathematical education“ (Jaromír Šimša, Eduard Fuchs, Roman Plch). We deal with problems of high-school mathematics and preparation of its teachers during their undergraduate and postgraduate studies. A special attention is devoted to problem solving strategies designed for gifted high-school students and to teaching mathematics in an E-learning environment.

STATISTICS AND MATHEMATICAL MODELLING

„Mathematical modelling“ (Zdeněk Pospíšil, Martin Kolář, Petr Lánský, Lenka Přibylová). Our main research activities are focused on establishing, analyzing and numerical treatment of mathematical models, both deterministic and stochastic ones. The models originate in fields of neurophysiology, bio-medicine, ecology and economy. We collaborate with the University Hospital, the Institute of Physiology AS CR and the Biocont Laboratory.

„Statistics and data analysis“ (Ivana Horová, Marie Budíková, Marie Forbelská, Jan Koláček, Martin Řezáč, Gejza Wimmer, Jiří Zelinka). Our research objectives include: nonparametric and robust statistical methods, kernel estimates of density, regression function and hazard function including applications to real data sets, discriminant analysis, generalized linear models, statistical models for elliptical contoured distributions, ROC curves, estimating and testing procedures in unbalanced heteroscedastic models and models of calibration of function parameters. Further objective consists in establishing, analyzing and numerical treatment of deterministic mathematical models. We cooperate with Institute of Biostatistics and Analyses. Our research addresses robustness, nonparametric methods, ROC curves, survival analysis. Another cooperation includes University Hospital and Masaryk Memorial Cancer Institute. One of our aims is to establish and improve cooperation of interdisciplinary research groups.