Seminars and Colloquia by Series

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.

Oral Exam: On Radial Symmetry of Uniformly Rotating/ Stationary Solutions to 2D Euler Equation

Series
Other Talks
Time
Tuesday, April 23, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jaemin ParkGeorgia Institute of Technology

We study whether all stationary solutions of 2D Euler equation must be radially symmetric, if the vorticity is compactly supported or has some decay at infinity. Our main results are the following:

(1) On the one hand, we are able to show that for any non-negative smooth stationary vorticity  that is compactly supported (or has certain decay as |x|->infty), it must be radially symmetric up to a translation.

(2) On the other hand, if we allow vorticity to change sign, then by applying bifurcation arguments to sign-changing radial patches, we are able to show that there exists a compactly-supported, sign-changing smooth stationary vorticity that is non-radial.

We have also obtained some symmetry results for uniformly-rotating solutions for 2D Euler equation, as well as stationary/rotating solutions for the SQG equation. The symmetry results are mainly obtained by calculus of variations and elliptic equation techniques. This is a joint work with Javier Gomez-Serrano, Jia Shi and Yao Yao.

Life after graduate school: Informal discussion with an ACO alumnus

Series
Other Talks
Time
Thursday, March 14, 2019 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles Atrium
Speaker
Chun-Hung LiuTexas A&amp;amp;M
Chun-Hung will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Mathapalooza!

Series
Other Talks
Time
Saturday, March 9, 2019 - 13:00 for 4 hours (half day)
Location
Ebster Recreation Center, Decatur
Speaker
Evans Harrell, Matt Baker, and GT Club Math, among othersGeorgia Tech, Emory, and others

Mathapalooza! is simultaneously a Julia Robinson Mathematics Festival and an event of the Atlanta Science Festival. There will be puzzles and games, a magic show by Matt Baker, mathematically themed courtroom skits by GT Club Math, a presentation about math and dance by Manuela Manetta, a presentation about math and music by David Borthwick, and a gallery of mathematical art curated by Elisabetta Matsumoto. It is free, and we anticipate engaging hundreds of members of the public in the wonders of mathematics. More info at https://mathematics-in-motion.org/about/Be there or B^2 !

ACO Director Interview Seminar by Prasad Tetali

Series
Other Talks
Time
Monday, February 25, 2019 - 14:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker