All Seminars
| Title: Steinberg groups for Jordan pairs |
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| Seminar: Algebra and number theory |
| Speaker: Erhard Neher of University of Ottawa |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2011-03-14 at 3:00PM |
| Venue: W306 |
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| Abstract: In this talk I will describe a concrete construction of groups via matrices or, more generally, as groups of automorphisms of certain Lie algebras and an abstract construction by generators and relations. The concrete groups in question cover most classical groups over rings. The abstract groups generalize the groups defined by Steinberg. The two types of groups are related via central extensions. The main methods to make the general constructions work come from Jordan pairs, but no prior knowledge of Jordan pairs will be assumed. |
| Title: Souls of some convex surfaces |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Eric Choi of Emory University |
| Contact: Eric Choi, echoi7@emory.edu |
| Date: 2011-03-01 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: The $soul$ of a complete, noncompact, connected Riemannian manifold $(M, g)$ of nonnegative sectional curvature is a compact, totally convex, totally geodesic submanifold such that $M$ is diffeomorphic to the normal bundle of the soul. Hence, understanding of the souls of $M$ can reduce the study of $M$ to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on $M$. In particular, little is understood about the case when $M = R^2$. Convex surfaces of revolution in $R^3$ are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces. % r_h(sis $c = r \sin \phi,$ where $\phi = \angle (\dot \g(t), \dot \sigma)$ ($\sigma$ is the meridian through $\g(t)$.). %the intervals for integration must be broken up as follows: $[r(s_1), r(s_0)), [r(s_0,$ |
| Title: EUMMA Jeopardy Night |
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| Seminar: N/A |
| Speaker: Faculty of Emory |
| Contact: Alex Carstairs, acarsta@emory.edu |
| Date: 2011-02-28 at 6:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: List Colorings of Dense Hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Alexander Kostochka of The University of Illinois at Urbana-Champaign |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-02-25 at 4:00PM |
| Venue: W306 |
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| Abstract: The {\em list chromatic number} $\chi_{\ell}(G)$ of a hypergraph $G=(V,E)$ is the minimum integer $s$ such that for every assignment of a list $L_v$ of $s$ colors to each vertex $v$ of $G$, there is a vertex coloring of $G$ in which the color of each vertex is in its list and there are no monochromatic edges. In nineties, Alon showed that the list chromatic number of every graph with average degree $d$ is at least $(0.5-o(1))\log_2 d$. In this talk, we discuss two related results by Alon and the speaker on list coloring of uniform hypergraphs. The first of them states that for $r\geq 3$, every $r$-uniform hypergraph in which at least half of the $(r-1)$-vertex subsets are contained in at least $d$ edges has list chromatic number at least $ \frac{\ln d}{(20r)^3}$. When $r$ is fixed, this is sharp up to a constant factor. In particular, $n$-vertex $r$-uniform hypergraphs may have average degree about $(n/r)^{r-2}$ and still be $2$-list-colorable. The second result concerns {\em simple} hypergraphs, that is, the hypergraphs in which any two distinct edges have at most one vertex in common. It is proved that for every fixed $r$, all $r$-uniform hypergraphs with high average degree have ``high" list chromatic number. The result implies that for any finite set of points $X$ in the plane, and for any finite integer $s$, one can assign a list of $s$ distinct colors to each point of the plane so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of $X$. |
| Title: Service-Oriented Computing: Emerging Approaches for Web-Based Software Engineering |
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| Colloquium: Computer Science |
| Speaker: M. Brian Blake of University of Notre Dame |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-02-18 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Emerging technologies facilitate an environment where web-based software or web services have well-defined, open interfaces and are discoverable across the Internet. Service-oriented computing is an emerging approach to software engineering that suggests that new specialized business processes can be created, on-demand, simply by integrating the services provided by others. However, in the real world, software developers tend to create applications that do not conform to consistent developmental practices even if they do use universal interface representations (e.g. the eXtensible Markup Language). Our research utilizes semantic approaches, enhanced syntactical methods, and contextual information to automate the integration of software services that are developed randomly from a wide array of diverse sources. This talk discusses our foundational lines of research and subsequent contributions in the areas of service discovery, composition, and evaluation. The talk will conclude with future work that leverages service-oriented paradigms in areas such as visual analytics, smart grid, and an “Internet of things”. |
| Title: Probabilistic Galois theory |
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| Colloquium: Number Theory |
| Speaker: David Zywina of University of Pennsylvania |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2011-02-17 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: A special case of Hilbert's irreducibility theorem says that a ``random" degree $n$ polynomial with integer coefficients will have the largest possible Galois group (i.e., the symmetric group on $n$ letters). Historically, the notion of ``random" used is that of natural density; the goal of this talk is to discuss alternate approaches that use legitimate probabilistic methods. This will lead us to consider random walks on certain graphs and their connection with the arithmetic of linear algebraic groups. |
| 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. |