Seminars and Colloquia Schedule

Action of the cork twist on Floer homology

Series
Geometry Topology Seminar
Time
Tuesday, April 26, 2011 - 10:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cagri Karakurt – UT Austin
Abstract: We utilize the Ozsvath-Szabo contact invariant to detect the action of involutions on certain homology spheres that are surgeries on symmetric links, generalizing a previous result of Akbulut and Durusoy. Potentially this may be useful to detect different smooth structures on $4$-manifolds by cork twisting operation. This is a joint work with S. Akbulut.

Global Regularity for Three-dimensional Navier-Stokes Equations and Relevant Geophysical Models

Series
PDE Seminar
Time
Tuesday, April 26, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Edriss Titi – UC Irvine and Wiezmann Institute –
The basic problem faced in geophysical fluid dynamics isthat a mathematical description based only on fundamental physicalprinciples, the so-called the ``Primitive Equations'', is oftenprohibitively expensive computationally, and hard to studyanalytically. In this talk I will survey the main obstacles inproving the global regularity for the three-dimensionalNavier-Stokes equations and their geophysical counterparts. Eventhough the Primitive Equations look as if they are more difficult tostudy analytically than the three-dimensional Navier-Stokesequations I will show in this talk that they have a unique global(in time) regular solution for all initial data.Inspired by this work I will also provide a new globalregularity criterion for the three-dimensional Navier-Stokesequations involving the pressure.This is a joint work with Chongsheng Cao.

Judicious Partitions of Graphs and Hypergraphs

Series
Dissertation Defense
Time
Tuesday, April 26, 2011 - 12:30 for 2 hours
Location
Skiles 005
Speaker
Jie Ma – School of Mathematics, Georgia Tech
Classical partitioning problems, like the Max-Cut problem, ask for partitions that optimize one quantity, which are important to such fields as VLSI design, combinatorial optimization, and computer science. Judicious partitioning problems on graphs or hypergraphs ask for partitions that optimize several quantities simultaneously. In this dissertation, we work on judicious partitions of graphs and hypergraphs, and solve or asymptotically solve several open problems of Bollobas and Scott on judicious partitions, using the probabilistic method and extremal techniques.

Dynamical localization in the disordered xy-spin chain

Series
Math Physics Seminar
Time
Wednesday, April 27, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Günter Stolz – Dept. of Math. University of Alabama at Birmingham
We will show that a quantum xy-spin chain which is exposed to a randomexterior magnetic field satisfies a zero-velocity Lieb-Robinson bound. Thiscan be interpreted as dynamical localization for the spin chain or asabsence of information transport. We will also discuss a general result,which says that zero velocity LR-bounds in a quantum spin system implyexponential decay of ground state correlations. This is joint work withRobert Sims and Eman Hamza and motivated by recent works of Burrell-Osborneas well as Hastings.

Roman domination on 2-connected graphs

Series
Graph Theory Seminar
Time
Thursday, April 28, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chun-Hung Liu – Math, GT
A Roman dominating function of a graph G is a function f which maps V(G) to {0, 1, 2} such that whenever f(v)=0, there exists a vertex u adjacent to v such that f(u)=2. The weight of f is w(f) = \sum_{v \in V(G)} f(v). The Roman domination number \gamma_R(G) of G is the minimum weight of a Roman dominating function of G. Chambers, Kinnersley, Prince and West conjectured that \gamma_R(G) is at most the ceiling 2n/3 for any 2-connected graph G of n vertices. In this talk, we will give counter-examples to the conjecture, and proves that \gamma_R(G) is at most the maximum among the ceiling of 2n/3 and 23n/34 for any 2-connected graph G of n vertices. This is joint work with Gerard Jennhwa Chang.

Graduate Student Probability Conference 2011

Series
Other Talks
Time
Friday, April 29, 2011 - 09:00 for 8 hours (full day)
Location
Klaus 1116
Speaker
Graduate Students Probability Conference – School of Mathematics, Georgia Tech

Other organizers include: Ruoting Gong, <br />
Huy Huynh, <br />
Jinyong Ma, <br />
Ruodu Wang, and<br />
Linwei Xin.

Georgia Tech School of Mathematics will host the 5th Annual Graduate Student Probability Conference (GSPC) from April 29 - May 1, 2011. The conference is open to all graduate students and post-doctoral fellows interested in probability. We will host two keynote speakers: Professor Nathalie Eisenbaum (Université Pierre et Marie Curie) and Professor Philip Protter (Columbia University). The conference will begin at 9:00 AM Friday, April 29 and end at noon on Sunday May 1.

A characterization of 4-ordered cycle in planar graphs

Series
SIAM Student Seminar
Time
Friday, April 29, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Jie Ma – School of Mathematics, Georgia Tech
Fix k vertices in a graph G, say a_1,...,a_k, if there exists a cycle that visits these vertices with this specified order, we say such a cycle is (a_1,a_2,...,a_k)-ordered. It is shown by Thomas and Wollan that any 10k-connected graph is k-linked, therefore any 10k-connected graph has an (a_1,a_2,...,a_k)-ordered for any a_1,...,a_k. However, it is possible that we can improve this bound when k is small. It is shown by W. Goddard that any 4-connected maximal planar graph has an (a_1,...,a_4)-ordered cycle for any choice of 4 vertices. We will present a complete characterization of 4-ordered cycle in planar graphs. Namely, for any four vertices a,b,c,d in planar graph G, if there is no (a,b,c,d)-ordered cycle in G, then one of the follows holds: (1) there is a cut S separating {a,c} from {b,d} with |S|\leq 3; (2) roughly speaking, a,b,d,c "stay" in a face of G with this order.

The Bohman-Frieze Process

Series
Combinatorics Seminar
Time
Friday, April 29, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Will Perkins – Courant Institute, NYU –
The Bohman-Frieze process is a simple modification of the Erdős-Rényi random graph that adds dependence between the edges biased in favor of joining isolated vertices. We present new results on the phase transition of the Bohman-Frieze process and show that qualitatively it belongs to the same class as the Erdős-Rényi process. The results include the size and structure of small components in the barely sub- and supercritical time periods. We will also mention a class of random graph processes that seems to exhibit markedly different critical behavior.