Seminars and Colloquia by Series

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.

Periodic Orbit Decomposition of Shear Flow Dynamics

Series
Other Talks
Time
Wednesday, January 29, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N201
Speaker
N. Burak Budanur IST, Austria
Several recent papers presented exact time-periodic solutions in shear flow simulations at moderate Reynolds numbers. Although some of these studies demonstrated similarities between turbulence and the unstable periodic orbits, whether one can utilize these orbits for turbulence modeling remained unclear. We argue that this can be achieved by measuring the frequency of turbulence's visits to the periodic orbits. To this end, we adapt methods from computational topology and develop a metric that quantifies shape similarity between the projections of turbulent trajectories and periodic orbits. We demonstrate our method by applying it in a numerical study of the three-dimensional Navier--Stokes equations under sinusoidal forcing. Streamed online: https://gatech.bluejeans.com/7678987299

From Lorenz to Lorenz: Principles and Possibilities in the Phase Space of Animal Behavior

Series
Other Talks
Time
Tuesday, January 28, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N202
Speaker
Gregory StephensVrije Universiteit Amsterdam
Animal behavior is often quantified through subjective, incomplete variables that may mask essential dynamics. Here, we develop a behavioral state space in which the full instantaneous state is smoothly unfolded as a combination of short-time posture dynamics. Our technique is tailored to multivariate observations and extends previous reconstructions through the use of maximal prediction. Applied to high-resolution video recordings of the roundworm C. elegans, we discover a low-dimensional state space dominated by three sets of cyclic trajectories corresponding to the worm's basic stereotyped motifs: forward, backward, and turning locomotion. In contrast to this broad stereotypy, we find variability in the presence of locally-unstable dynamics, and this unpredictability shows signatures of deterministic chaos: a collection of unstable periodic orbits together with a positive maximal Lyapunov exponent. The full Lyapunov spectrum is symmetric with positive, chaotic exponents driving variability balanced by negative, dissipative exponents driving stereotypy. The symmetry is indicative of damped, driven Hamiltonian dynamics underlying the worm's movement control.

Research proposal: Matchings in hypergraphs

Series
Other Talks
Time
Thursday, October 31, 2019 - 13:30 for 30 minutes
Location
Skiles 005
Speaker
Xiaofan YuanGeorgia Tech

I will introduce a minimum l-degree threshold for the existence of a nearly perfect (i.e., covering all but a constant number of vertices) matching in a k-graph where k ≥ 3 and k/2 < l ≤ k − 1. This is joint work with Hongliang Lu and Xingxing Yu.

This improves upon an earlier result of Hàn, Person, and Schacht for the range k/2 < l ≤ k − 1. In some cases, such a matching can in fact be near perfect (i.e., covering all but at most k vertices) and our bound on the minimum l-degree is best possible.

Oral Exam-Bounds on regularity of quadratic monomial ideals and Pythagoras numbers on projections of Rational Normal Curves

Series
Other Talks
Time
Friday, October 18, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jaewoo JungGeorgia Tech

In this talk, I will introduce my old(1.) and current works(2.).

1. Bounds on regularity of quadratic monomial ideals

We can understand invariants of monomial ideals by invariants of clique (or flag) complex of  corresponding graphs. In particular, we can bound the Castelnuovo-Mumford regularity (which is a measure of algebraic complexity) of the ideals by bounding homol0gy of corresponding (simplicial) complex. The construction and proof of our main theorem are simple, but it provides (and improves) many new bounds of regularities of quadratic monomial ideals.

2. Pythagoras numbers on projections of Rational Normal Curves

Observe that forms of degree $2d$ are quadratic forms of degree $d$. Therefore, to study the cone of  sums of squares of degree $2d$, we may study quadratic forms on Veronese embedding of degree $d$.  In particular,  the rank of sums of squares (of degree $2d$) can be studied via Pythagoras number  (which is a classical notion) on the Veronese embedding of degree $d$. In this part, I will compute the Pythagoras number on rational normal curve (which is a veronese embedding of $\mathbb{P}^1$) and discuss about how Pythagoras numbers are changed when we take some projections away from some points.

(Oral Exam) Mathematical Modeling and Analysis of Multidimensional Data

Series
Other Talks
Time
Tuesday, April 30, 2019 - 13:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Yuchen Roy He GT Math


Multidimensional data is ubiquitous in the application, e.g., images and videos. I will introduce some of my previous and current works related to this topic.
1) Lattice metric space and its applications. Lattice and superlattice patterns are found in material sciences, nonlinear optics and sampling designs. We propose a lattice metric space based on modular group theory and
metric geometry, which provides a visually consistent measure of dissimilarity among lattice patterns.  We apply this framework to superlattice separation and grain defect detection.
2) We briefly introduce two current projects. First, we propose new algorithms for automatic PDE modeling, which drastically improves the efficiency and the robustness against additive noise. Second, we introduce a new model for surface reconstruction from point cloud data (PCD) and provide an ADMM type fast algorithm.

 

 

 

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