Fachrichtung Mathematik

Seminar Algebra, Geometrie und Kombinatorik

Ein Seminar der Institute Algebra und Geometrie.

Do, 5.2.2015, 13:15 Uhr, WIL/C133 Invariants of group actions and their connection to amenability
Martin Schneider
Do, 29.1.2015, 13:15 Uhr, WIL/C133 Surprising divisibilities in group theory
Anton Klyachko (Moscow)

Abstract: I shall talk about a general theorem which implies some amusing facts. For instance, in any group, the number of elements whose 2015th powers belong to a given subgroup is always a multiple of the order of this subgroup. The talk is based on joint results with Anna Mkrtchyan.

Do, 15.1.2015, 13:15 Uhr, WIL/C133 Groups definable in two orthogonal sorts
Marcello Mamino

Abstract: We will investigate the following question. Let (Z,R) be a first order structure with two sorts Z and R, which is simply the disjoint union of a structure Z and a structure R -- i.e. there is no function and no relation in the language connecting the two structures. Can groups definable in (Z,R) be analyzed in terms of groups definable in Z and groups definable in R separately?

 
Do, 8.1.2015, 13:15 Uhr, WIL/C133 The Loebl-Komlos-Sos conjecture
Jan Hladky (Czech Academy of Sciences, Prague)

Abstract: Many problems in extremal graph theory fit in the following framework: Does a certain density condition imposed on a host graph guarantee the existence of a given subgraph? Perhaps the most famous example in this direction is Mantel's Theorem from 1907: If a graph on n vertices contains at more than n^2/4 edges, then it must contain a triangle. I will give further examples, explain the basic concepts of extremal graphs and stability, and show the role of the celebrated Szemeredi Regularity Lemma in proving similar results.
I will then report on joint progress with Janos Komlos, Diana Piguet, Miklos Simonovits, Maya Stein, Endre Szemeredi on the Loebl-Komlos-Sos conjecture, an extremal problem about containment of trees, which has been open for two decades.

Do, 11.12.2014, 13:15 Uhr, WIL/C133 PAC learning of FO definable concepts & nowhere dense graph classes
Isolde Adler

Abstract: In machine learning, the problem of "concept learning" is to identify an unknown set from a given concept class (i.e. a collection of sets). In the model of "probably approximately correct" (PAC) learning, the learner receives a number of samples and must be able to identify the unknown set approximately, in a probabilistic sense. It is well-known the the sample size for PAC learning is characterised by the Vapnik-Cervonenkis (VC) dimension of the concept class. We are interested in the VC dimension of concept classes that are definable in some logic on graph classes.
In 2004, Grohe and Turán showed that for any subgraph closed class C, monadic second-order definable concept classes have bounded VC dimension on C if and only if C has bounded tree-width. We show that for any subgraph closed class C, first-order definable concept classes have bounded VC dimension on C if and only if C is nowhere dense.

Do, 4.12.2014, 13:15 Uhr, WIL/C133 Diese Woche kein Seminar
Es findet der Geometrietag 2014 statt
Do, 27.11.2014, 13:15 Uhr, WIL/C133 Diese Woche kein Seminar
Do, 20.11.2014, 13:15 Uhr, WIL/C133 Der Product Replacement Algorithmus auf der symmetrischen Gruppe
Jan-Christoph Schlage-Puchta (U Rostock)

Der Product Replacement Algorithmus ist ein Standardverfahren zum Finden zufälliger Elemente in einer endlichen Gruppe G. Hierbei wird auf der Menge der erzeugenden k-Tupel von G eine Irrfahrt gestartet, und am Ende ein Element dieses Tupels ausgegeben. In der Praxis hat sich dieser Algorithmus gut bewährt, eine theoretische Analyse ist in den meisten Fällen jedoch nicht möglich. In diesem Vortrag werde ich für die symmetrische Gruppe S_n zeigen, dass der Graph auf dem die Irrfahrt abläuft einerseits für kleinere k zusammenhängend ist, als man bisher wusste, andererseits der Zusammenhang numerisch schwerer nachweisbar ist, als man zunächst dachte.

Do,13.11.2014, 13:15 Uhr, WIL/C133 Metric ultraproducts of finite simple groups
John Wilson (U Oxford)

Abstract: Metric ultraproducts of structures have arisen in a variety of contexts. The study of the case when the structures are finite groups is recent and motivated partly by the connection with sofic groups. We report on current joint work with Andreas Thom on the topological and algebraic properties of metric ultraproducts of finite simple groups.

Do, 6.11.2014, 13:15 Uhr, WIL/C133 Convex sets with semi-definite representations
Tim Netzer (Dresden)
Do, 30.10.2014, 13:15 Uhr, WIL/C133 Banach-Mazur games on categories
Wieslav Kubis (U Prag)

Abstract: We shall discuss a natural game played on a category with amalgamations, in the spirit of the classical Banach-Mazur game. Among´ applications, we obtain new characterizations of various ``generic" objects, including Fraisse limits, as well as a new tool for detecting generic structures in continuous model theory.

Do, 23.10.2014, 13:15 Uhr, WIL/C133 Sofic groups and applications
Andreas Thom
Do, 16.10.2014, 13:15 Uhr, WIL/C133 Ramsey Theory and Topological Dynamics
Manuel Bodirsky