## Seminars and Colloquia by Series

### Infinite-type surfaces and the omnipresent arcs by Tyrone Ghaswala

Series
Geometry Topology Seminar
Time
Monday, March 22, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Tyrone GhaswalaCIRGET, Université du Québec à Montréal

Please Note: A pre-talk will be given at 1 and office hours will be held at 3 (following the seminar talk).

In the world of finite-type surfaces, one of the key tools to studying the mapping class group is to study its action on the curve graph. The curve graph is a combinatorial object intrinsic to the surface, and its appeal lies in the fact that it is infinite-diameter and $\delta$-hyperbolic. For infinite-type surfaces, the curve graph disappointingly has diameter 2. However, all hope is not lost! In this talk I will introduce the omnipresent arc graph and we will see that for a large collection of infinite-type surfaces, the graph is infinite-diameter and $\delta$-hyperbolic. The talk will feature a new characterization of infinite-type surfaces, which provided the impetus for this project.

This is joint work with Federica Fanoni and Alan McLeay

### From little things big things grow by Tyrone Ghaswala

Series
Geometry Topology Seminar Pre-talk
Time
Monday, March 22, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Tyrone GhaswalaCIRGET, Université du Québec à Montréal

This pre-talk will be an introduction to infinite-type surfaces and big mapping class groups. I will have a prepared talk, but it will be extremely informal, and I am more than happy to take scenic diversions if the audience so desires!

### Hierarchical structure and computation of data-driven neuronal networks

Series
Mathematical Biology Seminar
Time
Friday, March 19, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Hannah ChoiGeorgia Tech

The complex connectivity structure unique to the brain network is believed to underlie its robust and efficient coding capability. Specifically, neuronal networks at multiple scales utilize their structural complexities to achieve different computational goals. I will first introduce functional implications that can be inferred from a weighted and directed “single” network representation of the brain. Then, I will consider a more detailed and realistic network representation of the brain featuring multiple types of connection between a pair of brain regions, which enables us to uncover the hierarchical structure of the brain network using an unsupervised method.  Finally, if time permits, I will discuss computational implications of the hierarchical organization of the brain network, focusing on a specific type of visual computation- predictive coding.

### Drift Analysis

Series
Combinatorics Seminar
Time
Friday, March 19, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
Speaker
Benjamin DoerrLaboratoire d&#039;Informatique (LIX), École Polytechnique

Drift analysis is the name for a collection of tools that allow to translate information about the one-step progress of a randomized process into information about first hitting times. Drift analysis is successfully used in the mathematical analysis of randomized search heuristics, most notably, evolutionary algorithms, but (for unclear reasons) much less in discrete mathematics or other areas of algorithms.

In this talk, I will give a brief introduction to drift analysis, show some classic and recent applications, and describe some open problems, both concerning drift methods and the mathematical runtime analysis of randomized search heuristics.

### The mechanics of finite-time blowup in an Euler flow

Series
CDSNS Colloquium
Time
Friday, March 19, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Dwight BarkleyU Warwick

One of the most fundamental issues in fluid dynamics is whether or not an initially smooth fluid flow can evolve over time to arrive at a singularity -- a state for which the classical equations of fluid mechanics break down and the flow field no longer makes physical sense.  While proof remains an open question, numerical evidence strongly suggests that a singularity arises at the boundary of a flow like that found in a stirred cup of tea.  The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity.  A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model generalizes Burger's equation and captures key features in the mechanics of the blowup scenario.

### Neural network and finite element functions

Series
School of Mathematics Colloquium
Time
Thursday, March 18, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Jinchao XuPennsylvania State University

Piecewise polynomials with certain global smoothness can be given by traditional finite element methods and also by neural networks with some power of ReLU as activation function. In this talk, I will present some recent results on the connections between finite element and neural network functions and comparative studies of their approximation properties and applications to numerical solution of partial differential equations of high order and/or in high dimensions.

### Equidistribution and Uniformity in Families of Curves

Series
Algebra Seminar
Time
Wednesday, March 17, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Lars KühneUniversity of Copenhagen

Please Note: This talk will be given via BlueJeans: https://bluejeans.com/531363037

In the talk, I will present an equidistribution result for families of (non-degenerate) subvarieties in a (general) family of abelian varieties. This extends a result of DeMarco and Mavraki for curves in fibered products of elliptic surfaces. Using this result, one can deduce a uniform version of the classical Bogomolov conjecture for curves embedded in their Jacobians, namely that the number of torsion points lying on them is uniformly bounded in the genus of the curve. This has been previously only known in few cases by work of David--Philippon and DeMarco--Krieger--Ye. Finally, one can obtain a rather uniform version of the Mordell-Lang conjecture as well by complementing a result of Dimitrov--Gao--Habegger: The number of rational points on a smooth algebraic curve defined over a number field can be bounded solely in terms of its genus and the Mordell-Weil rank of its Jacobian. Again, this was previously known only under additional assumptions (Stoll, Katz--Rabinoff--Zureick-Brown).

### Introduction to Knot Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, March 17, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Weizhe Shen

Knot Floer homology is an invariant for knots introduced by Ozsváth-Szabó and, independently, Rasmussen.  We will give a general introduction to the theory, sketching the definition and highlight its major properties and applications.

### Big mapping class groups and rigidity of the simple circle by Lvzhou Chen

Series
Geometry Topology Seminar
Time
Monday, March 15, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Lvzhou ChenUT Austin

Please Note: Office hours will be held 3-4 pm.

Surfaces of infinite type, such as the plane minus a Cantor set, occur naturally in dynamics. However, their mapping class groups are much less studied and understood compared to the mapping class groups of surfaces of finite type. Many fundamental questions remain open. We will discuss the mapping class group G of the plane minus a Cantor set, and show that any nontrivial G-action on the circle is semi-conjugate to its action on the so-called simple circle. Along the way, we will discuss some structural results of G to address the following questions: What are some interesting subgroups of G? Is G generated by torsion elements? This is joint work with Danny Calegari.

### Mathapalooza!

Series
Time
Sunday, March 14, 2021 - 13:00 for 4 hours (half day)
Location
https://2021.atlantasciencefestival.org/schedule/61
Speaker

Explore the light-hearted and artistic sides of math at Mathapalooza on the afternoon of Pi Day! There will be puzzles and games to amuse and challenge everyone from kids to rocket scientists. There will be mathematical music, magic (by Matt Baker), and artwork, and mathematical stories will be recounted on stage through dance, courtroom dramas, and circus acts.