All Seminars
| Title: Moments, Krylov subspace methods and model reduction with applications in ellipsometry |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Zdenek Strakos of Academy of Sciences of the Czech Republic |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2009-11-02 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: |
| Title: Search for robust algebraic preconditioners |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Miroslav Tuma of Academy of Sciences of the Czech Republic |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2009-11-02 at 4:45PM |
| Venue: MSC W201 |
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| Abstract: |
| Title: Analysis of Massive Information Networks |
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| Colloquium: Computer Science |
| Speaker: Philip S. Yu of University of Illinois at Chicago |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2009-10-30 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: With the ubiquity of information networks and their broad applications, there have been numerous studies on the construction, and mining of information networks in multiple disciplines, including social network analysis, World-Wide Web, database systems, data mining, machine learning, and networked communication and information systems. However, large graphs may often be disk resident, and such graphs cannot be efficiently processed. In this talk, we examine the issues of on-line analytic processing, summarization and indexing of large graphs. Specifically, the problem of connectivity in the context of massive graphs is considered. In many large communication networks, social networks and other graphs, it is desirable to determine the minimum-cut between any pair of nodes. We will discuss how a connectivity index can be developed for a massive-disk resident graph. A sampling based approach is deployed to create compressed representations of the underlying graph. Trade-off between processing efficiency and accuracy will be shown. Bio: Philip S. Yu is a Professor in the Department of Computer Science at the University of Illinois at Chicago and also holds the Wexler Chair in Information Technology. Before joining UIC, he spent most of his career at IBM Thomas J. Watson Research Center and was manager of the Software Tools and Techniques group. Dr. Yu is a Fellow of the ACM and the IEEE. He served as the Editor-in-Chief of IEEE Transactions on Knowledge and Data Engineering (2001-2004). He is an associate editor of ACM Transactions on Knowledge Discovery from Data and also ACM Transactions of the Internet Technology. He serves on the steering committee of IEEE Int. Conference on Data Mining. He was a member of the IEEE Data Engineering steering committee. Dr. Yu received a Research Contributions Award from IEEE Intl. Conference on Data Mining in 2003. His research interests include data mining, privacy, data stream, and database systems. He has published more than 560 papers in refereed journals and conferences. He holds or has applied for more than 300 US patents. Dr. Yu was an IBM Master Inventor when at IBM. |
| Title: Steenrod operations on Chow groups |
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| Seminar: Algebra |
| Speaker: Asher Auel of Emory University |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-27 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: A theorem of Gollnitz and its place in the theory of partitions |
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| Seminar: Algebra |
| Speaker: Krishna Alladi of University of Florida |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-26 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: A Rogers-Ramanujan type identity is a series=product identity which relates certain partitions into parts satisfying difference to partitions into parts satisfying congruence conditions. Rogers-Ramanujan type identities arise in a variety of settings ranging from Lie algebras to statistical mechanics. A supreme example of such a partition identity is the deep 1967 theorem of Gollnitz. We shall discuss a new approach to Gollnitz's theorem in which this partition result and its generalizations will emerge out of a remarkable $q$-hypergeometric identity in three free parameters. This leads to crucial connections with several fundamental results on partitions and $q$-series, a new combinatorial understanding of Jacobi's triple product identity for theta functions, and to some partition congruences modulo powers of 2. The talk will be accessible to non-experts. |
| Title: Hereditary quasirandom properties of hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2009-10-23 at 4:00PM |
| Venue: W306 |
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| Abstract: Thomason, and Chung, Graham and Wilson were the first to investigate systematically properties of quasirandom graphs. They have stated several quite disparate graph properties -- such as having uniform edge distribution or containing a prescribed number of certain subgraphs -- and proved that these properties are equivalent in a deterministic sense. Simonovits and Sos introduced a hereditary property (which we call S) stating the following: for a small fixed graph L, a graph G on n vertices is said to have the property S if for every subset X of V(G), the number of labeled copies of L in G[X] (the subgraph of G induced by the vertices of (X) is given by $2^{-e(L)} |X|^{v(L)} + o(n^{v(L)})$. They have shown that S is equivalent to the other quasirandom properties. In this talk we give a natural extension of the result of Simonovits and Sos to k-uniform hypergraphs, answering a question of Conlon et al. Our approach yields an alternative, and perhaps simpler, proof of their theorem. |
| Title: Accounting for Helicity in 3D NSE Computations |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Leo Rebholz of Clemson University |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2009-10-21 at 12:45PM |
| Venue: W306 |
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| Abstract: It has recently become known that helicity, defined as the mean streamwise vorticity, is a fundamentally important quantity of the 3D Navier-Stokes equations. Helicity is a conserved quantity of inviscid flow, is cascaded jointly with energy through the inertial range, and is physically interpreted to be the degree to which a flow's vortex lines are tangled and intertwined. Until recently however, helicity has been ignored in NSE computations. In this talk I will show how helicity can be more accurately treated in finite element computations of the 3D NSE, which in turn leads to more accurate simulations. I will discuss two numerical schemes: one which enforces helicity preservation by the NSE nonlinearity (to mimic the continuous case) - joint work with Vince Ervin, and a second that solves for helicity directly inside of a velocity-vorticity method - joint work with Maxim Olshanskii. Numerical examples will be given that demonstrate the effectiveness of the methods. |
| Title: Constructing elliptic curves of high rank over function fields |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: Doug Ulmer of Georgia Tech |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-20 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: There are now several constructions of elliptic curves of high rank over function fields, most involving high-tech things like $L$-functions, cohomology, and the Tate or BSD conjectures. I'll review some of this and then give a very down-to-earth, low-tech construction of elliptic curves of high ranks over the rational function field $\mathbf{F}_p(t)$. |
| Title: Using mass formulas to enumerate definite quadratic forms of class number one |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: Jonathan Hanke of University of Georgia |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-20 at 5:15PM |
| Venue: MSC W201 |
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| Abstract: This talk will describe some recent results using exact mass formulas to determine all definite quadratic forms of small class number in at least 3 variables, particularly those of class number one. The mass of a quadratic form connects the class number (i.e. number of classes in the genus) of a quadratic form with the volume of its adelic stabilizer, and is explicitly computable in terms of special values of zeta functions. Comparing this with known results about the sizes of automorphism groups, one can make precise statements about the growth of the class number, and in principle determine those quadratic forms of small class number. We will describe some known results about masses and class numbers (over number fields), then present some new computational work over the rational numbers, and perhaps over some totally real number fields. |
| Title: The coefficients of q-series and asymptotics for partition ranks and cranks |
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| Seminar: Algebra |
| Speaker: Karl Mahlburg of Princeton |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2009-10-19 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Dyson's rank and crank statistics have long been important in the combinatorial study of integer partitions. Both statistics were introduced in efforts to better understand the famous Ramanujan congruences for the partition function $p(n)$, and there is no apparent relation between their simple combinatorial definitions. The main results of this talk (essentially) prove a remarkable conjecture of Garvan that the moments of the crank are always larger than the moments of the rank. More generally, these inequalities are an important example of relations for the asymptotics of hypergeometric $q$-series that are governed by modularity properties. In this case, the crank is associated to a modular form, while the rank is associated to a mock theta function/harmonic Maass form. If time permits, I will also briefly discuss some ideas of Zagier for deriving asymptotic expansions in these settings. |