## Seminars and Colloquia by Series

### Tautological Bundles of Matroids

Series
Algebra Seminar
Time
Wednesday, March 3, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Chris EurStanford University

Matroid theory has seen fruitful developments arising from different algebro-geometric approaches, such as the K-theory of Grassmannians and Chow rings of wonderful compactifications. However, these developments have remained somewhat disjoint. We introduce "tautological bundles of matroids" as a new geometric framework for studying matroids. We show that it unifies, recovers, and extends much of these recent developments including log-concavity statements, as well as answering some open conjectures. This is an on-going work with Andrew Berget, Hunter Spink, and Dennis Tseng.

### Snowflake Conjectures for Mapping Class Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, March 3, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Santana Afton

The algebraic structure of mapping class groups is deep and beautiful; in this talk, we'll explore some curious conjectures and definite theorems about the structure and quality of different subgroups of the mapping class group.

### Induced Ramsey numbers for a star versus a fixed graph

Series
Graph Theory Seminar
Time
Tuesday, March 2, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Maria AxenovichKarlsruhe Institute of Technology

We write $F \rightarrow (H,G)$ for graphs $F$, $G$, and $H$, if for any coloring of the edges of $F$ in red and blue, there is either a red induced copy of $H$ or a blue induced copy of $G$. For graphs $G$ and $H$, let the induced Ramsey number $IR(H,G)$ be the smallest number of vertices in a graph $F$ such that $F \rightarrow (H,G)$. Deuber showed in 1975 that $IR(H,G)$ is well-defined for any graphs $H$ and $G$. Still, the determination of $IR(H,G)$ remains a challenge for most graphs. A striking contrast between induced and non-induced Ramsey numbers was demonstrated by Fox and Sudakov in 2008 by showing that $IR(H,G)$ is superlinear in $n$ when $H$ is a matching on $n$ edges and $G$ is a star on $n$ edges.

In this talk, I will address the case when $G= K_{1,n}$, a star on $n$ edges, for large $n$, and $H$ is a fixed graph. We prove that $$(\chi(H)-1) n \leq IR(H, K_{1,n}) \leq (\chi(H)-1)^2n + \epsilon n,$$ for any $\epsilon>0$, sufficiently large $n$, and $\chi(H)$ denoting the chromatic number of $H$. The lower bound is asymptotically tight for any fixed bipartite $H$. The upper bound is attained up to a constant factor, for example when $H$ is a clique.

This is a joint work with Izolda Gorgol.

### Single Particle Tracking with Applications to Lysosome Transport

Series
Mathematical Biology Seminar
Time
Friday, February 26, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Keisha CookTulane University

Live cell imaging and single particle tracking techniques have become increasingly popular amongst the mathematical biology community. We study endocytosis, the cellular internalization and transport of bioparticles. This transport is carried out in membrane-bound vesicles through the use of motor proteins. Lysosomes, known for endocytosis, phagocytic destruction, and autophagy, move about the cell along microtubules. Single particle tracking methods utilize stochastic models to simulate intracellular transport and give rise to rigorous analysis of the resulting properties, specifically related to transitioning between inactive to active states. This confidence in the stochastic modeling of particle tracking is useful not only for particle-containing lysosomes, but also broad questions of cellular transport studied with single particle tracking.

### The extremal number of surfaces

Series
Combinatorics Seminar
Time
Friday, February 26, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
Speaker
Andrey KupavskiiCNRS and MIPT (Grenoble and Moscow)

In 1973, Brown, Erdős and Sós proved that if H is a 3-uniform hypergraph on n vertices which contains no triangulation of the sphere, then H has at most O(n^{5/2}) edges, and this bound is the best possible up to a constant factor. Resolving a conjecture of Linial, also reiterated by Keevash, Long, Narayanan, and Scott, we show that the same result holds for triangulations of the torus. Furthermore, we extend our result to every closed orientable surface S.

Joint work with Alexandr Polyanskii, István Tomon and Dmitriy Zakharov, see https://arxiv.org/abs/2010.07191

### Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds

Series
CDSNS Colloquium
Time
Friday, February 26, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Jorge GonzalezGeorgia Tech

We will discuss a new method for proving the existence of diffusion in some systems with Normally Hyperbolic Invariant Manifolds (NHIM). We apply this approach to the generalized standard map to show the existence of drift orbits for an explicit range of actions.  The method consists of verifying a finite number of conditions on a computer (keywords: NHIM, shadowing, scattering map, Chirikov Standard model, Parameterization Method, Interval Newton Method).

### Another interpretation of tropical rank.

Series
Student Algebraic Geometry Seminar
Time
Friday, February 26, 2021 - 09:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Tianyi ZhangGeorgia Tech

Tropical rank is defined in terms of determinant in the literature. I will introduce a rank in terms of linear dependence and show it equals the tropical rank. This fact is nontrivial because we do not have row reduction which is a key tool to prove the equality for matrices over fields. This talk is based on the paper "the tropical rank of a tropical matrix" written by Z. Izhakian.

### Large Values of the Riemann Zeta Function in Small Intervals

Series
Stochastics Seminar
Time
Thursday, February 25, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Louis-Pierre ArguinBaruch College, CUNY

I will give an account of the recent progress in probability and in number theory to understand the large values of the zeta function in small intervals of the critical line. This problem has interesting connections with the extreme value statistics of IID and log-correlated random variables.

### Impossibility results in ergodic theory and smooth dynamical systems

Series
School of Mathematics Colloquium
Time
Thursday, February 25, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Matthew ForemanUniversity of California, Irvine

The talk considers the equivalence relations of topological conjugacy and measure isomorphism on diffeomorphisms of compact manifolds of small dimension. It is shown that neither is a Borel equivalence relation.  As a consequence, there is no inherently countable method that,  for general diffeomorphisms $S$ and $T$, determines whether $S\sim T$. It is also shown that the Time Forward/Time Backward problem for diffeomorphisms of the 2-torus  encodes most mathematical questions, such as the Riemann Hypothesis.

This work is joint with B Weiss and A Gorodetski.

### Uniform Asymptotic Growth of Symbolic Powers of Ideals

Series
Algebra Seminar
Time
Wednesday, February 24, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker