## Seminars and Colloquia Schedule

### Weights and Automorphisms of Cyclic Subspace Codes.

Series
Algebra Seminar
Time
Monday, August 29, 2022 - 13:30 for 1 hour (actually 50 minutes)
Location
Clough 125 classroom
Speaker
Hunter LehmannGeorgia Institute of Technology

Cyclic orbit codes are subspace codes generated by the action of the Singer subgroup F_{q^n}^* on an F_q-subspace U of F_{q^n}. The weight distribution of a code is the vector whose ith entry is the number of codewords with distance i to a fixed reference generator of the code. We will investigate the weight distribution for a few categories of cyclic orbit codes, including optimal codes. Further, we want to know when two cyclic orbit codes with the same weight distribution are isometric. To answer this question, we determine the possible automorphism groups for cyclic orbit codes.

### Combinatorial Surgery Graphs on Unicellular Maps by Abdoul Karim Sane

Series
Geometry Topology Seminar
Time
Monday, August 29, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Abdoul Karim SaneGeorgia Tech

A map (respectively, a unicellular map) on a genus g surface Sg is the Homeo+(Sg)-orbit of a graph G embedded on Sg such that Sg-G is a collection of finitely many disks (respectively, a single disk). The study of maps was initiated by W. Tutte, who was interested in counting the number of planar maps. However, we will consider maps from a more graph theoretic perspective in this talk. We will introduce a topological operation called surgery, which turns one unicellular map into another. Then, we will address natural questions (such as connectedness and diameter) about surgery graphs on unicellular maps, which are graphs whose vertices are unicellular maps and where two vertices share an edge if they are related by a single surgery. We will see that these problems translate to a well-known combinatorial problem: the card shuffling problem.

### Convergence of denoising diffusion models

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 29, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Valentin DE BORTOLICNRS and ENS Ulm
Generative modeling is the task of drawing new samples from an underlying distribution known only via an empirical measure. There exists a myriad of models to tackle this problem with applications in image and speech processing, medical imaging, forecasting and protein modeling to cite a few.  Among these methods score-based generative models (or diffusion models) are a  new powerful class of generative models that exhibit remarkable empirical performance. They consist of a noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a denoising'' process defined by approximating the time-reversal of the diffusion.

In this talk I will present some of their theoretical guarantees with an emphasis on their behavior under the so-called manifold hypothesis. Such theoretical guarantees are non-vacuous and provide insight on the empirical behavior of these models. I will show how these results imply generalization bounds on denoising diffusion models. This presentation is based on https://arxiv.org/abs/2208.05314

### Non-uniqueness of Leray solutions of the forced Navier-Stokes equations

Series
PDE Seminar
Time
Tuesday, August 30, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Dallas AlbrittonPrinceton University

In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative, within the `forced' category, by exhibiting two distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo.

### Thresholds for Latin squares and Steiner triple systems

Series
Graph Theory Seminar
Time
Tuesday, August 30, 2022 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tom KellyGeorgia Tech

An order-n Latin square is an $n \times n$ matrix with entries from a set of $n$ symbols, such that each row and each column contains each symbol exactly once.  Suppose that $L_{i,j} \subseteq [n]$ is a random subset of $[n]$ where each $k \in [n]$ is included in $L_{i,j}$ independently with probability $p$ for each $i,j\in[n]$.  How likely does there exist an order-$n$ Latin square where the entry in the $i$th row and $j$th column lies in $L_{i,j}$?  This question was initially raised by Johansson in 2006, and later Casselgren and H{\"a}ggkvist and independently Luria and Simkin conjectured that $\log n / n$ is the threshold for this property.  In joint work with Dong-yeap Kang, Daniela K\"{u}hn, Abhishek Methuku, and Deryk Osthus, we proved that for some absolute constant $C$, if $p > C \log^2 n / n$, then asymptotically almost surely there exists such a Latin square.  We also prove analogous results for Steiner triple systems and $1$-factorizations of complete graphs.

### Dynamics is our best shot!

Series
Time
Friday, September 2, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Christopher Jones UNC-CH, GMU
https://gatech.zoom.us/j/95197085752?pwd=WmtJUVdvM1l6aUJBbHNJWTVKcVdmdz09

Two of the aims in using mathematics in real world applications are: (1) understanding the mechanisms responsible for different effects and phenomena, and (2) predicting the future state of the system under study. Dynamical systems provides a perspective and a lens for addressing these two questions. The system under study is formulated as an evolving set of state variables and the set of trajectories with different initializations are viewed geometrically.

I will use this lens to look at a pressing problem in climate science: how a climate subsystem might abruptly “tip” from its current state into a completely different state. This is a problem that requires dynamical systems to understand, and I will show how we can decode different ways in which the tipping might happen.

Dynamical systems models tend to be simplified; extraneous forces are ignored to produce models which attempt to capture the key mechanisms. The inclusion of data from observations is a way to connect these models with reality and I will discuss the area of data assimilation that achieves a balance between data and physical models in a systematic way.

### Concept Portfolios: project-based assessment for more equitable course design

Series
Other Talks
Time
Friday, September 2, 2022 - 13:00 for
Location
Skiles 005
Speaker
Claire Gibbons & Emerald T. Stacy

Beginning in Spring 2020, we stepped away from traditional exams and collaboratively developed the concept portfolio assessment with the aim of creating a more equitable learning experience for students. Since then, we have implemented this model of assessment in courses from Pre-Calculus through Number Theory as faculty at a community college and a small liberal arts college. For the concept portfolio, students choose a subset of the topics covered in the course and synthesize the topics by providing a summary and annotated examples. The portfolio is completed iteratively where students submit rough drafts and engage in peer review. During this talk, we will share our motivation to design an equitable alternative to exams, compare and contrast our implementations of the concept portfolio assessment, and discuss student feedback.

__________________

The talk is delivered in a hybrid format Everyone is welcome to join via zoom
https://gatech.zoom.us/j/94287395719?pwd=U216WTlIZHdMNVErZlFWUGlleDBiQT09
but we have also reserved 005 to attend the talk all together, hoping discussion will be easier.

### Bandit Algorithms for Prophet Inequality and Pandora's Box

Series
ACO Student Seminar
Time
Friday, September 2, 2022 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 368
Speaker
Yifan WangGeorgia Tech CS

The Prophet Inequality and Pandora's Box problems are fundamental stochastic problems. A usual assumption for both problems is that the probability distributions of the n underlying random variables are given as input to the algorithm. In this talk, we assume the distributions are unknown, and study them in the Multi-Armed Bandits model: We interact with the unknown distributions over T rounds. In each round we play a policy and receive only bandit feedback. The goal is to minimize the regret, which is the difference in the total value of the optimal algorithm that knows the distributions vs. the total value of our algorithm that learns the distributions from the bandit feedback. Our main results give near-optimal  O(poly(n)sqrt{T}) total regret algorithms for both Prophet Inequality and Pandora's Box.

### Exponential mixing by shear flows

Series
CDSNS Colloquium
Time
Friday, September 2, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006; Zoom streaming available
Speaker
Bill CoopermanUniversity of Chicago

Given a divergence-free vector field on the torus, we consider the mixing properties of the associated flow. There is a rich body of work studying the dependence of the mixing scale on various norms of the vector field. We will discuss some interesting examples of vector fields that mix at the optimal rate, and an improved bound on the mixing scale under the extra assumption that the vector field is a shear at each time.