## Seminars and Colloquia by Series

### Towards robust and efficient mean estimation

Series
Stochastics Seminar
Time
Thursday, September 16, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stas MinskerUniversity of Southern California

Several constructions of the estimators of the mean of a random variable that admit sub-Gaussian deviation guarantees and are robust to adversarial contamination under minimal assumptions have been suggested in the literature. The goal of this talk is to discuss the size of constants appearing in the bounds, both asymptotic and non-asymptotic, satisfied by the median-of-means estimator and its analogues. We will describe a permutation-invariant version of the median-of-means estimator and show that it is asymptotically efficient, unlike its “standard" version. Finally, applications and extensions of these results to robust empirical risk minimization will be discussed.

Series
Geometry Topology Student Seminar
Time
Wednesday, September 15, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hugo ZhouGeorgia Tech

How do we build a knot table? We will discuss Conway’s paper “an enumeration of knots and links” and Hoste, Thistlethwaite and Weeks’ paper “the first 1701936 knots”.

### Maximizing insight with minimal (and erroneous) information: The case of COVID-19

Series
Mathematical Biology Seminar
Time
Wednesday, September 15, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Juan B. GutiérrezUniversity of Texas at Saint Antonio

This talk presents novel approaches to old techniques to forecast COVID-19: (i) a modeling framework that takes into consideration asymptomatic carriers and government interventions, (ii) a method to rectify daily case counts reported in public databases, and (iii) a method to study socioeconomic factors and propagation of disinformation. In the case of (i), results were obtained with a comprehensive data set of hospitalizations and cases in the metropolitan area of San Antonio through collaboration with local and regional government agencies, a level of data seldom studied in a disaggregated manner. In the case of (ii), results were obtained with a simple approach to data rectification that has not been exploited in the literature, resulting in a non-autonomous system that opens avenues of mathematical exploration. In the case of (iii), this talk presents a methodology to study the effect of socioeconomic and demographic factors, including the phenomenon of disinformation and its effect in public health; currently there are few mathematical results in this important area.

### Induced subgraphs and treewidth

Series
Graph Theory Seminar
Time
Tuesday, September 14, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Sophie SpirklUniversity of Waterloo

Treewidth, introduced by Robertson and Seymour in the graph minors series, is a fundamental measure of the complexity of a graph. While their results give an answer to the question, “what minors occur in graphs of large treewidth?,” the same question for induced subgraphs is still open. I will talk about some conjectures and recent results in this area. Joint work with Tara Abrishami, Maria Chudnovsky, Cemil Dibek, Sepehr Hajebi, Pawel Rzazewski, Kristina Vuskovic.

### (Differential) primary decomposition of modules

Series
Algebra Seminar
Time
Tuesday, September 14, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin ChenICERM/Georgia Tech

Primary decomposition is an indispensable tool in commutative algebra, both theoretically and computationally in practice. While primary decomposition of ideals is ubiquitous, the case for general modules is less well-known. I will give a comprehensive exposition of primary decomposition for modules, starting with a gentle review of practical symbolic algorithms, leading up to recent developments including differential primary decomposition and numerical primary decomposition. Based on joint works with Yairon Cid-Ruiz, Marc Harkonen, Robert Krone, and Anton Leykin.

### Incorporating Symmetry for Improved Deep Dynamics Learning

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 13, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/457724603/4379
Speaker
Prof. Rose YuUCSD

While deep learning has been used for dynamics learning, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to real world. In this talk, I will demonstrate how to incorporate symmetries into deep neural networks and significantly improve the physical consistency, sample efficiency, and generalization in learning dynamics. I will showcase the applications of these models to challenging problems such as turbulence forecasting and trajectory prediction for autonomous vehicles.

### A curve graph for Artin groups

Series
Geometry Topology Seminar
Time
Monday, September 13, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Rose Morris-WrightUCLA

Please Note: Meeting URL https://bluejeans.com/770198652/3456?src=join_info Meeting ID 770 198 652 Participant Passcode 3456 Want to dial in from a phone? Dial one of the following numbers: +1.408.419.1715 (United States (San Jose)) +1.408.915.6290 (United States (San Jose)) (see all numbers - https://www.bluejeans.com/numbers) Enter the meeting ID and passcode followed by # Connecting from a room system? Dial: bjn.vc or 199.48.152.152 and enter your meeting ID & passcode

Artin groups are a generalization of braid groups, first defined by Tits in the 1960s. While specific types of Artin groups have many of the same properties as braid groups, other examples of Artin groups are still very mysterious. Braid groups are can be thought of as the mapping class groups of a punctured disc. The combinatorial and geometric structure of the mapping class group is reflected in a Gromov-hyperbolic space called the curve graph of the mapping class group. Using the curve graph of the mapping class group of a punctured disc, we can define a graph associated to a given braid group. In this talk, I will discuss how to generalize this construction to more general classes of Artin groups. I will also discuss the current known properties of this graph and further open questions about what properties of the curve graph carry over to this new graph.

### A new approach to the Fourier extension problem for the paraboloid

Series
Analysis Seminar
Time
Wednesday, September 8, 2021 - 03:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Itamar OliveiraCornell University

An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $L^{2+\frac{2}{d}}([0,1]^{d})$ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1})$ for every $\varepsilon>0$. It has been fully solved only for $d=1$ and there are many partial results in higher dimensions regarding the range of $(p,q)$ for which $L^{p}([0,1]^{d})$ is mapped to $L^{q}(\mathbb{R}^{d+1})$. In this talk, we will take an alternative route to this problem: one can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $g$  of the form $g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d})$. Time permitting, we will also address multilinear versions of the statement above and get similar results, in which we will need only one of the many functions involved in each problem to be of such kind to obtain the desired conjectured bounds, as well as almost sharp bounds in the general case. This is joint work with Camil Muscalu.

### Polynomial $\chi$-binding functions for $t$-broom-free graphs

Series
Graph Theory Seminar
Time
Tuesday, September 7, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Joshua SchroederGeorgia Institute of Technology

For any positive integer $t$, a $t$-broom is a graph obtained from $K_{1,t+1}$ by subdividing an edge once.  In this paper, we show that, for graphs $G$ without induced $t$-brooms, we have $\chi(G) = o(\omega(G)^{t+1})$, where  $\chi(G)$ and $\omega(G)$ are the chromatic number and clique number of $G$, respectively. When $t=2$, this answers a question of  Schiermeyer and Randerath. Moreover, for $t=2$, we strengthen the bound on $\chi(G)$ to $7.5\omega(G)^2$, confirming a conjecture of Sivaraman. For $t\geq 3$ and {$t$-broom, $K_{t,t}$}-free graphs, we improve the bound to $o(\omega^{t-1+\frac{2}{t+1}})$. Joint work with Xiaonan Liu, Zhiyu Wang, and Xingxing Yu.

### Long cycles in essentially 4-connected projective-planar graphs

Series
Graph Theory Seminar
Time
Tuesday, August 31, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael WigalGeorgia Institute of Technology

Tutte paths have a critical role in the study of Hamiltonicity for 4-connected planar and other graph classes. We show quantitative Tutte path results in which we bound the number of bridges of the path. A corollary of this result is near optimal circumference bounds for essentially 4-connected planar and projective-planar graphs. Joint work with Xingxing Yu.