Ostrava Mathematical Seminar
(formerly Ostrava Seminar on Mathematical Physics)

University of Ostrava
(how to get here)

Seminar founder: Olga Rossi

Organizers: Diana Barseghyan, Pasha Zusmanovich

Upcoming and planned talks

Sometime after the end of coronavirus outbreak

Martyna Maciaszczyk (Silesian University of Technology, Gliwice)
Ideals and zero divisors in the ring \(T(\infty,F)\)
In this talk I give description of the ideals and zero divisors in the ring \(T(\infty,F)\) of infinite \(\mathbb N \times \mathbb N\) uppertriangular matrices over the field \(F\). I show solution of Suškevič's problem using strong linear independence. In the description of ideals I use the concept of zero pattern.
1. P. Vermes, Non-associative rings of infinite matrices, Nederl. Akad. Wetensch. Proc. Ser. A. 55 = Indag. Math. 14 (1952), 245-252.
2. A.K. Sushkevich, On an infinite algebra of triangular matrices, Kharkov. Gos. Univ. Uch. Zap. 34 = Zap. Mat. Otd. Fiz.-Mat. Fak. i Kharkov. Mat. Obshch. 22 (1950), 77-93 (in Russian).
3. W. Hołubowski, M. Maciaszczyk, S. Żurek, Note on Suškevič's problem on zero divisors, Comm. Algebra 45 (2017), no.8, 3274-3277.

Bartłomiej Pawlik (Silesian University of Technology, Gliwice)
Properties of Cayley graphs of Sylow subgroups of symmetric groups \(S_{2^n}\) on diagonal bases
I present the description of the polynomial (Kaloujnine) representation of Sylow subgroups of symmetric groups. Then, I discuss the selected results concerning Cayley graphs of above-mentioned groups in regards to the problem of the isomorphism of the graphs.
1. L. Kaloujnine, La structure des p-groupes de Sylow des groupes symétriques finis, Ann. Sci. Ecole Norm. Sup. 65 (1948), 239-276.
2. B. Pawlik, The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs, Algebra Discr. Math. 21 (2016), no.2, 264-281
3. B. Pawlik, The girth of Cayley graphs over Sylow 2-subgroups of the symmetric groups \(S_{2^n}\) with diagonal bases, J. Algebra Appl. 18 (2019), no.12, 1950237
4. A. Słupik, V. Sushchansky, Minimal generating sets and Cayley graphs of Sylow p-subgroups of finite symmetric groups, Algebra Discrete Math. 8 (2009), no.4, 167-184.
Hông Vân Lê (Institute of Mathematics, Czech Academy of Sciences, Prague)
The \(SL(9,\mathbb R)\)-orbit space of trivectors on \(\mathbb R^9\) and Galois cohomology
A classification of 3-vectors on \(\mathbb R^9\), understood as a description of the orbit space of the standard \(GL(9,\mathbb R)\)-action on \(\Lambda^3 \mathbb R^9\), is related to geometry defined by 3-forms in dimensions up to 9 and to the \(\theta\)-representation of the \(\mathbb Z_3\)-graded split Lie algebra \(e_{8(8)}\). In this talk I shall outline a method of classification of 3-vectors on \(\mathbb R^9\) based on Vinberg-Elashivili classification of 3-vectors on \(\mathbb C^9\) and on our joint work in progress with M. Borovoi and W. de Graaf, in which we utilize Galois cohomology to find real forms of a complex orbit.
Past talks
2020   2019   2018   2017   2016

Thanks are due to Kamil Keprt for the logo.
Created: Mon Jan 25 2016
Last modified: Fri Mar 13 13:08:27 CET 2020