Posted February 11, 20169:00 am - 10:00 am Keisler Lounge
A Conversation with Dr. Carol Woodward (LLNL)
Posted February 9, 201611:00 am - 12:00 pm Keisler Lounge
A Conversation with Professor James Nagy (Emory University)
Posted November 2, 20151:00 pm - 5:00 pm Sunday, March 13, 2016 Digital Media Center Theatre
Scientific Computing Around Louisiana (SCALA) 2016
Posted January 29, 2016
Last modified February 1, 2016
Fang-Ting Tu, National Center for Theoretical Sciences, Taiwan
Modular Forms on Shimura Curves and Hypergeometric Functions
Posted January 30, 2016
Last modified February 11, 2016
Gang Bao, Zhejiang University
Inverse Problems for PDEs: Analysis, Computation, and Applications
Abstract: Inverse problems for PDEs arise in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, near-field and nano optical imaging, and medical imaging. A model problem in wave propagation is concerned with a plane wave incident on a medium enclosed by a bounded domain. Given the incident field, the direct problem is to determine the scattered field for the known scatterer. The inverse problem is to determine the scatterer from the boundary measurements of near field currents densities. Although this is a classical problem in mathematical physics, mathematical issues and numerical solution of the inverse problems remain to be challenging since the problems are nonlinear, large-scale, and most of all ill-posed! The severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. In this talk, the speaker will first introduce inverse problems for PDEs and discuss the state of the arts of the inverse problems. Our recent progress in mathematical analysis and computational studies of the inverse boundary value problems will be reported. Several classes of inverse problems will be studied, including inverse medium problems, inverse source problems, inverse obstacle problems, and inverse waveguide problems. A novel stable continuation approach based on the uncertainty principle will be presented. By using multi-frequency or multi-spatial frequency boundary data, our approach is shown to overcome the ill-posedness for the inverse problems. New stability results and techniques for the inverse problems will be presented. Related topics will be highlighted.
Posted December 2, 2015
Last modified January 15, 2016
Mehmet Kıral, Texas A&M University
The Voronoi formula and double Dirichlet series
A Voronoi formula is an identity where on one side, there is a weighted sum of Fourier coefficients of an automorphic form twisted by additive characters, and on the other side one has a dual sum where the twist is perhaps by more complicated exponential sums. It is a very versatile tool in analytic studies of L-functions. In joint work with Fan Zhou we come up with a proof of the identity for L-functions of degree N. The proof involves an identity of a double Dirichlet series which in turn yields the desired equality for a single Dirichlet coefficient. The proof is robust and applies to L-functions which are not yet proven to come from automorphic forms, such as Rankin-Selberg L-functions.
Posted January 7, 2016
Last modified February 8, 2016
Abhijit Champanerkar, CSI NY/CUNY
Virtual Seminar: "Densities and semi-regular tilings"
Abstract: For a hyperbolic knot or link $K$ the volume density is a ratio of hyperbolic volume to crossing number, and the determinant density is the ratio of 2pilog(det(K)) to the crossing number. We explore limit points of both densities for families of links approaching semi-regular biperiodic alternating links. We explicitly realize and relate the limits for both using techniques from geometry, topology, graph theory, dimer models, and Mahler measure of two-variable polynomials. This is joint work with Ilya Kofman and Jessica Purcell.
Posted February 11, 20163:30 pm - 4:20 pm Lockett 277
Thomas Parker, Michigan State University
Holomorphic curves, strings, and the GV conjecture
This is a talk on counting solutions of non-linear elliptic PDEs. After presenting the basic idea, I will explain, from two completely different perspectives, how the search for simple examples leads -- rather surprisingly -- to considering holomorphic maps into Calabi-Yau 3-folds X. Such maps are counted by the Gromov-Witten invariants of X, which are an infinite set of rational numbers. In 1998, physicists R. Gopakumar and C. Vafa conjectured that these Gromov-Witten invariants have a hidden structure: they are obtained, by a specific transform, from a set of more fundamental "BPS numbers", which are integers. The talk will conclude with a pictorial proof of the GV conjecture (joint work with E. Ionel) based on the idea of using deformations of almost complex structures to count the contributions of "clusters of curves".