Seminars and Colloquia by Series

Fractional chromatic number of planar graphs

Series
Graph Theory Seminar
Time
Monday, April 28, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zdenek Dvorak – Charles University
Grötzsch's theorem implies that every planar triangle-free graph is 3-colorable. It is natural to ask whether this can be improved. We prove that every planar triangle-free graph on n vertices has fractional chromatic number at most 3-1/(n+1/3), while Jones constructed planar triangle-free n-vertex graphs with fractional chromatic number 3-3/(n+1). We also investigate additional conditions under that triangle-free planar graphs have fractional chromatic number smaller than 3-epsilon for some fixed epsilon > 0.(joint work with J.-S. Sereni and J. Volec)

Bounded gaps between primes in Chebotarev sets

Series
Algebra Seminar
Time
Monday, April 28, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jesse Thorner – Emory University
A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes $p_1,p_2$ with $|p_1-p_2|\leq 600$ as a consequence of the Bombieri-Vinogradov Theorem. We apply his general method to the setting of Chebotarev sets of primes. We study applications of these bounded gaps with an emphasis on ranks of prime quadratic twists of elliptic curves over $\mathbb{Q}$, congruence properties of the Fourier coefficients of normalized Hecke eigenforms, and representations of primes by binary quadratic forms.

Analysis and synthesis methods in compressive signal processing

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 28, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Deanna Needell – Claremont McKenna College
In this talk we will discuss results for robust signal reconstruction from random observations via synthesis and analysis methods in compressive signal processing (CSP). CSP is a new and exciting field which arose as an efficient alternative to traditional signal acquisition techniques. Using a (usually random) projection, signals are measured directly in compressed form, and methods are then needed to recover the signal from those measurements. Synthesis methods attempt to identify the low-dimensional representation of the signal directly, whereas analysis type methods reconstruct in signal space. We also discuss special cases including provable near-optimal reconstruction guarantees for total-variation minimization and new techniques in super-resolution.

Patient-Specific Computational Fluid Dynamic Simulations for Predicting Inferior Vena Cava Filter Performance

Series
Mathematical Biology Seminar
Time
Monday, April 28, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
IBB 1128
Speaker
Suzanne M. Shontz – Department of Mathematics and Statistics, Mississippi State University.

Please Note: Speaker is visiting the School of Biology, Georgia Tech

Pulmonary embolism (PE) is a potentially-fatal disease in which blood clots (i.e., emboli) break free from the deep veins in the body and migrate to the lungs. In order to prevent PE, anticoagulants are often prescribed; however, for some patients, anticoagulants cannot be used. For such patients, a mechanical filter, namely an inferior vena cava (IVC) filter, is inserted into the IVC to trap the blood clots and prevent them from reaching the lungs. There are numerous IVC filter designs, and it is not well understood which particular IVC filter geometry will result in the best treatment for a given patient. Patient-specific computational fluid dynamic (CFD) simulations may be used to predict the performance of IVC filters and hence can aid physicians in IVC filter selection and placement. In this talk, I will first describe our computational pipeline for prediction of IVC filter performance. Our pipeline involves several steps including image processing, geometric model construction, in vivo stress state estimation, surface and volume mesh generation based on virtual IVC filter placement, and CFD simulation of IVC hemodynamics. I will then present the results of our IVC hemodynamics simulations obtained for two patient IVCs. This talk represents joint work with several researchers at The Pennsylvania State University, Penn State Hershey Medical Center, the Penn State Applied Research Lab, and the University of Utah.

Atlanta Lecture Series in Combinatorics and Graph Theory XII

Series
Other Talks
Time
Saturday, April 26, 2014 - 13:00 for 5 hours
Location
Skiles 006
Speaker
Bruce Reed – McGill University
Emory University, Georgia Tech and Georgia State University, with support from the National Science Foundation and the National Security Agency, will continue the series of mini-conferences and host a series of 9 new mini-conferences from 2014-2017. The 12th of these mini-conferences will be held at Georgia Tech during April 26-27, 2014. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding researchers each giving one fifty minute lecture. There will also be several 25 minute lecturers by younger researchers or graduate students. For more details, see the schedule

Flag algebras and the stable coefficients of the Jones polynomial

Series
Dissertation Defense
Time
Friday, April 25, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thao Vuong – Georgia Institute of Technology –
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose elements give invariants of alternating links which strictly refine the first four stable coefficients. We conjecture that all stable coefficients are elements of this algebra, and give experimental evidence for the fifth and sixth stable coefficient. We illustrate our results in tables of all alternating links with at most 10 crossings and all irreducible planar graphs with at most 6 vertices.

ARC Theory Day

Series
Other Talks
Time
Friday, April 25, 2014 - 09:00 for 8 hours (full day)
Location
Klaus 1116E
Speaker
ARC Theory Day – Algorithms and Randomness Center, Georgia Tech
Algorithms and Randomness Center (ARC) Theory Day is an annual event that features hour-long lectures focusing on recent innovative results in theoretical computer science, spanning a wide array of topics several of which are inspired by practical problems. See the complete list of titles and times of talks.

Sidon sets and extremal graph theory

Series
Combinatorics Seminar
Time
Thursday, April 24, 2014 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Craig Timmons – UC San Diego
Let G be an abelian group. A subset A of G is a Sidon set if A has the property that no sum of two elements of A is equal to another sum of two elements of A. These sets have a rich history in combinatorial number theory and frequently appear in the problem papers of Erdos. In this talk we will discuss some results in which Sidon sets were used to solve problems in extremal graph theory. This is joint work with Mike Tait and Jacques Verstraete.

Legendrian Torus Knots

Series
Geometry Topology Student Seminar
Time
Wednesday, April 23, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ece Gülşah Çolak – Bülent Ecevit University and Georgia Tech –
We will discuss Etnyre and Honda's proof of the classification of Legendrian positive torus knots in the tight contact 3-sphere up to Legendrian isotopy by using the tools from convex surface theory.

CANCELLED: Pathogen strategies and the shape of epidemics

Series
Mathematical Biology Seminar
Time
Wednesday, April 23, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zoi Rapti – University of Illinois at Urbana-Champaign
We will introduce a PDE model to investigate how epidemic metrics, such as the basic reproductive ratio R_0 and infection prevalence, depend on a pathogen's virulence. We define virulence as all harm inflicted on the host by the pathogen, so it includes direct virulence (increased host mortality and decreased fecundity) and indirect virulence (increased predation on infected hosts). To study these effects we use a Daphnia-parasite disease system. Daphnia are freshwater crustaceans that get infected while feeding, by consuming free-living parasite spores. These spores after they are ingested, they start reproducing within the host and the host eventually dies. Dead hosts decay releasing the spores they contain back in the water column. Visual predators, such as fish, can detect infected hosts easier because they become opaque, hence they prey preferentially on them. Our model includes two host classes (susceptible and infected), the free-living propagules, and the food resource (algae). Using experimental data, we obtain the qualitative curves for the dependence of disease-induced mortality and fecundity reduction on the age of infection. Among other things, we will show that in order the predator to keep the host population healthy, it needs to (i) detect the infected hosts very soon after they become infected and (ii) show very high preference on consuming them in comparison to the uninfected hosts. In order to address questions about the evolution of virulence, we will also discuss how we defined the invasion fitness for this compartmental model. We will finish with some pairwise invasibility plots, that show when a mutant strain can invade the resident strain in this disease system.

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