## Seminars and Colloquia by Series

### 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.

### Mathematical Ideas for Graph Generation

Series
Other Talks
Time
Thursday, March 3, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Bluejeans https://bluejeans.com/562725550/0392
Speaker
Gilad LermanSchool of Math, University of Minnesota

Generative networks have made it possible to generate meaningful signals such as images and texts. They were also extended to graphs and applied, for example, to generate molecules. However, the mathematical properties of generative methods are unclear, and training good generative models is difficult. Moreover, some basic and intuitive ideas of generative networks for signals and images do not apply to graphs and we thus focus on this talk on graph generation. An earlier joint work of the speaker generalized Mallat's scattering transform to graphs and later used it as an encoder within an autoencoder for graph generation (while applying a simple Gaussianization procedure to the output of the encoder) . For the graph scattering component, this work proved asymptotic invariance to permutations and stability to graph manipulations. The issue is that the decoder of this graph generation component used two fully connected networks and was not adapted to the graph structure. In fact, many other graph generation methods do not sufficiently utilize the graph structure. In order to address this issue, I will present a new recent joint work that develops a novel and trainable graph unpooling layer for effective graph generation. Given a graph with features, the unpooling layer enlarges this graph and learns its desired new structure and features. Since this unpooling layer is trainable, it can be applied to graph generation either in the decoder of a variational autoencoder or in the generator of a generative adversarial network (GAN). We establish connectivity and expressivity. That is, we prove that the unpooled graph remains connected and any connected graph can be sequentially unpooled from a 3-nodes graph. We apply the unpooling layer within the GAN generator and address the specific task of molecular generation. This is a joint work with Yinglong Guo and Dongmian Zou.

### Graphs, Geometry and Gerrymandering

Series
Other Talks
Time
Saturday, October 23, 2021 - 16:00 for 1 hour (actually 50 minutes)
Location
Clough auditorium and via Bluejeans
Speaker
Moon DuchinTufts University

Please Note: This is a public talk the School of Math is co-sponsoring with the Gathering 4 Gardner Foundation. I will be viewable both in the Clough Auditoria or by Bluejeans at https://primetime.bluejeans.com/a2m/live-event/wbxzuakh .

What are all the ways to draw the lines, when you're dividing up a state to get representation? If you can't find them all, can you choose a good sample? I'll discuss some surprisingly simple questions about graphs and geometry that can help us make advances in policy and civil rights.

### Alice in Königsberg

Series
Other Talks
Time
Thursday, October 22, 2020 - 20:00 for 30 minutes
Location
ONLINE at https://zoom.us/j/93502013825
Speaker
Evans Harrell and GT Club Math studentsGeorgia Tech

This skit recounts one of the foundation stories of mathematics, the puzzle of the Seven Bridges of Königsberg, solved by Euler in 1726.  Except that it all takes place in a mad courtroom, and you are the jury!

### Mathapalooza After Dark!

Series
Other Talks
Time
Monday, March 16, 2020 - 19:00 for 2 hours
Location
Highland Ballroom, 644 North Highland Ave.
Speaker

A math-themed variety show including music, improv comedy, a poetry slam, juggling, a fashion show (audience members can join in)  and more, right there on the stage of the fabulous Highland Ballroom!   Tickets  are \$10.00.

### Mathapalooza!

Series
Other Talks
Time
Sunday, March 15, 2020 - 13:00 for 4 hours (half day)
Location
MLK Recreation Center, 110 Hilliard St. SE
Speaker

An afternoon of public engagement of mathematics through puzzles, games, and the arts, including:  magic (by Matt Baker), juggling and other circus arts, music, dance, an art gallery, and a live construction of a Fibonacci-based sculpture (by Akio Hizume).  It is free and open to the public, but our partner the Julia Robinson Mathematics Festival recommends registering at https://jrmf.org/event-details/mathapalooza .  If you want to get involved, please contact Evans Harrell directly.

### Open Forum: Pierre-Emmanuel Jabin

Series
Other Talks
Time
Friday, February 21, 2020 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pierre-Emmanuel JabinUniversity of Maryland, College Park

This is the open forum for Pierre-Emmanuel   Jabin (https://home.cscamm.umd.edu/~jabin/)

as a candidate for Elaine M. Hubbard Chair in Mathematics.