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Special Colloquium Lecture: Zarankiewicz, VC-dimension, and incidence geometry

Title: Zarankiewicz, VC-dimension, and incidence geometry

Speaker: Dr. Cosmin Pohoata, Yale University
For your reference, here is Dr. Pohoata’s website: https://pohoatza.wordpress.com/

Time: Jan 28, 2022 04:00 PM Central Time (US and Canada)

Abstract:  The Zarankiewicz problem is a central problem in extremal graph theory, which lies at the intersection of several areas of mathematics. It asks for the maximum number of edges $\operatorname{ex}(n,K_{s,t})$ in a bipartite graph on $2n$ vertices, where each side of the bipartition contains $n$ vertices, and which does not contain the complete bipartite graph $K_{s,t}$ as a subgraph. One of the reasons this problem is particularly interesting is that, for various (rather mysterious) reasons, the extremal graphs seem to have to be of algebraic nature, which is not always the case for Tur\’an-type problems. The most tantalizing case is by far the symmetric problem where $s=t:=k$, for which the value of $\operatorname{ex}(n,K_{k,k})$ is completely unknown for most values of $k$. In this talk, we will discuss a rather surprising new phenomenon related to an important variant of this problem, which is the analogous question in bipartite graphs with VC-dimension at most $d$, where $d$ is a fixed integer such that $k \geq d \geq 2$. We will also present a few consequences of our result in incidence geometry, which improve upon classical results. Based on joint work with Oliver Janzer (ETH).

Location: Join Zoom Meeting
https://memphis.zoom.us/j/87547314942?pwd=aWFsbVpHZGg1ZjJVMVFFNmo5ZTg4QT09

Meeting ID: 875 4731 4942
Passcode: 220994

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Special Colloquium Lecture: Splitting quasi-transitive infinite graphs

Title: Splitting quasi-transitive infinite graphs

Speaker: Dr. Matthias Hamann, University of Warwick
For you reference, attached is the CV of Dr. De Boeck, and the following is a link to his webpage.
www.math.uni-hamburg.de/home/hamann/

Time: Jan 27, 2022 01:00 PM Central Time (US and Canada)

Location: see the link below.

Abstract: We will look at multi-ended quasi-transitive graphs and obtain results for them that are generalisations of major theorems from geometric group theory such as Stallings’ splitting theorem of multi-ended groups or
Dunwoody’s accessibility theorem of finitely presented groups.

The central notion that we will use is due to Mohar: tree amalgamations. Starting with two quasi-transitive graphs, it allows us to construct a new quasi-transitive graph. We will consider the question whether the reverse also holds, i.e. whether every multi-ended quasi-transitive graph is a tree amalgamation of two other quasi-transitive graphs. To
answer this, we will use canonical tree-decompositions and their recently obtained theory and we will see how tree amalgamations and tree-decompositions relate to each other.

Location: Join Zoom Meeting
https://memphis.zoom.us/j/82607051522?pwd=RzBGbkQ4b1VjUHdmR2RYTG9kWE1vQT09
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Special Colloquium Lecture: Neumaier graphs

Title: Neumaier graphs

Speaker: Dr. Maarten De Boeck, University of Rijeka

Time: Jan 26, 2022 01:00 PM Central Time (US and Canada)

Abstract:  This is joint work with A. Abiad, W. Castryck, J. Koolen and S. Zeijlemaker.

A Neumaier graph is an edge-regular graph with a regular clique. A lot of strongly regular graphs (but clearly not all of them) are indeed Neumaier, but in [3] it was asked whether there are Neumaier graphs that are not strongly regular. This question was only solved recently (see [2]), so now we know there are so-called strictly Neumaier graphs. In this talk I will discuss several new results on (strictly) Neumaier graphs, including (non)-existence results. I will focus on a new construction producing an infinite number of strictly Neumaier graphs, described in [1]. The proofs rely on several results from number theory. I will also discuss a few directions for future research about Neumaier graphs.

References

[1] A. Abiad and W. Castryck and M. De Boeck and J.H. Koolen and S. Zeijlemaker, An infinite class of Neumaier graphs and non-existence results, arXiv:2109.14281 (2021), 22 pp.
[2] G.R. Greaves and J.H. Koolen, Edge-regular graphs with regular cliques, European J. Combin. 71(2018), 194–201.
[3] A. Neumaier, Regular cliques in graphs and special 1 1/2-designs, Finite Geometries and Designs, London Math. Soc. Lecture Note Series vol. 49 (1981), 244–25

Location: Join Zoom Meeting
https://memphis.zoom.us/j/86824870127?pwd=OHU3RTFWUUozR21mTVJ3OWllSnpVQT09
Meeting ID: 868 2487 0127
Passcode: 561211
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Special Colloquium Lecture: H-percolation

Title: H-percolation

Speaker: Bret Kolesnik , UCSD,
For your reference, here is Dr. Kolesnik’s website: https://mathweb.ucsd.edu/~bkolesnik/

Abstract: A graph G is said to H-percolate if all missing edges can be added eventually by iteratively completing copies of H minus an edge. This process was introduced by Bollobás (1967) and studied more recently by Balogh, Bollobás and Morris (2012) in the case that G is the Erdős–Rényi graph G(n,p). In this talk, we will discuss our recent work with Zsolt Bartha, which locates the critical percolation threshold p_c for all “reasonably balanced” graphs H.

Time: Jan 21, 2022 05:00 PM Central Time (US and Canada)

Join Zoom Meeting: https://memphis.zoom.us/j/89379811191?pwd=SDBQS3pnSUVTMmFmcEN1Z2NsNXJPQT09

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The Dirichlet Problem

Speaker 

Professor Wolfgang Arendt, University of Ulm, Germany

Abstract

The Dirichlet problem has a long history: Dirchlet tried to solve it by variational methods, Perron found an ingenious weak solution, Wiener obtained a characterization of well posedness in terms of his famous capacity condition, Stampacchia – in the light of the Di Giorgi-Nash result – investigated the Dirichlet problem for general elliptic operators.

We will tell the story of this fascinating problem explaining also some very new results in cases where the maximum principle does not hold. We also explain how the solution of the Dirichlet problem can be used to solve a parabolic problem via semigroup theory.

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Problems and Recent Methods in Operator Theory 2015

PLENARY SPEAKERS:

Aim & Scope:

This workshop gathered a group of leading researchers in Operator Theory, early career mathematicians and graduate students. There were six plenary lectures and a poster session with 12 participants. The lectures, posters and informal periods for discussion fostered ties for further collaboration and possibly promoted an active mathematical network.

Contact Info: Please send an Email

Organizer: Fernanda Botelho

This workshop is in Cooperation with the Association for Women in Mathematics (AWM) and supports their Non-Discrimination Statement. This workshop is also in collaboration with the Center for Research and Innovation in STEM Teaching and Learning (CRISTAL). This workshop is funded by The National Science Foundation Award DMS-1546799. This workshop is also sponsored by Pearson, The University of Memphis – College of Arts and Sciences, and the Office of the Provost.