All Seminars
| Title: Algebraic aspects of statistical field theory |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-09-17 at 4:00PM |
| Venue: W306 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| Abstract: |
| Title: The arithmetic-geometric mean and p-adic limits of modular forms |
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| 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 |
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| 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 |
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| Seminar: Combinatorics |
| Speaker: Paul Wrayno of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-09-10 at 4:00PM |
| Venue: W306 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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. |
| Title: Counting number fields, and applications to low-lying zeros of Dedekind zeta functions of number fields |
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| Seminar: Algebra and Number Theory |
| Speaker: Andy Yang of Dartmouth |
| Contact: Ken Ono, ono@mathcs.emory.edu |
| Date: 2010-08-31 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: Abstract: We will discuss various results, mainly due to Harold Davenport and Hans Heilbronn, and later Manjul Bhargava, on the number of number fields of some fixed degree and Galois group whose absolute discriminant is less than X, as X tends to infinity. In particular, we will focus on the cases where we consider cubic fields with Galois group $S_{3}$ and quartic fields with Galois group $S_{4}$.\\ \\ We will then discuss an application of these results to the problem of understanding the distribution of low-lying zeros of the Dedekind zeta functions associated to these fields, in the sense of the Katz-Sarnak philosophy. |