Research Seminar in Discrete Mathematics and Algebra (DMA)
by
Johannes Carmesin,
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Organisers:  Prof Johannes Carmesin, Dr Jan Kurkofka, Prof Friedrich Martin Schneider 
Time:  Wednesdays, 14:30  16:00 
Location:  Prü1103 
Current semester:

23.10.2024 Various speakers: Open problems workshop.

30.10.2024 Will J. Turner : matroid reconstruction

6.11.2024 Olga Varghese (Düsseldorf) : Automatic continuity
Abstract: The automatic continuity problem asks the following question: Given two topological groups $L$ and $G$ and an algebraic morphism $\varphi\colon L\to G$, can we find conditions on the groups $L$ and $G$ ensuring that $\varphi$ is continuous? In this talk we will give an introduction to this problem focusing on the case where $L$ is a locally compact Hausdorff group and $G$ is a geometric group.

13.11.2024 Tim Planken : linear time algorithms in graph connectivity

20.11.2024 No seminar (public holiday)

27.11.2024 TBA

4.12.2024 Igor Balla (Brno) TBA
Abstract: TBA

15.1.2025 Joseph Devine : TBA (Attention: different time!)

22.1.2025 Paul Knappe (Hamburg) TBA
Abstract: TBA

29.1.2025 Aleksandra Kwiatkowska (Münster) : TBA
Abstract: TBA

5.2.2025 Žaneta Semanišinová (Dresden) : TBA
Abstract: TBA
Previous years
Summer Semester 2024
Organisers:  Prof Johannes Carmesin, Dr Jan Kurkofka, Prof Friedrich Martin Schneider 
Time:  Wednesdays, 11:30  12:30 
Location:  MIB1108 or MIB1113 

10.7.2024 Various speakers: Workshop on sofic graphs.

3.7.2024 Will J. Turner: Local Separators of Cayley Graphs: Proof Strategy.
Abstract: Stallings' Theorem (1971) states that a finitelygenerated group splits
over a finite subgroup if its Cayley graphs have more than one end. In
2010, Bernhard Krön gave a short proof of Stallings' Theorem using separators of graphs. In this project, we move towards a finite version
of Stallings' Theorem using local separators. We show that a
finitelygenerated group (with bounded nilpotency), having a certain
local separator in one of its Cayley graphs, is necessarily cyclic,
dihedral or decomposes as a direct product of a cycle and an involution.
In particular, we assume the existence of a dlocal cutvertex or a
dlocal 2separator, for d bounded below in terms of the group's
nilpotency. A rlocal cutvertex u in a graph is a vertex which
disconnects the subgraph induced on a ball of diameter d centred at u. A
dlocal 2separator is defined so that it works in a similarly intuitive
way.

5.6.2024 Paula Kahl: Introduction to amenability and related properties of groups.
Abstract: Introduced by Gromov in the late 1990s, the notion of a sofic group turned out to be very fruitful. Within a short period of time several longstanding grouptheoretic conjectures, such as Gottschalk's surjunctivity conjecture or Kaplansky's direct finiteness conjecture (both still open for arbitrary groups), were proved for sofic groups. This suggests to think of soficity as a strong property only few groups satisfy. However, until now, there is not a single group known to be nonsofic. Starting from the older and stronger notion of amenability, the talk provides an introduction to soficity, hyperlinearity and the Haagerup property, as well as the relations between them. In particular we are going to prove that amenability implies soficity.

22.5.2024 Will J. Turner: Local Separators of Cayley Graphs: Towards a StallingsType Theorem for
Finite Groups.
Abstract: Stallings' Theorem (1971) states that a finitelygenerated group splits
over a finite subgroup if its Cayley graphs have more than one end. In
2010, Bernhard Krön gave a short proof of Stallings' Theorem using separators of graphs. In this project, we move towards a finite version
of Stallings' Theorem using local separators. We show that a
finitelygenerated group (with bounded nilpotency), having a certain
local separator in one of its Cayley graphs, is necessarily cyclic,
dihedral or decomposes as a direct product of a cycle and an involution.
In particular, we assume the existence of a dlocal cutvertex or a
dlocal 2separator, for d bounded below in terms of the group's
nilpotency. A rlocal cutvertex u in a graph is a vertex which
disconnects the subgraph induced on a ball of diameter d centred at u. A
dlocal 2separator is defined so that it works in a similarly intuitive
way.

15.5.2024 Tim Planken: Colouring ddimensional triangulations.
Abstract: We consider ddimensional triangulations and show structural equivalences for (d+1)colourability and (d+2)colourability of the vertices of such triangulations. In particular, we show that a ddimensional triangulation admits a proper (d+1)colouring if and only if every (d2)cell is incident with an even number of (d1)cells. Moreover, a ddimensional triangulation C admits a proper (d+2)colouring if and only if there exists a triangulation C' that contains C such that for every (d2)cell in C', the number of incident (d1)cells is divisible by three.

8.5.2024 Josefin Bernhard: Automatic continuity of topological groups.
Abstract: Many concrete groups come equipped with a nontrivial compatible topology. In some natural examples of topological groups, the topology is determined already by the algebraic structure. Such situation is closely linked with the automatic continuity property: a topological group is said to have automatic continuity if every homomorphism from it into any separable topological group is continuous. In the talk, examples and applications of this phenomenon will be given and we will discuss methods of proving this property for a given group.

29.4.2024 Arkady Leiderman (BenGurion, Israel): Embedding the free topological group F(X^n) into F(X).