## Seminars and Colloquia Schedule

### 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.

### Low Dimensional Topology and Cobordism Groups: Organizing spaces using algebra

Series
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.

### 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.

### 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
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