All Seminars
| Title: Quadratic forms over function fields of p-adic curves |
|---|
| Colloquium: Algebra |
| Speaker: Suresh Venapally of Emory University |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-26 at 4:00PM |
| Venue: MSC W201 |
| Download Flyer |
| 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 |
|---|
| 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 |
| Download Flyer |
| 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 |
|---|
| 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 |
| Download Flyer |
| 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 |
|---|
| 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 |
| Download Flyer |
| 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. |
| Title: Kac-Wakimoto characters and mock theta functions |
|---|
| Colloquium: Algebra |
| Speaker: Amanda Folsom of University of Wisconsin, Madison |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-12 at 4:00PM |
| Venue: MSC W201 |
| Download Flyer |
| Abstract: In this talk I will discuss the role of certain "strange" functions called "mock theta functions" as a liaison between two different areas of mathematics: modular forms, which are complex analytic functions with certain symmetries, and the representation theory of a large class of lie algebras. Despite their "strange" appearance, the mock theta functions in their most classical guises date back to the first part of the 20th century, however their roles in mathematics were not well understood. Only within the last 7 years have we finally begun to understand and develop a greater theory around the mock theta functions in mathematics - relating modular forms and representation theory is just one of their many interesting facets. This talk is intended to be an introduction to this theory. |
| Title: Designing lenses with help from geometry and optimal transport |
|---|
| Seminar: Analysis and Differential Geometry |
| Speaker: Vladimir Oliker of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-02-09 at 4:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: This is a continuation (and, hopefully, conclusion) of the report on the topic discussed in previous two seminars. |
| Title: Generalized Borcherds Products and Two number theoretic applications |
|---|
| Colloquium: Algebra |
| Speaker: Ken Ono of University of Wisconsin at Madison |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-08 at 3:00PM |
| Venue: MSC W201 |
| Download Flyer |
| Abstract: In his 1994 ICM lecture, Borcherds famously introduced an entirely new concept in the theory of modular forms. He established that modular forms with very special divisors can be explicitly constructed as infinite products. Motivated by problems in geometry, number theorists recognized a need for an extension of this theory to include a richer class of automorphic form. In joint work with Bruinier, the speaker has generalized Borcherds's construction to include modular forms whose divisors are the twisted Heegner divisors introduced in the 1980s by Gross and Zagier in their celebrated work on the Birch and Swinnerton-Dyer Conjecture. This generalization, which depends on the new theory of harmonic Maass forms, has many applications. The speaker will illustrate the utility of these products by resolving open problems on the following topics: 1) Parity of the partition function 2) Birch and Swinnerton-Dyer Conjecture and ranks of elliptic curves. |
| Title: Mathematical Approaches to Two Problems Related to Intravascular Blood |
|---|
| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Aaron Fogelson of University of Utah |
| Contact: Alessandro Veneziani, ale@mathcs.emory.edu |
| Date: 2010-02-04 at 2:30PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: Damage to the lining of a blood vessel triggers the intertwined processes of platelet aggregation and coagulation that result in the formation of a thrombus (clot) at the injury site. The thrombus itself is made up of platelets adherent to the vessel and to one another, and of a fibrin protein gel surrounding and between the platelets. An enzyme thrombin is critical to both platelet deposition and to fibrin gelation and is produced by a complex network of reactions on the vascular surface, in the blood plasma, and on the surfaces of platelets. This process happens under flow and, in turn, can strongly influence the flow. I will present work addressing two problems related to these processes: 1) How do platelet deposition and coagulation up through thrombin production interact under flow? 2) How can the rate at which thrombin produces fibrin momoners affect the ultimate branching structure of the fibrin gel? |
| Title: Mock theta functions, q-series, combinatorial probability, and percolation models |
|---|
| Seminar: Algebra |
| Speaker: Karl Mahlburg of Princeton University |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2010-02-04 at 4:00PM |
| Venue: MSC W201 |
| Download Flyer |
| Abstract: In probabilistic percolation models (such as the Ising model for ferromagnetism), the sites of a lattice are randomly set to be active or inactive through an independent Bernoulli process. The system then evolves through simple deterministic growth rules that allow active sites to ``flow'' to inactive neighbors; for example, an inactive site may become active if at least two of its neighbors are active. These systems are very interesting due to the fact that they possess critical behavior, which means that there is a sharp density cutoff below which the system experiences very little growth, and above which almost every site is likely to eventually become active. Furthermore, as the size of the lattice grows to infinity, the critical probability approaches zero, and the critical window follows a finite-size (threshold) scaling relationship in this limit. Amazingly, this limiting process also leads to the surprise appearance of functions of combinatorial and number theoretic interest, including Ramanujan's famous mock theta functions as well as the generating functions for partitions without sequences. The interplay between combinatorial probability, hypergeometric q-series, and automorphic forms leads to new proofs of conjectures posed by both probabilists and number theorists, involving slow convergence results for metastability thresholds and improved asymptotics for the generating functions of partitions without k-sequences. |
| Title: Chow groups of quadrics II |
|---|
| Seminar: Algebra |
| Speaker: Asher Auel of Emory University |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-02-02 at 4:00PM |
| Venue: MSC W303 |
| Download Flyer |
| Abstract: |