All Seminars
| Title: On randomizing two derandomized greedy algorithms |
|---|
| Seminar: Combinatorics |
| Speaker: Kevin Costello of The Georgia Institute of Technology |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-10-01 at 4:00PM |
| Venue: W306 |
| Download Flyer |
| Abstract: Many of the simplest and easiest implemented approximation algorithms can be thought of as derandomizations of the naive random algorithm. Here we consider the question of whether performing the algorithm on a random reordering of the variables provides an improvement in the worst case expected performance.\\ \\ (1) For Johnson's algorithm for Maximum Satisfiability, this indeed turns out to be the case: While in the worst case Johnson's algorithm only provides a 2/3 approximation, the additional randomization step guarantees a 2/3+c approximation for some positive c.\\ \\ (2) For the greedy algorithm for MAX-CUT, it turns out that the randomized version does NOT provide a 1/2+c approximation for any c on general graphs. This is in contrast to a result of Mathieu and Sc hudy showing it provides a 1-epsilon approximation on dense graphs.\\ \\ Joint with Asaf Shapira and Prasad Tetali. |
| Title: Algebraic aspects of statistical field theory |
|---|
| Seminar: Algebra and number theory |
| Speaker: David Borthwick of Emory University |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2010-09-28 at 3:00PM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: We'll give an introduction to the role that representation theory plays in the construction of models for phase transitions in physics. In particular, we'll introduce the Virasoro algebra and the "minimal models'' which are essentially its simplest unitary representations. We'll also consider some related models based on Lie algebras. The talk will mainly focus on the algebra of these models, but we'll try to explain how certain aspects of the constructions have significance in the physical theories. |
| Title: Conformal invariants of Jordan domains |
|---|
| Seminar: Analysis and Differential Geometry |
| Speaker: Professor Shanshuang Yang of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-09-21 at 4:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: Several conformal invariants will be introduced for Jordan domains in connection with the theory of quasiconformal mappings. These invariants (including reflection constant and quasi-circle constant) capture certain geometric feature of Jordan domains. We will discuss how they are related and how to estimate the values of these constants for certain domains such as ellipses and rectangles. |
| Title: Regular subgraphs of 3-uniform hypergraphs |
|---|
| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-09-17 at 4:00PM |
| Venue: W306 |
| Download Flyer |
| Abstract: Every graph on n vertices with at least n edges necessarily contains a 2-regular subgraph (a cycle). It is much more difficult to determine how many edges are necessary for a graph to contain a k-regular subgraph and the best known bounds so far are due to Pyber, Rödl and Szemerédi. In this talk I will present our recent attempt to answer these type of questions in the setting of 3-uniform hypergraphs.\\ \\ (This research was partially done at the Banff workshop 2010 in collaboration with P. Haxell, T. Luczak, D. Mubayi, B. Nagle, Y. Person, V. Rödl, M. Schacht, J. Verstraete) |
| Title: Conformal field theory models for phase transitions |
|---|
| Seminar: Special topics |
| Speaker: David Borthwick of Emory University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2010-09-16 at 4:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: We will attempt to explain how quantum field theory describes the continuum limit of discrete statistical models. (As in the previous talk, our focus will be on simple Ising models.) At phase transitions the divergence of the correlation length translates to local conformal invariance in the corresponding quantum field theory. The goal is to explain how a particular field theory model applies to the phase transition in the cobalt niobate experiment. |
| Title: EUMMA Event - Career Counseling |
|---|
| Seminar: N/A |
| Speaker: Dr. Paul Fowler of Emory University |
| Contact: Jodi-Ann Wray, jcwray@emory.edu |
| Date: 2010-09-15 at 6:00PM |
| Venue: B. Jones building |
| Download Flyer |
| Abstract: |
| Title: The arithmetic-geometric mean and p-adic limits of modular forms |
|---|
| Seminar: Algebra and Number Theory |
| Speaker: Matthew Boylan of University of South Carolina |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2010-09-14 at 3:00PM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: The arithmetic-geometric mean of Gauss is the coincident limit of two sequences which arise naturally from systematically taking arithmetic and geometric means. Gauss proved that these sequences and their limit, the AGM, are parametrizable by values of modular forms. In this talk, we exhibit a sequence of weakly holomorphic modular forms whose p-adic limit parametrizes values of the AGM. The p-adic limit arises via the interplay between classical modular forms and harmonic weak Maass forms. The recent successes connecting harmonic Maass forms to partitions, Ramanujan's mock theta functions, Lie algebras, probability, and mathematical physics motivates independent interest in their study. |
| Title: Edges in 2-factor Isomorphic Graphs |
|---|
| Seminar: Combinatorics |
| Speaker: Paul Wrayno of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-09-10 at 4:00PM |
| Venue: W306 |
| Download Flyer |
| Abstract: A graph G is considered 2-factor isomorphic if it contains a 2-factor F, and all other 2-factors are isomorphic to F. In other words, if F is viewed as a multiset of the unlabeled cycles it contains, then all other 2-factors may be viewed as the same multiset. Faudree, Gould, and Jacobson calculated the maximum number of edges for 2-factor hamiltonian graphs as a function of |V(G)|. In this talk I will generalize this result to any chosen 2-factor, any 2-factor with a fixed number of cycles, and any unspecified 2-factor. Constructions of graphs that attain these bounds arise naturally from the calculations. |
| Title: Principal homogeneous spaces and zero cycles of degree one |
|---|
| Seminar: Algebra and number theory |
| Speaker: Jodi Black of Emory University |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-09-07 at 3:00PM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: Let $X$ be a principal homogeneous space under a connected linear algebraic group $G$ and over a field $k$. We show that for some of these groups $G$, if $X$ admits a zero cycle of degree one, then $X$ has a $k$-rational point. This gives a positive answer for these groups to a question posed by Serre. |
| Title: A brief introduction to the the Ising model and phase transitions in statistical physics |
|---|
| Seminar: Analysis and Differential Geometry |
| Speaker: David Borthwick of Emory University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2010-09-07 at 4:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: In this very introductory talk we'll introduce the Ising spin chain model, which is the basic physics model underlying this experiment. The Ising model is extremely simple to describe, and yet its behavior is complex enough to provide a good model for phase transitions in real materials. The main point of this talk will be to describe how phase transitions (e.g., ice melting to water) are understood in terms of simple statistical physics models. |