All Seminars
| Title: IBM’s Watson: From a Modest DeepQA Machine To a Formidable Jeopardy! |
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| Colloquium: Computer Science |
| Speaker: Dr. Bill Murdock of IBM's Watson Research Center |
| Contact: Valerie Summet, valerie@mathcs.emory.edu |
| Date: 2011-02-16 at 3:00PM |
| Venue: White Hall 207 |
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| Abstract: Watch IBM’s Watson on Jeopardy! compete against two of its most successful and celebrated contestants -- Ken Jennings and Brad Rutter on February 14 and 15. Then come hear Dr. Bill Murdock provide an overview of the road to Watson becoming a formidable contestant on Jeopardy! The game of Jeopardy! makes great demands on its players – from the range of topical knowledge covered to the nuances in language employed in the clues. Can the analytical power of a computer system – normally accustomed to executing precise requests – overcome these obstacles? Can the troves of knowledge written in human terms become searchable by a machine in order to deliver a single, precise answer? Can a quiz show help advance science? We’ll find out! Bill Murdock helps Watson distinguish correct answers from wrong answers by building components that apply logic, learning, and analogy to the results of natural language processing. J. William Murdock is a member of the DeepQA research team in IBM's Watson Research Center. He has been working on the IBM Jeopardy! challenge since the initial feasibility study for the project in 2006. He developed many of the DeepQA components used in the Watson question answering system, particularly in the areas of typing answers and evaluating evidence from passages. In 2001, he received a Ph.D. in Computer Science from Georgia Tech. He worked as a post-doc with David Aha at the United States Naval Research Laboratory. His research interests include natural-language semantics, analogical reasoning, knowledge-based planning, machine learning, and self-aware artificial intelligence. |
| Title: Hyperelliptic curves, L-polynomials, and random matrices |
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| Seminar: Algebra |
| Speaker: Andrew Sutherland of Massachusetts Institute of Technology |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2011-02-15 at 3:00PM |
| Venue: W306 |
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| Abstract: For a smooth projective curve C/Q, the zeta function $Z(C/F_p;T)$ is a rational function whose numerator $L_p(T)$ encodes arithmetic data attached to the curve. We consider the distribution of normalized L-polynomials of C as p varies over primes where C has good reduction. For a typical hyperelliptic curve of genus g, the Katz-Sarnak model implies that this distribution matches the distribution of characteristic polynomials of random matrices in the unitary symplectic group $USp(2g)$, which may be viewed as a generalization of the Sato-Tate conjecture. But there are many atypical cases: in genus 2 we already find 27 exceptional distributions. I will describe the large scale numerical experiments (involving more than 10 billion curves) that eventually led to a theoretical model that explains all of the exceptional distributions that have been observed in genus 2, and predicts that there are no others. Some key computational tools include: fast group operations in the Jacobian (borrowed from cryptography), and a method to quickly classify unknown distributions by approximating their moment sequences. This is joint work with Kiran Kedlaya. |
| Title: Explicit modular approaches to generalized Fermat equations |
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| Colloquium: Number Theory |
| Speaker: David Brown of University of Wisconsin - Madison |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2011-02-14 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Let $a,b,c \geq 2$ be integers satisfying $1/a + 1/b + 1/c > 1$. Darmon and Granville proved that the generalized Fermat equation $x^a + y^b = z^c$ has only finitely many coprime integer solutions; conjecturally something stronger is true: for $a,b,c \geq 3$ there are no non-trivial solutions and for $(a,b,c) = (2,3,n)$ with $n \geq 10$ the only solutions are the trivial solutions and $(\pm 3,-2,1)$ (or $(\pm 3,-2,\pm 1)$ when n is even). I'll explain how the modular method used to prove Fermat's last theorem adapts to solve generalized Fermat equations and use it to solve the equation $x2 + y3 = z^{10}$. |
| Title: MCDB: The Monte Carlo Database System |
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| Seminar: Computer Science |
| Speaker: Chris Jermaine of Rice University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-02-11 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Analysts working with large data sets often use statistical models to "guess" at unknown, inaccurate, or missing information associated with the data stored in a database. For example, an analyst for a manufacturer may wish to know, "What would my profits have been if I'd increased my margins by 5% last year?" The answer to this question naturally depends upon the extent to which the higher prices would have affected each customer's demand, which is undoubtedly guessed via the application of some statistical model. In this talk, I'll describe MCDB, which is a prototype database system that is designed for just such a scenario. MCDB allows an analyst to attach arbitrary stochastic models to the database data in order to "guess" the values for unknown or inaccurate data, such as each customer's unseen demand function. These stochastic models are used to produce multiple possible database instances in Monte Carlo fashion (a.k.a. "possible worlds"), and the underlying database query is run over each instance. In this way, fine-grained stochastic models become first-class citizens within the database. MCDB can be used for diverse tasks such as risk assessment and large-scale, data-driven simulation. |
| Title: On division algebras having the same maximal subfields |
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| Seminar: Algebra and number theory |
| Speaker: Andrei Rapinchuk of University of Virginia |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-02-08 at 3:00PM |
| Venue: W306 |
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| Abstract: The talk will be built around the following question: let $D_1$ and $D_2$ be two central quaternion division algebras over the same field $K$; when does the fact that $D_1$ and $D_2$ have the same maximal subfields imply that $D_1$ and $D_2$ are actually isomorphic over $K$? I will discuss the motivation for this question that comes from the joint work with G.~Prasad on length-commensurable locally symmetric spaces, and will then talk about some available results. One of the results (joint with I.~Rapinchuk) states that if the answer to the above question is positive over a field $K$ (of characteristic not 2) then it is also positive over any finitely generated purely transcendental extension of $K$. I will also discuss some generalizations to algebras of degree $> 2$. |
| Title: Ricci solitons and warped product Einstein metrics. |
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| Seminar: Analysis and Differential Geometry |
| Speaker: William Wylie of University of Pennsylvania |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2011-02-08 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: One of the fundamental questions in geometry is, given a space what is the "best" geometry we can put on it? In the context of Riemannian geometry, the Ricci flow is a tool that has produced a number of exciting recent breakthroughs in understanding this basic question. Ricci solitons appear prominently in some of these developments as singularity models for the flow and as natural new candidates for optimal geometries. On the other hand, gradient Ricci solitons also have a natural interpretation in terms of Riemannian manifolds with measure. In this talk we will explore this second perspective and discuss some recent classification results that have arisen from this viewpoint.. A natural connection between gradient Ricci solitons and warped product Einstein metrics also arises and we will discuss some recent developments in understanding this connection. |
| Title: Computational models and challenges in tokamak fusion reactors |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Alfredo Portone of Analysis and Codes Group Fusion for Energy |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2011-02-04 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The aim of this presentation is twofold. Firstly the key concepts about magnetic fusion with tokamaks are introduced by focusing the attention on the key dimensioning parameters as well as on the basic operational principles of a tokamak reactor. In the second part of the talk the main models used in tokamak plasmas simulation and in the most challenging engineering problems are presented. With respect to tokamak plasmas the MHD approximations and models are introduced (e.g. single fluid MHD, ideal MHD, etc.). The attention is then focused to the key problem of magnetic equilibrium and stability computation. As far as the engineering applications are concerned, three areas of interested are discussed, namely (1) the computation of transient electromagnetics in the metallic structures surrounding the plasma, (2) the stability problem of low-temperature superconductors and (3) the main features in 14 MeV neutron shielding. |
| Title: The fractional version of Hedetniemi's Product Conjecture - Part 2 |
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| Seminar: Combinatorics |
| Speaker: Dwight Duffus of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-02-04 at 4:00PM |
| Venue: W306 |
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| Abstract: Recently Xuding Zhu has verified the fractional version of Hedetniemi's conjecture that the chromatic number of the product of two n-chromatic graphs is n-chromatic. This settles a conjecture of Burr, Erdos and Lovasz on chromatic Ramsey numbers. In this second talk, we will see how the second conjecture follows and outline the proof of Zhu's result. |
| Title: Mini-Apps for Modern Architectures |
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| Seminar: Scientific Computing |
| Speaker: Benjamin Bergen of Los Alamos National Laboratory |
| Contact: James Nagy, nagy@compute.mathcs.emory.edu |
| Date: 2011-02-02 at 12:50PM |
| Venue: W306 |
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| Abstract: A mini-app is a simulation code that captures the fundamental complexity of some aspect of a full-scale solver. For classified applications, this is advantageous because the mini-app may be shared with vendors or academics, while the original code may not. In this presentation, we describe such a mini-app that is designed to capture the cardinal aspects of an Adaptive Mesh Refinement (AMR) framework for multi-physics problems in astrophysics and weapons science. The approach introduced here can be classified as block-structured AMR with the addition of a novel data decomposition technique that helps address many of the issues that arise when considering the challenges of exascale computing, e.g., fault tolerance, data migration--for load balancing--and adaptability to accelerated architectures. The work discussed in this presentation will be in the context of a multi-physics solver for radiation hydrodynamics simulations to help us better understand Inertial Confinement Fusion (ICF) experiments underway at the National Ignition Facility (ICF) at Lawrence Livermore National Laboratory. |
| Title: Moments of zeta and L-functions |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: K. Soundararajan of Stanford University |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-02-01 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: An important theme in number theory is to understand the values taken by the Riemann zeta-function and related L-functions. While much progress has been made, many of the basic questions remain unanswered. I will discuss what is known about this question, explaining in particular the work of Selberg, random matrix theory and the moment conjectures of Keating and Snaith, and recent progress towards estimating the moments of zeta and L-functions. |