Seminars and Colloquia by Series

TBA by

Series
Stochastics Seminar
Time
Thursday, March 14, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
TBA – SOM, GaTech

Strong edge colorings and edge cuts

Series
Graph Theory Working Seminar
Time
Wednesday, March 13, 2019 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
James Anderson – Georgia Tech
Erdős and Nešetřil conjectured in 1985 that every graph with maximum degree Δ can be strong edge colored using at most 5/4 Δ^2 colors. The conjecture is still open for Δ=4. We show the conjecture is true when an edge cut of size 1 or 2 exists, and in certain cases when an edge cut of size 4 or 3 exists.

The Bishop-Phelps-Bolloba ́s Property for Numerical Radius in the space of summable sequnces

Series
Analysis Seminar
Time
Wednesday, March 13, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Olena Kozhushkina – Ursinus college –
The Bishop-Phelps-Bolloba ́s property for numerical radius says that if we have a point in the Banach space and an operator that almost attains its numerical radius at this point, then there exist another point close to the original point and another operator close to the original operator, such that the new operator attains its numerical radius at this new point. We will show that the set of bounded linear operators from a Banach space X to X has a Bishop-Phelps-Bolloba ́s property for numerical radius whenever X is l1 or c0. We will also discuss some constructive versions of the Bishop-Phelps- Bolloba ́s theorem for l1(C), which are an essential tool for the proof of this result.

Eulerian dynamics with alignment interactions

Series
PDE Seminar
Time
Tuesday, March 12, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Changhui Tan – University of South Carolina –
The Euler-Alignment system arises as a macroscopic representation of the Cucker-Smale model, which describes the flocking phenomenon in animal swarms. The nonlinear and nonlocal nature of the system bring challenges in studying global regularity and long time behaviors. In this talk, I will discuss the global wellposedness of the Euler-Alignment system with three types of nonlocal alignment interactions: bounded, strongly singular, and weakly singular interactions. Different choices of interactions will lead to different global behaviors. I will also discuss interesting connections to some fluid dynamics systems, including the fractional Burgers equation, and the aggregation equation.

Comparison of sequences generated by a hidden Markov model

Series
Dissertation Defense
Time
Tuesday, March 12, 2019 - 13:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
George Kerchev – Georgia Tech
The length LC_n of the longest common subsequences of two strings X = (X_1, ... , X_n) and Y = (Y_1, ... , Y_n) is a way to measure the similarity between X and Y. We study the asymptotic behavior of LC_n when the two strings are generated by a hidden Markov model (Z, (X, Y)) and we build upon asymptotic results for LC_n obtained for sequences of i.i.d. random variables. Under some standard assumptions regarding the model we first prove convergence results with rates for E[LC_n]. Then, versions of concentration inequalities for the transversal fluctuations of LC_n are obtained. Finally, we outline a proof for a central limit theorem by building upon previous work and adapting a Stein's method estimate.

Coloring graphs with no K5-subdivision: disjoint paths in graphs

Series
Dissertation Defense
Time
Tuesday, March 12, 2019 - 10:00 for 1.5 hours (actually 80 minutes)
Location
203 Classroom D.M. Smith
Speaker
Qiqin Xie – Georgia Institute of Technology
The Four Color Theorem states that every planar graph is 4-colorable. Hajos conjectured that for any positive integer k, every graph containing no K_{k+1}-subdivision is k-colorable. However, Catlin disproved Hajos' conjecture for k >= 6. It is not hard to prove that the conjecture is true for k <= 3. Hajos' conjecture remains open for k = 4 and k = 5. We consider a minimal counterexample to Hajos' conjecture for k = 4: a graph G, such that G contains no K_5-subdivision, G is not 4-colorable, and |V (G)| is minimum. We use Hajos graph to denote such counterexample. One important step to understand graphs containing K_5-subdivisions is to solve the following problem: let H represent the tree on six vertices, two of which are adjacent and of degree 3. Let G be a graph and u1, u2, a1, a2, a3, a4 be distinct vertices of G. When does G contain a topological H (i.e. an H-subdivision) in which u1, u2 are of degree 3 and a1, a2, a3, a4 are of degree 1? We characterize graphs with no topological H. This characterization is used by He, Wang, and Yu to show that graph containing no K_5-subdivision is planar or has a 4-cut, establishing conjecture of Kelmans and Seymour. Besides the topological H problem, we also obtained some further structural information of Hajos graphs.

Using 2-torsion to obstruct topological isotopy

Series
Geometry Topology Seminar
Time
Monday, March 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Hannah Schwartz – Bryn Mawr
It is well known that two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other. In this talk, we will examine a family of smooth 4-manifolds in which the analogue of this fact does not hold, i.e. each manifold contains a pair of smoothly embedded, homotopic 2-spheres that are related by a diffeomorphism, but are not smoothly isotopic. In particular, the presence of 2-torsion in the fundamental groups of these 4-manifolds can be used to obstruct even a topological isotopy between the 2-spheres; this shows that Gabai's recent ``4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.

Sectional monodromy groups of projective curves

Series
Algebra Seminar
Time
Monday, March 11, 2019 - 12:50 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Borys Kadets – MIT –

Let X be a degree d curve in the projective space P^r.

A general hyperplane H intersects X at d distinct points; varying H defines a monodromy action on X∩H. The resulting permutation group G is the sectional monodromy group of X. When the ground field has characteristic zero the group G is known to be the full symmetric group.

By work of Harris, if G contains the alternating group, then X satisfies a strengthened Castelnuovo's inequality (relating the degree and the genus of X).

The talk is concerned with sectional monodromy groups in positive characteristic. I will describe all non-strange non-degenerate curves in projective spaces of dimension r>2 for which G is not symmetric or alternating. For a particular family of plane curves, I will compute the sectional monodromy groups and thus answer an old question on Galois groups of generic trinomials.

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