Seminars and Colloquia by Series

Taut foliations and Dehn surgery along positive braid knots

Series
Geometry Topology Seminar
Time
Monday, November 30, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Siddhi KrishnaGeorgia Tech

The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3--manifold Y. In particular, it predicts exactly which 3-manifolds admit a ``taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of ``positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.

https://bccte.zoom.us/j/91883463721

Meeting ID: 918 8346 3721

 

Weak saturation numbers of complete bipartite graphs

Series
Graph Theory Seminar
Time
Tuesday, November 24, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Taísa MartinsUniversidade Federal Fluminense

The notion of weak saturation was introduced by Bollobás in 1968. A graph $G$ on $n$ vertices is weakly $F$-saturated if the edges of $E(K_n) \setminus  E(G)$ can be added to $G$, one edge at a time, in such a way that every added edge creates a new copy of $F$. The minimum size of a weakly $F$-saturated graph $G$ of order $n$ is denoted by $\mathrm{wsat}(n, F)$. In this talk, we discuss the weak saturation number of complete bipartite graphs and determine $\mathrm{wsat}(n, K_{t,t})$ whenever $n > 3t-4$. For fixed $1

Frames by Operator Orbits

Series
Analysis Seminar
Time
Tuesday, November 24, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Carlos CabrelliUniversity of Buenos Aires

I will review some results on the question of when the orbits $\{ T^j g : j \in J, g \in G \}$ of a bounded operator $T$ acting on a Hilbert space $\mathcal{H}$ with $G \subset \mathcal{H}$ form a frame of $\mathcal{H}$. I will also comment on recent advances. This is motivated by the Dynamical Sampling problem that consists of recovering a time-evolving signal from its space-time samples. 

Low Dimensional Topology and Cobordism Groups: Organizing spaces using algebra

Series
Undergraduate Seminar
Time
Monday, November 23, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Bluejeans meeting https://bluejeans.com/759112674
Speaker
Dr. Miriam KuzbaryGeorgia Tech

Determining when two objects have “the same shape” is difficult; this difficulty depends on the dimension we are working in. While many of the same techniques work to study things in dimensions 5 and higher, we can better understand dimensions 1, 2, and 3 using other methods. We can think of 4-dimensional space as the “bridge” between low-dimensional behavior and high-dimensional behavior. One way to understand the possibilities in each dimension is to examine objects called cobordisms: if an (n+1)-dimensional space has an ``edge,”  then that edge is itself an n-dimensional space. We say that two n-dimensional spaces are cobordant if together they form the edge of an (n+1)-dimensional space. Using the idea of spaces related by cobordism, we can form a group. In this way, we can attempt to understand higher dimensions using clues from lower dimensions and organize this information using algebra. In this talk, I will discuss different types of cobordism groups and how to study them using tools from a broad range of mathematical areas.

Time-parallel wave propagation in heterogeneous media aided by deep learning

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 23, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/884917410
Speaker
Richard TsaiUT Austin

 

We present a deep learning framework for learning multiscale wave propagation in heterogeneous media. The framework involves the construction of linear feed-forward networks (experts) that specialize in different media groups and a nonlinear "committee" network that gives an improved approximation of wave propagation in more complicated media.  The framework is then applied to stabilize the "parareal" schemes of Lions, Maday, and Turinici, which are time-parallelization schemes for evolutionary problems. 

Prague dimension of random graphs

Series
ACO Student Seminar
Time
Friday, November 20, 2020 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Kalen PattonMath, Georgia Tech

Various notions of dimension are important throughout mathematics, and for graphs the so-called Prague dimension was introduced by Nesetril, Pultr and Rodl in the 1970s. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order $n/\log n$ for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size $O(\log n)$.

Based on joint work with He Guo and Lutz Warnke.

New Classes of Multivariate Covariance Functions

Series
Stochastics Seminar
Time
Thursday, November 19, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a
Speaker
Tatiyana ApanasovichGeorge Washington University

The class which is refereed to as the Cauchy family allows for the simultaneous modeling of the long memory dependence and correlation at short and intermediate lags. We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a Cauchy family. We present the conditions on the parameter space that result in valid models with varying degrees of complexity. Practical implementations, including reparameterizations to reflect the conditions on the parameter space will be discussed. We show results of various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Cauchy model is illustrated on a dataset from the field of Satellite Oceanography.

Link to Cisco Webex meeting: https://gatech.webex.com/gatech/j.php?MTID=mee147c52d7a4c0a5172f60998fee267a

Hodge theory for tropical varieties 2

Series
Algebra Seminar
Time
Wednesday, November 18, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Omid Amini

Please Note: Part 2 of 3-part series

The aim of these two talks is to give an overview of our work on tropical Hodge theory. We show that cohomology groups of smooth projective tropical varieties verify hard Lefschetz property and Hodge-Riemann relations. Providing a description of the Chow groups of matroids in terms of cohomology groups of specific smooth projective tropical varieties, these results can be regarded as a generalization of the work of Adiprasito-Huh-Katz to more general tropical varieties. We also prove that smooth projective tropical varieties verify the analogue in the tropical setting of the weight-monodromy conjecture, affirming a conjecture of Mikhalkin and Zharkov.

BlueJeans link: https://bluejeans.com/476849994

Grid Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 18, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Sally Collins

Grid homology is a purely combinatorial description of knot Floer homology in which the counting of psuedo-holomorphic disks is replaced with a counting of polygons in grid diagrams. This talk will provide an introduction to this theory, and is aimed at an audience with little to no experience with Heegaard Floer homology. 

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