All Seminars
| Title: On Serre-Grothendieck and Purity conjectures for groups of type $F_4$ |
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| Seminar: Algebra |
| Speaker: Vladimir Chernousov of University of Alberta |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-03-16 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The Grothendieck-Serre conjecture asserts that for a reductive group $G$ over a smooth affine scheme $X$ a rationally trivial $G$-torsor is trivial in Zariski topology or more generally if $R$ is a regular local ring and $G$ is a reductive group scheme over $R$ then the natural mapping $f:H^1(R,G)\to H^1(K,G)$ has trivial kernel. Here $K$ is a fraction field of $R$. The image of $f$ is described by the purity conjecture which says that a $G$-torsor over $K$ is in the image of $f$ if and ony if it is unramified everywhere in codimension $1$. These two conjectures are known for many groups of classical types and type $G_2$. In my talk we discuss next open case of groups of type $F_4$. |
| Title: Weakly quasirandom hypergraphs |
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| Seminar: SIAM Student Chapter |
| Speaker: Mathias Schacht of Emory University |
| Contact: Vojtech Rodl, rodl@mathcs.emory.edu |
| Date: 2010-03-15 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: We consider quasi-random properties of $k$-uniform hypergraphs. The central notion is uniform edge distribution with respect to large vertex sets. We find several equivalent characterisations of this property and this work can be viewed as a natural extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs.\\ \\ Those charecterisation for hypergraphs have an interesting consequence for the theory of quasi-random graphs. Let $K_k$ be the complete graph on $k$ vertices and let $M(k)$ be the line graph of the graph of the $k$-dimensional hypercube. We show that the pair of graphs $(K_k,M(k))$ has the following property: if the number of copies of both $K_k$ and $M(k)$ in another (large) graph $G$ are as expected in the random graph of density $d$, then $G$ is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to $d$. Those pairs of non-bipartite graphs with this property. |
| Title: American Mathematics from Approximate Nullity to the Verge of Parity with Europe, 1890-1913 |
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| Graduate Student Seminar: History Of Mathematics |
| Speaker: Steve Batterson of Emory University |
| Contact: Pascal Philipp, pphilip@emory.edu |
| Date: 2010-03-03 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: |
| Title: On the Near-Field Reflector Problem and Optimal Transport |
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| Dissertation Defense: Analysis and Differential Geometry |
| Speaker: Tobias Graf of Emory University |
| Contact: Tobias Graf, tgraf2@emory.edu |
| Date: 2010-03-02 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We will discuss the connection between optimal transport and the near-field reflector problem. In the near-field reflector problem, we are given a point source of light with some radiation intensity and a target set at a finite distance. The design problem consists of constructing a reflector that reflects the rays emitted by the source so that a given irradiance distribution on the target is produced. \\ \\ In recent years, the optimal transport framework has been applied successfully to various open problems in the design of free-form lenses and reflectors. In this talk, we will investigate the near-field problem in this context. In particular, we will see that the notion of a weak solution to the near-field problem as an envelope of ellipsoids of revolution leads to a generalized Legendre transform. Aside from some interesting properties of this transform, it also gives rise to a variational problem that is naturally associated with the near-field reflector problem. Furthermore, the resulting variational problem resembles a generalized optimal transport problem and exhibits interesting analogies to other optimal transport problems arising in optical design and geometry, particularly to the far-field reflector problem. However, we will see that for the near-field problem the solutions to the associated variational problem do not solve the reflector problem in general. This is in strong contrast to the problems that have been studied previously in the optimal transport framework. Interestingly, we can still establish a connection between the solutions to the near-field problem and the variational problem. In particular, for discrete target sets we will present an approximation result, which shows that under a suitable choice of the admissible set the variational solution produces an irradiance distribution arbitrarily close to the prescribed irradiance distribution. |
| Title: A cryptic letter to Thomas Jefferson |
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| Public lecture: N/A |
| Speaker: Lawren Smithline of Center for Communications Research, Princeton |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2010-03-02 at 7:00PM |
| Venue: MSC E208 |
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| Abstract: On Christmas Day, 1801, Thomas Jefferson received a letter from University of Pennsylvania professor Robert Patterson. The last page of the letter was written using the cipher described in the earlier pages, and Patterson withheld the key, writing, ``I may safely defy the united ingenuity of the whole human race to decypher [such writing] to the end of time." The first successful cryptanalysis was done by the speaker in 2007. This talk will describe Patterson's cipher, its place in history, and its solution. This talk is co-sponsored by the Hightower Fund and by the Department of Mathematics and Computer Science. |
| Title: The Riemannian Penrose inequality revisited |
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| Colloquium: Analysis and Differential Geometry |
| Speaker: Professor Gilbert Weinstein of University of Alabama at Birmingham |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-02-26 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: We present an alternative proof of the Riemannian Penrose inequality using a different conformal flow based on the conformal Laplacian instead of the Laplacian used in H. Bray's original argument. The flow fixes the mass and increases the area of the outermost horizon rather than vice versa. Our main motivation for this modified argument is our plan to adapt it to prove a version of the Riemannian Penrose inequality taking charge into account. A counter example we previously constructed shows that Bray's original argument is not suitable to prove this charged version of the inequality. |
| Title: Quadratic forms over function fields of p-adic curves |
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| Colloquium: Algebra |
| Speaker: Suresh Venapally of Emory University |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-26 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Let Qp be the p-adic completion of the field of rational numbers Q at the discrete valuation given by a prime p. Every quadratic form in 5 variables over Qp has a non-trivial zero. It has been a long standing open question whether every quadratic form in 9 variables over the rational function field Qp(t) over Qp has a non-trivial zero. In this talk we shall trace the history of this question as well as the current status. |
| Title: Deformations of unbounded convex bodies and hypersurfaces |
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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: 2010-02-23 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We study the topology of the space K of complete convex hypersurfaces of n-dimensional Euclidean space which are homeomorphic to a hyperplane. In particular, using Minkowski sums, we construct a deformation retraction of K onto the Grassmannian space of hyperplanes. So every hypersurface in K may be flattened in a canonical way. Further, the total curvature of each hypersurface evolves continuously and monotonically under this deformation. We also show that, modulo proper rotations, the subspaces of K consisting of smooth, strictly convex, or positively curved hypersurfaces are each contractible, which settles a question of H. Rosenberg. |
| Title: Leveraging Grid Technologies in Imaging Based Clinical Trials |
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| Seminar: Computer Science |
| Speaker: Ashish Sharma of Center for Comprehensive Informatics Emory University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2010-02-19 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Imaging has evolved into a routine modality in clinical and biomedical research, as well as becoming a major biomarker in clinical trials. Both these domains however pose their own set of challenges spanning data locality, size and interpretation. Complicating this is the multitude of standards and proprietary systems that are used in data acquisition and interpretation. In this talk I'll be presenting some of our recent work in leveraging technologies such as grid services to facilitate the various use cases from both clinical research and trial domains. Finally a lot of this work has been accomplished under the NCI caBIG Imaging Workspace and I'll also talk about the work that has been done by that community. Bio: Ashish Sharma is an Assistant Professor in the Dept of Biomedical Engineering and a Sr. Systems Architect in the Center for Comprehensive Informatics. His research is in the areas of medical imaging, imaging and clinical informatics, massive data processing, scientific visualization and grid computing. Recent research projects have included the application of grid computing in medical imaging, image analysis of microscopy data, multi-resolution image processing, graph algorithms for analyzing material properties and scientific visualization of massive datasets on highly immersive and interactive systems. |
| Title: Twin primes for elliptic curves |
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| Colloquium: Algebra |
| Speaker: Alina Carmen Cojocaru of University of Illinois at Chicago |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-16 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The classical twin prime conjecture states that there are infinitely many primes p such that p + 2 is also a prime. Though still unproven, the twin prime conjecture has generated many important developments in the theory of numbers. Motivated by elliptic curve cryptography, in 1988 Neal Koblitz formulated an analogue of this conjecture in the context of elliptic curves. The talk will focus on partial results concerning Koblitz's Conjecture. In particular, it will focus on a recent result of A. Balog (Budapest), C. David (Montreal) and the speaker stating that, for ``most'' elliptic curves over Q, Koblitz's Conjecture is indeed true. |