Seminars and Colloquia by Series

Symplectic Fillings of Contact Structures

Series
Geometry Topology Student Seminar
Time
Wednesday, September 2, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Agniva RoyGeorgia Tech

Finding fillings of contact structures is a question that has been studied extensively over the last few decades. In this talk I will discuss some motivations for studying this question, and then visit a few ideas involved in the earliest results, due to Eliashberg and McDuff, that paved the way for a lot of current research in this direction.

Saturation problems in Ramsey theory, ordered sets and geometry

Series
Graph Theory Seminar
Time
Tuesday, September 1, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/681348075/????. (replace ???? with password) For password, please email Anton Bernshteyn (bahtoh~at~gatech.edu)
Speaker
Zhiyu WangGeorgia Tech

A graph G is F-saturated if G is F-free and G+e is not F-free for any edge not in G. The saturation number of F, is the minimum number of edges in an n-vertex F-saturated graph. We consider analogues of this problem in other settings.  In particular we prove saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets. We also consider semisaturation problems, wherein we only require that any extension of the combinatorial structure creates new copies of the forbidden configuration.  In this setting, we prove a semisaturation version of the Erdös-Szekeres theorem on convex k-gons, as well as multiple semisaturation theorems for sequences and posets. Joint work with Gábor Damásdi, Balázs Keszegh, David Malec, Casey Tompkins, and Oscar Zamora.

Integral neural networks with weight penalization

Series
Analysis Seminar
Time
Tuesday, September 1, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87104893132
Speaker
Armenak PetrosyanGeorgia Tech

Artificial neural networks have gained widespread adoption as a powerful tool for various machine learning tasks in recent years. Training a neural network to approximate a target function involves solving an inherently non-convex problem. In practice, this is done using stochastic gradient descent with random initialization. For the approximation problem with neural networks error rate guarantees are established for different classes of functions however these rates are not always achieved in practice due to many  local minima of the resulting optimization problem. 

The challenge we address in this work is the following. We want to find small size shallow neural networks that can be trained algorithmically and which achieve guaranteed approximation speed and precision. To maintain the small size we apply penalties on the weights of the network. We show that under minimal requirements, all local minima of the resulting problem are well behaved and possess a desirable small size without sacrificing precision. We adopt the integral neural network framework and use techniques from optimization theory and harmonic analysis to prove our results. In this talk, we will discuss our existing work and possible future promising areas of interest where this approach can potentially be adopted. 

Mathematics, Lots of Data, and Uncertainty

Series
Undergraduate Seminar
Time
Monday, August 31, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Devilered live remotely via Bluejeans https://bluejeans.com/759112674
Speaker
Dr. Michael LaceyGeorgia Tech

Please Note: Join us live via Bluejeans https://bluejeans.com/759112674 for this talk.

Mathematics can help all of us sort through some complicated scenarios, with changing inputs, and changing conclusions.  I will illustrate this with some examples.  Porker hands and Jury selection bias:  Expert testimony that I gave in a death penalty case.  Specificity of testing:  A random person tests positive for COVID.  Do they have the disease?  Designing pooled testing for the disease.  When is it effective?

Triple linking and Heegaard Floer homology.

Series
Geometry Topology Seminar
Time
Monday, August 31, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Allison MooreVirginia Commonwealth University

We will describe several appearances of Milnor’s invariants in the link Floer complex. This will include a formula that expresses the Milnor triple linking number in terms of the h-function. We will also show that the triple linking number is involved in a structural property of the d-invariants of surgery on certain algebraically split links. We will apply the above properties toward new detection results for the Borromean and Whitehead links. This is joint work with Gorsky, Lidman and Liu.

Exponentially Many Hypergraph Colourings

Series
Combinatorics Seminar
Time
Friday, August 28, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/???? (Replace ???? with the password sent via email)
Speaker
Lutz WarnkeGeorgia Institute of Technology

We shall discuss a recent paper of Wanless and Wood (arXiv:2008.00775), which proves a Lovász Local Lemma type result using inductive counting arguments.
For example, in the context of hypergraph colorings, under LLL-type assumptions their result typically gives exponentially many colorings (usually more than the textbook proof of LLL would give).
We will present a probabilistic proof of the Wanless-Wood result, and discuss some applications to k-SAT, Ramsey number lower bounds, and traversals, as time permits.

The Alexander method and recognizing maps

Series
Geometry Topology Student Seminar
Time
Wednesday, August 26, 2020 - 14:30 for 30 minutes
Location
Online
Speaker
Roberta ShapiroGeorgia Tech

 How can we recognize a map given certain combinatorial data? The Alexander method gives us the answer for self-homeomorphisms of finite-type surfaces. We can determine a homeomorphism of a surface (up to isotopy) based on how it acts on a finite number of curves. However, is there a way to apply this concept to recognize maps on other spaces? The answer is yes for a special class of maps, post-critically finite quadratic polynomials on the complex plane (Belk-Lanier-Margalit-Winarski). 

            In this talk, we will discuss Belk-Lanier-Margalit-Winarski’s methods, as well zome difficulties we face when trying to extend their methods to other settings.

Using and Understanding Torsion in Big Mapping Class Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, August 26, 2020 - 14:00 for 30 minutes
Location
Speaker
Santana AftonGeorgia Tech

An infinite-type surface is a surface whose fundamental group is not finitely generated. These surfaces are “big,” having either infinite genus or infinitely many punctures. Recently, it was shown that mapping class groups of these infinite-type surfaces have a wealth of subgroups; for example, there are infinitely many surfaces whose mapping class group contains every countable group as a subgroup. By extending a theorem for finite-type surfaces to the infinite-type case — the Nielsen realization problem — we give topological obstructions to continuous embeddings of topological groups, with a few interesting examples.

Distributed algorithms and infinite graphs

Series
Graph Theory Seminar
Time
Tuesday, August 25, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/954562826
Speaker
Anton BernshteynGeorgia Tech

In the last twenty or so years, a rich theory has emerged concerning combinatorial problems on infinite graphs endowed with extra structure, such as a topology or a measure. It turns out that there is a close relationship between this theory and distributed computing, i.e., the area of computer science concerned with problems that can be solved efficiently by a decentralized network of processors. In this talk I will outline this relationship and present a number of applications.
 

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