All Seminars
| Title: Applications and Theory of a Continuum-Mechanics-Based Immersed Boundary Method |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Dharshi Devendran of New York University |
| Contact: Michele Benzi, benzi@mathcs.emrory.edu |
| Date: 2012-01-30 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Fluid-structure interaction problems, in which the dynamics of a deformable structure is coupled to the dynamics of a fluid, are prevalent in biology. For example, the heart can be modeled as an elastic boundary that interacts with the blood circulating through it. The immersed boundary method is a popular method for simulating fluid-structure problems. The traditional immersed boundary method discretizes the elastic structure using a network of springs. This makes it difficult to use material models from continuum mechanics within the framework of the immersed boundary method. In this talk, I present a new immersed boundary method that uses continuum mechanics to discretize the elastic structure, with a finite-element-like discretization. This method is first applied to a warm-up problem, in which a viscoelastic incompressible material fills a two-dimensional periodic domain. Next, we apply the method to a three-dimensional fluid-structure interaction problem. Finally, I will present theory for this new immersed boundary method. |
| Title: Crowd-Powered Systems |
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| Seminar: Computer Science |
| Speaker: Michael Bernstein of MIT CSAIL |
| Contact: Eugene Agichtein, eugene@mathcs.emory.edu |
| Date: 2012-01-27 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: By combining machine and crowd intelligence, we can open up a broad new class of software systems that solve problems neither approach could solve alone. However, while crowds are increasingly adept at straightforward parallel tasks, they struggle with complex work because participants vary in quality, well-intentioned contributions can introduce errors, and future participants amplify and propagate those errors. I introduce techniques that decompose complex tasks into simpler, verifiable steps, and return crowd results in realtime. I use these techniques to create crowd-powered systems: interactive applications that react with a combination of human and algorithmic intelligence. These systems support goals like rewriting and shortening text, polling opinions within seconds, and taking better photographs. |
| Title: 5-Coloring Graphs on Surfaces |
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| Seminar: Combinatorics |
| Speaker: Luke Postle of Georgia Institute of Technology |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-01-25 at 3:00PM |
| Venue: W306 |
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| Abstract: Graph coloring is a much studied subfield of graph theory. Theorems concerning coloring graphs on topological surfaces, such as the Four Color Theorem or the Heawood Bound, are a useful avenue to understanding graph coloring in general. A deep theorem of Thomassen from the 1990's shows that for any surface that there are only finitely many 6-critical graphs that embed on that surface. We discuss the history of this modern approach and its realisation for small surfaces. We also give a shorter self-contained proof of Thomassen's result by showing that for any 6-critical graph G that embeds on a surface of genus $g$, that the number of vertices is at most linear in $g$. Finally, we discuss generalizations to 5-list coloring,such as a recent solution to Albertson's conjecture that a planar graph with distant precolored vertices has a 5-list-coloring. |
| Title: Degeneration and the Determinant of the Laplacian |
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| Seminar: Analysis and Differential Geometry |
| Speaker: David Sher of Stanford University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2012-01-24 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: When doing analysis on singular spaces, it is often useful to approximate them by smooth manifolds. In this spirit, we consider a family of smooth manifolds which degenerate to a manifold with a conical singularity, and analyze the behavior of various spectral-theoretic quantities under this degeneration. In particular, when we consider the behavior of the eigenvalues of the Laplacian and of the heat kernel, interesting structure becomes apparent. In this talk, I'll discuss this structure, and then discuss how it can be used to give an asymptotic expansion for the determinant of the Laplacian under conic degeneration. I'll also discuss applications and directions for further research. |
| 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. |