All Seminars
| Title: Eta-quotients and theta functions |
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| Seminar: Algebra and number theory |
| Speaker: Robert Lemke Oliver of Emory University |
| Contact: Ken Ono, ono@mathcs.emory.edu |
| Date: 2010-11-09 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: The Jacobi Triple Product Identity gives a closed form for many infinite product generating functions that arise naturally in combinatorics and number theory. Of particular interest is its application to Dedekind's eta-function $\eta(z)$, defined via an infinite product, giving it as a certain kind of infinite sum known as a theta function. Using the theory of modular forms, we classify all eta-quotients that are theta functions. |
| Title: Special values of function field Dirichlet L-functions |
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| Seminar: Algebra |
| Speaker: Matt Papanikolas of Texas A\&M University |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2010-11-02 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: Similar to Euler's formula that values of the Riemann zeta function at positive even integers are rational multiples of powers of pi, one knows that values of Dirichlet L-functions at positive integers are also expressible in terms of powers of pi and values of polylogarithms at algebraic numbers. In this talk we will focus on finding analogies of these results over function fields of positive characteristic. In particular, we will consider special values of Goss L-functions for Dirichlet characters, which take values in the completion of the rational function field in one variable over a finite field. Building on work of Anderson for the case of L(1,chi), we deduce various power series identities on tensor powers of the Carlitz module that are "log-algebraic" and in turn use these formulas to determine exact values of L(n,chi) for arbitrary n > 0. Moreover, we relate these L-series values to powers of the Carlitz period and values of Carlitz polylogarithms at algebraic points. |
| Title: Celebration of Mind - The Mathematics, Magic and Mystery of Martin Gardner |
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| Seminar: Combinatorics |
| Speaker: Colm Mulcahy of Spelman College |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-10-29 at 4:00PM |
| Venue: W306 |
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| Abstract: Martin Gardner (1914-2010) "brought more mathematics to more millions than anyone else," according to Elwyn R. Berlekamp, John H. Conway and Richard K. Guy. Who was this man, how was he so influential, and will his legacy matter in the 22nd century? We'll try to answer these questions. This event is part of a global celebration this month of the life of Martin Gardner. \\ \\ See www.g4g-com.org and www.spelman.edu/~colm |
| Title: Metanumerical computing for partial differential equations: the Sundance project |
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| Seminar: Scientific Computing |
| Speaker: Robert Kirby of Department of Mathematics and Statistics, Texas Tech University |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2010-10-28 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Metanumerical computing deals with computer programs that use abstract mathematical structure to manipulate, generate, and/or optimize compute-intensive numerical codes. This idea has gained popularity over the last decade in several areas of scientific computing, including numerical linear algebra, signal processing, and partial differential equations. The Sundance project is such an example, using high-level software-based differentiation of variational forms to automatically produce high-performance finite element implementations, all within a C++ library. In addition to automating the discretization of PDEs by finite elements, recent work is demonstrating how to produce block-structured matrices and streamline the implementation of advanced numerical methods. I will conclude with some examples of this for some incompressible flow problems. |
| Title: The special fiber of a parahoric group scheme |
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| Seminar: Algebra and number theory |
| Speaker: George McNinch of Tufts University |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2010-10-26 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: Let $G$ be a connected and reductive algebraic group over the field of fractions $K$ of a complete discrete valuation ring $A$ with residue field $k$. Bruhat and Tits have associated with $G$ certain smooth $A$-group schemes $P$ --- called parahoric group schemes --- which have generic fiber $P/K = G$. The special fiber $P/k$ of such a group scheme is a linear algebraic group over $k$, and in general it is not reductive. In some recent work, it was proved that $P/k$ has a Levi factor in case $G$ splits over an unramified extension of $K$. Even more recently, this result was (partially) extended to cover the case where G splits over a tamely ramified extension. The talk will discuss these results and some applications. In particular, it will mention possible applications to the description of the scheme-theoretic centralizer of suitable nilpotent sections in Lie$(P)(A)$. |
| Title: Directed immersions of closed manifolds |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Professor Mohammad Ghomi of Georgia Institute of Technology |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-10-26 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Given any finite subset X of the sphere $S^n, n>1$, which includes no pairs of antipodal points, we explicitly construct smooth immersions of closed hypersurfaces in Euclidean space $R^{n+1}$ whose Gauss map misses X. In particular, this answers a question of Gromov. |
| Title: Computing and Autism: A role for technology and technologists |
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| Seminar: Computer Science |
| Speaker: Professor Gregory Abowd of Georgia Institute of Technology |
| Contact: Valerie Summet, valerie@mathcs.emory.edu |
| Date: 2010-10-22 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Within the past two decades, autism has gone from being a hidden condition to a rather prominent phenomenon. Almost everyone knows someone impacted by autism, and I am no exception. I have two boys on the autism spectrum, and this experience has driven me to consider how information technology research can play a role in understanding and supporting the many challenges individuals and our society faces. In this talk, I will give an overview of my research in this area. This is not simply a feel good story of one researcher doing work to benefit himself and others. It is a story of how to connect life's real challenges to the work computing researchers do without having to sacrifice a career, or the career of others. I will present a human-centered research agenda with deep ties into areas of computer science, an agenda I hope will cause others to rethink how to motivate their own work. Gregory Abowd is a Distinguished Professor in the School of Interactive Computing and the W. George Professor and Director of the Health Systems Institute at the Georgia Institute of Technology. His research since 1994 has been in the area of ubiquitous computing, and he has attempted to create living laboratories of this third generation of computing in offices, classrooms, and homes. Some of his major project efforts are Classroom 2000 and the Aware Home Research Initiative. Over the past decade, he has focused on problems relating to home and health, with a particular emphasis on technology and autism. He is an ACM Fellow and member of the CHI Academy. In 2007, he received the ACM SIGCHI Social Impact Award and in 2009, he received the ACM Eugene Lawler Humanitarian Award. |
| Title: More-part Sperner Families and Transversals |
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| Seminar: Combinatorics |
| Speaker: Peter Erdos of A. Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2010-10-22 at 4:00PM |
| Venue: W306 |
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| Abstract: In this talk we give a short (and far from complete) survey of developments on the theory of more-part Sperner problems over the past 5 years. A complete list of all maximum 2-part Sperner families will be reported. We also will discuss the connection of these problems with (generalized) transversals. Finally some consequences for mixed orthogonal arrays will be presented. |
| Title: Quadratic field, cubic equation and the first derivative of L-functions |
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| Seminar: Algebra and Number Theory |
| Speaker: Wei Zhang of Harvard University |
| Contact: Zachary Kent, kent@mathcs.emory.edu |
| Date: 2010-10-21 at 3:00PM |
| Venue: MSC E408 |
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| Abstract: There has been a long history on how to construct all rational solutions of cubic equations of two variables like $y^2=4x^3+ax+b$. We will see how imaginary quadratic fields, together with the study of some L-functions, can be used to partially solve the question. We will also mention some recent progress that leads us to a broader perspective. |
| Title: EUMMA-Graduate Student Panel |
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| Seminar: N/A |
| Speaker: Dr. Yang, Dr. Summet of Emory University |
| Contact: Jodi-Ann Wray, jcwray@emory.edu |
| Date: 2010-10-20 at 7:00PM |
| Venue: MSC W301 |
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| Abstract: |