## Seminars and Colloquia Schedule

### 3-manifolds that bound no definite 4-manifold

Series
Geometry Topology Seminar
Time
Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Marco GollaUniversité de Nantes

All 3-manifolds bound 4-manifolds, and many construction of 3-manifolds automatically come with a 4-manifold bounding it. Often times these 4-manifolds have definite intersection form. Using Heegaard Floer correction terms and an analysis of short characteristic covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite 4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.

### Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE https://bluejeans.com/884917410
Speaker
Prof. Sergio BlanesUniversidad Politécnica de Valencia

We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard leapfrog/Verlet without impairing in any way the quality of the samples. They are based on a suitable modification of the   processing technique first introduced by J.C. Butcher. The idea of modified processing may also be useful for other purposes, like the construction of high-order splitting integrators with positive coefficients.

Joint work with Mari Paz Calvo, Fernando Casas, and Jesús M. Sanz-Serna

### Universal graph product structures

Series
Graph Theory Seminar
Time
Tuesday, April 20, 2021 - 17:45 for 1 hour (actually 50 minutes)
Location
Speaker
David WoodMonash University

Note the unusual time: 5:45pm.

This talk will survey recent results that describe graphs as subgraphs of products of simpler graphs. The starting point is the following theorem: every planar graph is a subgraph of the strong product of some treewidth 7 graph and a path. This result has been the key to solving several open problems, for example, regarding the queue-number and nonrepetitive chromatic number of planar graphs. The result generalises to provide a universal graph for planar graphs. In particular, if $T^7$ is the universal treewidth 7 graph (which is explicitly defined), then every countable planar graph is a subgraph of the strong product of $T^7$ and the infinite 1-way path. This result generalises in various ways for many sparse graph classes: graphs embeddable on a fixed surface, graphs excluding a fixed minor, map graphs, etc. For example, we prove that for every fixed graph $X$, there is an explicitly defined countable graph $G$ that contains every countable $X$-minor-free graph as a subgraph, and $G$ has several desirable properties such as every $n$-vertex subgraph of $G$ has a $O(\sqrt{n})$-separator. On the other hand, as a lower bound we strengthen a theorem of Pach (1981) by showing that if a countable graph $G$ contains every countable planar graph, then $G$ must contain an infinite complete graph as a minor.

### An analytical study of intermittency through Riemann’s non-differentiable functions

Series
Analysis Seminar
Time
Wednesday, April 21, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE — see abstract for the Zoom link
Speaker
Victor Vilaça Da RochaGeorgia Tech

Intermittency is a property observed in the study of turbulence. Two of the most popular ways to measure it are based on the concept of flatness, one with structure functions in the physical space and the other one with high-pass filters in the frequency space. Experimental and numerical simulations suggest that the two approaches do not always give the same results. In this talk, we prove they are not analytically equivalent. For that, we first adapt them to a rigorous mathematical language, and we test them with generalizations of Riemann’s non-differentiable function. This work is motivated by the discovery of Riemann’s non-differentiable function as a trajectory of polygonal vortex filaments.

The seminar will be held on Zoom.  Here is the link

https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09

### An Alexander method for infinite-type surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, April 21, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Roberta Shapiro

Given a surface S, the Alexander method is a combinatorial tool used to determine whether two homeomorphisms are isotopic. This statement was formalized in A Primer on Mapping Class Groups in the case that S is of finite type. We extend the Alexander method to include infinite-type surfaces, which are surfaces with infinitely generated fundamental groups.

In this talk, we will introduce a technique useful in proofs dealing with infinite-type surfaces. Then, we provide a "proof by example" of an infinite-type analogue of the Alexander method.

### A modern take on Huber regression

Series
School of Mathematics Colloquium
Time
Thursday, April 22, 2021 - 12:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Po-Ling LohUniversity of Cambridge

Note the unusual time: 12:00pm.

In the first part of the talk, we discuss the use of a penalized Huber M-estimator for high-dimensional linear regression. We explain how a fairly straightforward analysis yields high-probability error bounds that hold even when the additive errors are heavy-tailed. However, the parameter governing the shape of the Huber loss must be chosen in relation to the scale of the error distribution. We discuss how to use an adaptive technique, based on Lepski's method, to overcome the difficulties traditionally faced by applying Huber M-estimation in a context where both location and scale are unknown.

In the second part of the talk, we turn to a more complicated setting where both the covariates and responses may be heavy-tailed and/or adversarially contaminated. We show how to modify the Huber regression estimator by first applying an appropriate "filtering" procedure to the data based on the covariates. We prove that in low-dimensional settings, this filtered Huber regression estimator achieves near-optimal error rates. We further show that the commonly used least trimmed squares and least absolute deviation estimators may similarly be made robust to contaminated covariates via the same covariate filtering step. This is based on joint work with Ankit Pensia and Varun Jog.

### Learning Gaussian mixtures with algebraic structure

Series
Stochastics Seminar
Time
Thursday, April 22, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/129119189
Speaker
Victor-Emmanuel BrunelENSAE/CREST

We will consider a model of mixtures of Gaussian distributions, called Multi-Reference Alignment, which has been motivated by imaging techniques in chemistry. In that model, the centers are all related with each other by the action of a (known) group of isometries. In other words, each observation is a noisy version of an isometric transformation of some fixed vector, where the isometric transformation is taken at random from some group of isometries and is not observed. Our goal is to learn that fixed vector, whose orbit by the action of the group determines the set of centers of the mixture. First, we will discuss the asymptotic performances of the maximum-likelihood estimator, exhibiting two scenarios that yield different rates. We will then move on to a non-asymptotic, minimax approach of the problem.

### Contact structures on hyperbolic L-spaces

Series
Dissertation Defense
Time
Friday, April 23, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Hyunki MinGeorgia Tech

Ever since Eliashberg distinguished overtwisted from tight contact structures in dimension 3, there has been an ongoing project to determine which closed, oriented 3–manifolds support a tight contact structure, and on those that do, whether we can classify them. This thesis studies tight contact structures on an infinite family of hyperbolic L-spaces, which come from surgeries on the Whitehead link. We also present partial results on symplectic fillability on those manifolds.

### Normal form and existence time for the Kirchhoff equation

Series
CDSNS Colloquium
Time
Friday, April 23, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Emanuele HausUniversity of Roma Tre

In this talk I will present some recent results on the Kirchhoff equation with periodic boundary conditions, in collaboration with Pietro Baldi.

Computing the first step of quasilinear normal form, we erase from the equation all the cubic terms giving nonzero contribution to the energy estimates; thus we deduce that, for small initial data of size $\varepsilon$ in Sobolev class, the time of existence of the solution is at least of order $\varepsilon^{-4}$ (which improves the lower bound $\varepsilon^{-2}$ coming from the linear theory).

In the second step of normal form, there remain some resonant terms (which cannot be erased) that give a non-trivial contribution to the energy estimates; this could be interpreted as a sign of non-integrability of the equation. Nonetheless, we show that small initial data satisfying a suitable nonresonance condition produce solutions that exist over a time of order at least $\varepsilon^{-6}$.

### On Scalable and Fast Langevin-Dynamics-Based Sampling Algorithms

Series
Dissertation Defense
Time
Friday, April 23, 2021 - 15:00 for 1.5 hours (actually 80 minutes)
Location
ONLINE
Speaker
Ruilin LiGeorgia Institute of Technology