Seminars and Colloquia by Series

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.

 

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.

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 Kelly – Georgia 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.  

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 Albritton – Princeton 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.

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 BORTOLI – CNRS 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

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 Sane – Georgia 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.

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 Lehmann – Georgia 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.

Mapping Class Groups of Sliced Loch Ness Monsters by Ryan Dickmann

Series
Geometry Topology Seminar
Time
Monday, August 22, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Ryan Dickmann – Georgia Tech

This talk will focus on surfaces (orientable connected 2-manifolds) with noncompact boundary. Since a general surface with noncompact boundary can be extremely complicated, we will first consider a particular class called Sliced Loch Ness Monsters. We will discuss how to show the mapping class group of any Sliced Loch Ness Monster is uniformly perfect and automatically continuous. Depending on the time remaining, we will also discuss the classification of surfaces with noncompact boundary due to Brown and Messer, and how Sliced Loch Ness Monsters are used to prove results about the mapping class groups of general surfaces.

 

 

Rank inequalities for the knot Floer homology of (1,1)-satellites

Series
Other Talks
Time
Thursday, August 18, 2022 - 09:30 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Weizhe Shen – Georgia Tech

Please Note: Oral Comprehensive Exam

One application of the immersed-curve technique, introduced by Hanselman-Rasmussen-Watson, is to study rank inequalities for Heegaard Floer homology in the presence of certain degree-one maps. Another application, discovered by Chen, is to describe the knot Floer homology of satellite knots with (1,1)-patterns. We will discuss similar rank inequalities for the knot Floer homology of (1,1)-satellites.

Trellis Decoding And Applications For Quantum Error Correction

Series
Time
Tuesday, August 2, 2022 - 09:45 for
Location
Online
Speaker
Eric Sabo – School Of Math –

Compact, graphical representations of error-correcting codes called trellises are a crucial tool in classical coding theory, establishing both theoretical properties and performance metrics for practical use. The idea was extended to quantum error-correcting codes by Ollivier and Tillich in 2005. Here, we use their foundation to establish a practical decoder able to compute the maximum-likely error for any stabilizer code over a finite field of prime dimension. We define a canonical form for the stabilizer group and use it to classify the internal structure of the graph. Similarities and differences between the classical and quantum theories are discussed throughout. Numerical results are presented which match or outperform current state-of-the-art decoding techniques. New construction techniques for large trellises are developed and practical implementations discussed. We then define a dual trellis and use algebraic graph theory to solve the maximum-likely coset problem for any stabilizer code over a finite field of prime dimension at minimum added cost.

Classical trellis theory makes occasional theoretical use of a graph product called the trellis product. We establish the relationship between the trellis product and the standard graph products and use it to provide a closed form expression for the resulting graph, allowing it to be used in practice. We explore its properties and classify all idempotents. The special structure of the trellis allows us to present a factorization procedure for the product, which is much simpler than that of the standard products. 

Finally, we turn to an algorithmic study of the trellis and explore what coding-theoretic information can be extracted assuming no other information about the code is available. In the process, we present a state-of-the-art algorithm for computing the minimum distance for any stabilizer code over a finite field of prime dimension. We also define a new weight enumerator for stabilizer codes over F_2 incorporating the phases of each stabilizer and provide a trellis-based algorithm to compute it.

--------------------------------------------------------------------------------------------------

Advisor: Dr. Evans Harrell, School of Mathematics, Georgia Institute of Technology

Committee:
Dr. Evans Harrell, School of Mathematics, Georgia Institute of Technology
Dr. Matthew Baker, School of Mathematics, Georgia Institute of Technology
Dr. Martin Short, School of Mathematics, Georgia Institute of Technology
Dr. Moinuddin Qureshi, School of Computer Science, Georgia Institute of Technology
Dr. Kenneth Brown, Pratt School of Engineering, Duke University

Reader: Dr. Kenneth Brown, Pratt School of Engineering, Duke University

Link: https://gatech.zoom.us/j/98306382257

Pages