All Seminars
| Title: Fast pair-wise and node-wise algorithms for Katz scores and commute times |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: David Gleich of Purdue University, Computer Science Department |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2012-01-20 at 12:45PM |
| Venue: W306 |
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| Abstract: We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adopt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pair-wise commute time method and column-wise Katz algorithm both have attractive theoretical properties and empirical performance. |
| Title: Prehomogeneous vector spaces and their zeta functions |
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| Seminar: Algebra |
| Speaker: Frank Thorne of University of South Carolina |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2012-01-20 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: Last year, I spoke about my work with Takashi Taniguchi in estimating the number of cubic fields of bounded discriminant. Our work related on the Shintani zeta functions associated to the space of binary cubic forms. My previous talk (and to a lesser extent, my paper with Takashi) used these zeta functions essentially as a black box. In this talk I will discuss the zeta functions themselves. I have proved a couple of results about them which I will mention. However, the main focus of my talk will be the underlying theory as developed by Sato, Shintani, and others. I will explain what prehomogeneous vector spaces are and why zeta functions can be associated to them. I will also describe some interesting open questions about these zeta functions -- resolutions of which would lead to new results about quartic and quintic fields. |
| Title: A new Computational Paradigm in Multiscale Simulations: Application to Brain Blood Flow |
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| Seminar: Scientific Computing |
| Speaker: Dr. Leopold Grinberg of Division of Applied Mathematics, Brown University |
| Contact: Alessandro Veneziani, ale@mathcs.emory.edu |
| Date: 2012-01-16 at 11:00AM |
| Venue: MSC W301 |
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| Abstract: Interfacing atomistic-based with continuum-based simulation codes is now required in many multiscale physical and biological systems. We present the computational advances that have enabled the first multiscale simulation on about 300K processors by coupling a high-order (spectral element) Navier-Stokes solver with a stochastic (coarse-grained) Molecular Dynamics solver based on Dissipative Particle Dynamics (DPD). We study blood flow in a patient specific cerebrovasculature with a brain aneurysm, and analyze the interaction of blood cells with the arterial walls causing thrombus formation and possibly aneurysm rupture. The blood flow patterns are resolved by Nektar - a spectral element solver (about 3 billion unknowns); the blood microrheology within the aneurysm is resolved by an in-house version of DPDLAMMPS (about 10 billions unknowns).\\ \\ Biosketch of the speaker:\\ Leopold Grinberg obtained his PhD from Brown University in 2009. He is currently a Senior Research Associate at Brown University, Division of Applied Mathematics working with Prof. G.E. Karniadakis. His research interests encompass diverse topics in computational science, specifically High Performance Scientific Computing with applications in biomedical research. The major fields of Dr. Grinberg's research are:\\ \\ * Multi-scale simulations\\ * Integration of available patient-specific data into numerical simulations\\ * One- and three-dimensional modeling of a blood flow in large arterial networks\\ * Developing scalable algorithms for solutions of tightly and loosely coupled systems\\ * High-order methods\\ * Multi-scale visualization\\ |
| Title: Mock modular forms and characters of Kac-Wakimoto |
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| Seminar: Algebra and Number Theory |
| Speaker: Amanda Folsom of Yale University |
| Contact: TBA |
| Date: 2011-12-06 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: In this talk I will discuss the role of mock theta functions, which are certain peculiar $q$-series, as a liaison between modular forms and the representation theory of affine lie algebras. The mock theta functions in their most classical guises date back to the first part of the 20th century, however their roles within mathematics and number theory are still being discovered. Relating modular forms and representation theory is just one of the their many interesting facets. We will introduce the modular theory surrounding mock theta functions, and discuss their relationship to characters associated to affine Lie superalgebras due to Kac and Wakimoto. |
| Title: Anabelian geometry and obstructions to solving equations |
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| Colloquium: N/A |
| Speaker: Kirsten Wickelgren of Harvard University |
| Contact: Emily Hamilton, emh@mathcs.emory.edu |
| Date: 2011-12-06 at 4:00PM |
| Venue: W306 |
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| Abstract: Grothendieck's anabelian conjectures say that hyperbolic curves over certain fields should be $K(pi,1)$'s in algebraic geometry. It follows that conjecturally the solutions to equations defining such a curve are the sections of etale $pi_1$ of the structure map. These conjectures are analogous to equivalences between fixed points and homotopy fixed points of Galois actions on related topological spaces. This talk will start with an introduction to the etale fundamental group, Grothendieck's anabelian conjectures, and their topological analogues, and then present a 2 nilpotent real section conjecture. |
| Title: Rays and Souls on von Mangoldt Planes |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Eric Choi of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-11-29 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Knowledge of rays and critical points of infinity in von Mangoldt planes can be applied to understanding the structure of open complete manifolds with lower radial curvature bounds. We will show how the set of souls is computed for every von Mangoldt plane of nonnegative curvature. We will also make some observations on the structure of the set of critical points of infinity for von Mangoldt planes with negative curvature. |
| Title: Geometric methods for Lens Design |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Vladimir Oliker of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-11-22 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: This is a continuation of an earlier talk by H. Palta. I will discuss an alternative approach to the problem of lens design. |
| Title: It Doesn’t Work Like that! Computers in the Movies and on TV |
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| Seminar: EUMMA Undergrad Talk |
| Speaker: Dr. Valerie Summet of Emory University |
| Contact: Erin Nagle, erin@mathcs.emory.edu |
| Date: 2011-11-17 at 6:00PM |
| Venue: MSC W301 |
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| Abstract: |
| Title: It doesn't work like that!: Computers in the Movies and on TV |
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| EUMMA Talk: N/A |
| Speaker: Valerie Summet of Emory University |
| Contact: Erin Nagle, erin@mathcs.emory.edu |
| Date: 2011-11-17 at 6:00PM |
| Venue: MSC W301 |
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| Abstract: |
| Title: Gaussian Markov Random Field Priors and MCMC for Inverse Problems |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Johnathan Bardsley of Department of Mathematical Sciences, University of Montana |
| Contact: Jim Nagy, nagy@mathcs.emory.edu |
| Date: 2011-11-16 at 12:50PM |
| Venue: W306 |
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| Abstract: In this talk I will explore the connections between Bayesian statistics and inverse problems. In particular, I will show how familiar quadratic regularization functions can be viewed as prior probability densities arising from Gaussian Markov Random Fields (GMRFs). GMRFs, in turn, correspond to concrete probabilistic assumptions regarding the value of the unknown image at a specific pixel based on the value of its neighbors. With a GMRF prior in hand, I will then show how to perform MCMC sampling of the unknown image and of the noise and prior precision values. The image sampling step is a large-scale structured linear algebra problem that has seen little attention by the numerical linear algebra community. The samples outputted by the MCMC method can be used to compute a reconstructed image, e.g. the sample mean, as well as estimates of the precision parameters, which can in turn be used to estimate the regularization parameter. |