Mathematical structures in algebra, geometry and logic












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            * Mathematical structures in algebra, geometry and logic
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            Foundations of the research in algebra, geometry and logic at the Faculty were laid in the

            Eduard Čech and Petr Vopěnka. Over the past decade, activities of the Eduard Čech Institut
            Excellence (ECI and ECC) have fostered research in these areas.


            Since 2018, the seven year University Research Center (UNCE) project “Methods in Algebra a
            is running at the Faculty, headed by a renown expert in proof complexity, Jan Krajíček [ U
            www.karlin.mff.cuni.cz/~krajicek/"] . Applications of universal algebra to constraint sati

            are a major topic pursued by the group of Libor Barto [ URL "http://www.karlin.mff.cuni.cz
            the support by his CoCoSym [ URL "https://cordis.europa.eu/project/rcn/213446/factsheet/en

            Grant of the ERC. Algebraic topics include representation theory, and its connections to h
            (Jan Šťovíček [ URL "https://www.karlin.mff.cuni.cz/~stovicek/index.php/en/homepage"] ) an
            homological algebra (Jan Šaroch). Since 2019, the five year EXPRO project “Homotopy and ho

            and tools related to mathematical physics’’ is financed by GAČR. It includes research in a
            (Petr Somberg [ URL "http://www.karlin.mff.cuni.cz/~somberg/"] ), differential geometry (V
            [ URL "http://www.karlin.mff.cuni.cz/~soucek/"] ), and applications in theoretical physics

            Jurčo).





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            * Selected outputs
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            • Barto, L. Finitely related algebras in congruence modular varieties have few subpowers [

              www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=20&iss=6&rank=3&srch=search
              J. European Math. Soc. 20(2018), 1439-1471.
            • Jurčo, B. (with Vysoký, J.) Poisson–Lie T-duality of string effective actions: A new app

              dilaton puzzle [ URL "https://www.sciencedirect.com/science/article/pii/S039304401830174
              J. of Geom. and Physics 130(2018), 1-26.
            • Krajíček, J. Proof Complexity [ URL "https://www.cambridge.org/core/books/proof-

              complexity/80BDF46F373753B475550D04F58098A3"] , Encyclopedia of Math. and Its Appl., vol
              Univ. Press, 2019, 588 pp.
            • Somberg, P. (with Hu, P., and Kříž, I.) Derived representation theory of Lie algebras an

              homotopy categorification of sl_k [ URL "https://www.sciencedirect.com/science/article/p
              S0001870818304389?via%3Dihub"] Adv. Math., 341 (2019), 367- 439.
            • Souček, V. (with Cap, A.) Relative BGG sequences; II. BGG machinery and invariant operat

              "https://www.sciencedirect.com/science/article/pii/S0001870816313482?via%3Dihub"] Adv. M
              1009-1062
            • Šaroch, J On the non-existence of right almost split maps [ URL "https://link.springer.c

              article/10.1007%2Fs00222-016-0712-2"] Invent. math. 209(2017), 463-479.
            • Šťovíček, J. (with Groth, M.) Tilting theory via stable homotopy theory [ URL "https://
              www.degruyter.com/view/j/crelle.2018.2018.issue-743/crelle-2015-0092/crelle-2015-0092.xm

              angew. Math. 743(2018), pp. 29-90.