Seminars and Colloquia by Series

Dependent random choice, statistical physics, and the local rank of tensors

Series
Other Talks
Time
Friday, November 15, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel ZhuPrinceton

We present a lemma, inspired by dependent random choice and sampling procedures from statistical physics, for finding dense structure in arbitrary $d$-partite $d$-uniform hypergraphs. We will then discuss how this lemma leads to the concept of local rank, a notion of tensor rank which is instrumental in proving a "structure vs. randomness" result for tensors (and by extension, polynomials): namely, a relation between the partition and analytic ranks of tensors over finite fields. This is joint work with Guy Moshkovitz.

Intersections of balls and a no-dimensional Tverberg theorem

Series
Other Talks
Time
Monday, March 11, 2024 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander PolyanskiiEmory University

The aim of my talk is to discuss the following result, its variations and its connections with a no-dimensional Tverberg theorem. For any n red and n blue points in the Euclidean d-space, there exists a perfect red-blue matching M such that the balls whose diameters are edges of M share a common point.

(Joint works with O. Pirahmad, A. Vasilevskii, and P. Barabanshchikova.)

Appearance of multistability and hydra effect in a discrete-time epidemic model

Series
Other Talks
Time
Friday, August 18, 2023 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lauren ChildsVirginia Tech

Please Note: This seminar will be delivered in a hybrid Zoom format. The in-person version is held in Skiles 005 while the Zoom version is held at this link: https://gatech.zoom.us/j/99424341824

One-dimensional discrete-time population models, such as Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Incorporating epidemiological interactions through the addition of an infectious class causes an interesting complexity of new behaviors. Here, we examine a two-dimensional susceptible-infectious (SI) model with underlying Ricker population growth. In particular, the system with infection has a distinct bifurcation structure from the disease-free system. We use numerical bifurcation analysis to determine the influence of infection on the types and appearance of qualitatively distinct long-time dynamics. We find that disease-induced mortality leads to the appearance of multistability, such as stable four-cycles and chaos dependent upon the initial condition. Furthermore, previous work showed that infection that alters the ability to reproduce can lead to unexpected increases in total population size. A similar phenomenon is seen in some models where an increase in population size with a decreased growth rate occurs, known as the ‘hydra effect.’ Thus, we examine the appearance and extent of the hydra effect, particularly when infection is introduced during cyclic or chaotic population dynamics.

Dynamics of excitable cells: neurons and cardiomyocytes

Series
Other Talks
Time
Wednesday, May 10, 2023 - 11:00 for 1 hour (actually 50 minutes)
Location
PLOS (second floor of Howey)
Speaker
Roberto BarrioUniv. of Zaragoza
In recent years, much attention has been paid to the description of excitable media,
such as the dynamics of the brain and heart.
In both cases, the building blocks are excitable cells, neurons, and cardiomyocytes,
and a detailed look at the mathematics behind some of their mathematical models provides
a good starting point for answering some observed phenomena.
In this talk we show how some apparently  simple phenomena,
such as the spike-adding process,
have important consequences in the models and how various elements intervene behind their formation,
such as homoclinic bifurcations, fast-slow decompositions, "canards",
the completion of the Smale topological template, the formation of Morse surfaces
creating geometric bifurcations, etc.
Finally, we will illustrate its relevance in insect gait patterns and in the formation of cardiac arrhythmias.
 

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.

 

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 ShenGeorgia 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.

Symmetric Tropical Rank 2 Matrix Completion

Series
Other Talks
Time
Monday, May 23, 2022 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
May Cai

An important recent topic is matrix completion, which is trying to recover a matrix from a small set of observed entries, subject to particular requirements. In this talk, we discuss results on symmetric tropical and symmetric Kapranov rank 2 matrices, and establish a technique of examining the phylogenetic tree structure obtained from the tropical convex hulls of their columns to construct the algebraic matroid of symmetric tropical rank 2 $n \times n$ matrices. This matroid directly answers the question of what entries of a symmetric $n \times n$ matrix needs to be specified generically to be completable to a symmetric tropical rank 2 matrix, as well as to a symmetric classical rank 2 matrix.

This is based on joint work with Cvetelina Hill and Kisun Lee.

Rigidity percolation in a random tensegrity via analytic graph theory

Series
Other Talks
Time
Tuesday, April 19, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Zeb RocklinGT Physics

Tensegrities are mechanical structures that include cable-like elements that are strong and lightweight relative to rigid rods yet support only extensile stress. From suspension bridges to the musculoskeletal system to individual biological cells, humanity makes excellent use of tensegrities, yet the sharply nonlinear response of cables presents serious challenges to analytical theory. Here we consider large tensegrity structures with randomly placed cables (and struts) overlaid on a regular rigid backbone whose corresponding system of inequalities is reduced via analytic theory to an exact graph theory. We identify a novel coordination number that controls two rigidity percolation transitions: one in which global interactions between cables first support external loads and one in which the structure becomes fully rigid.  We show that even the addition of a few cables strongly modifies conventional rigidity percolation, both by modifying the sharpness of the transition and by introducing avalanche effects in which a single constraint can eliminate multiple floppy modes. 

Also ONLINE: https://gatech.zoom.us/j/99313032175

 

Mathematics in Motion

Series
Other Talks
Time
Sunday, March 13, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Drew Charter School, 300 Eva Davis Way SE, Atlanta 30317
Speaker
Evans Harrell, Dan Margalit, GT students, local artistsGT and others

The math-themed show at the Atlanta Science Festival will be less elaborate than in the last few years, but we are back to apearing live on stage!  We are also hoping to arrange for live-streaming.  Mathematics in Motion will use dance and circus arts to engage the public.   (Dan and Evans and several GT students are involved, but don't worry, mathematicians won't be doing the dancing!)

There will be two shows on Sunday the 13th, begininng at 2:00 and 5:00 pm.

Partial Permutation Synchronization via Cycle-Edge Message Passing

Series
Other Talks
Time
Friday, March 4, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Bluejeans https://bluejeans.com/562725550/0392
Speaker
Gilad LermanSchool of Math, University of Minnesota

The problem of partial permutation synchronization (PPS) provides a global mathematical formulation for the multiple image matching problem. In this matching problem, one is provided with possibly corrupted matches (i.e., partial permutations) between keypoints in pairs of images and the underlying task is to match keypoints in each image to universal 3D scene points (resulting in other partial permutations). For structure-from-motion (SfM) common datasets, previous PPS algorithms for image matching often become computationally intractable and demand an exceedingly large amount of memory. We address this issue by extending the recent framework of Cycle-Edge Message Passing (CEMP) to the setting of PPS despite the fact that partial permutations do not have a full group structure.  We emphasize mathematical difficulties that arise when extending CEMP to PPS and also explain the mathematical guarantees for the performance of the modified CEMP algorithm in the setting of adversarial corruption and sufficiently small noise. This is a joint work with Shaohan Li and Yunpeng Shi.

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