Seminars and Colloquia by Series

Research proposal: Matchings in hypergraphs

Series
Other Talks
Time
Thursday, October 31, 2019 - 13:30 for 30 minutes
Location
Skiles 005
Speaker
Xiaofan Yuan – Georgia 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 Jung – Georgia 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 Park – Georgia 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. 

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 others – Georgia 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
Prasad Tetali – Georgia Tech
Georgia Tech is leading the way in Creating the Next in higher education.In this talk I will present (1) My vision for ACO and (2) how my research relates naturally to ACO both where the A,C,O fields are going, and my own specific interests

AWM Lunch Talk Series - Anna Kirkpatrick: Markov Chain Monte Carlo and RNA Secondary Structure

Series
Other Talks
Time
Wednesday, February 20, 2019 - 12:00 for 30 minutes
Location
005
Speaker
Anna Kirkpatrick – Georgia Tech –
Understanding the structure of RNA is a problem of significant interest to biochemists. Thermodynamic energy functions are often key to this pursuit, but it is well-established that these energy functions do not perform well when applied to longer RNA sequences. This work specifically investigates the branching properties of RNA secondary structures, viewed as plane trees. By employing Markov chain Monte Carlo techniques, we sample from the probability distributions determined by these thermodynamic energy functions. We also investigate some of the challenges in employing Markov chain Monte Carlo, in particular the existence of local energy minima in transition graphs. This talk will give background, share preliminary results, and discuss future avenues of investigation.

CANCELLED - Control through canalization in modeling the innate immune response to ischemic injury - CANCELLED

Series
Other Talks
Time
Thursday, January 31, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Elena Dimitrova – Clemson University –

Please Note: This is a SCMB MathBioSys Seminar posted on behalf of Melissa Kemp (GT BME)

Constriction of blood vessels in the extremities due to traumatic injury to halt excessive blood loss or resulting from pathologic occlusion can cause considerable damage to the surrounding tissues with significant morbidity and mortality. Optimal healing of damaged tissue relies on the precise balance of pro-inflammatory and pro-healing processes of innate inflammation. In this talk, we will present a discrete multiscale mathematical model that spans the tissue and intracellular scales, and captures the consequences of targeting various regulatory components. We take advantage of the canalization properties of some of the functions, which is a type of hierarchical clustering of the inputs, and use it as control to steer the system away from a faulty attractor and understand better the regulatory relations that govern the system dynamics.EDIT: CANCELLED

Classical mechanisms of recollision and high harmonic generation

Series
Other Talks
Time
Monday, December 3, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Simon Berman – Georgia Tech (Physics)
Thesis defense: Advisors: Turgay Uzer and Cristel Chandre Summary: Thirty years after the demonstration of the production of high laser harmonics through nonlinear laser-gas interaction, high harmonic generation (HHG) is being used to probe molecular dynamics in real time and is realizing its technological potential as a tabletop source of attosecond pulses in the XUV to soft X-ray range. Despite experimental progress, theoretical efforts have been stymied by the excessive computational cost of first-principles simulations and the difficulty of systematically deriving reduced models for the non-perturbative, multiscale interaction of an intense laser pulse with a macroscopic gas of atoms. In this thesis, we investigate first-principles reduced models for HHG using classical mechanics. On the microscopic level, we examine the recollision process---the laser-driven collision of an ionized electron with its parent ion---that drives HHG. Using nonlinear dynamics, we elucidate the indispensable role played by the ionic potential during recollisions in the strong-field limit. On the macroscopic level, we show that the intense laser-gas interaction can be cast as a classical field theory. Borrowing a technique from plasma physics, we systematically derive a hierarchy of reduced Hamiltonian models for the self-consistent interaction between the laser and the atoms during pulse propagation. The reduced models can accommodate either classical or quantum electron dynamics, and in both cases, simulations over experimentally-relevant propagation distances are feasible. We build a classical model based on these simulations which agrees quantitatively with the quantum model for the propagation of the dominant components of the laser field. Subsequently, we use the classical model to trace the coherent buildup of harmonic radiation to its origin in phase space. In a simplified geometry, we show that the anomalously high frequency radiation seen in simulations results from the delicate interplay between electron trapping and higher energy recollisions brought on by propagation effects.

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