Georgia Institute of Technology College of Sciences

The purpose of the GSC Symposium is to provide an opportunity for professors, postdocs, and graduate students in the Atlanta area to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. Certainly, the symposium is open to whole mathematics and computer sciences communities. The previous meetings were held at Emory University (2009), Georgia Institute of Technology (2010), Emory University (2011) and University of Georgia (2012). The 2013 GSC Symposium will be held at the Georgia State University campus and is organized by Alexandra Smirnova and Vladimir Bondarenko in the Department of Mathematics and Statistics, Georgia State. The following researchers have agreed to give invited plenary lectures: Hao Gao, Department of Mathematics and Computer Science, Department of Radiology and Imaging Sciences, Emory University; Guillermo Goldsztein, School of Mathematics, Georgia Institute of Technology; Yi Jiang, Department of Mathematics and Statistics, Georgia State University; Caner Kazanci, Department of Mathematics, University of Georgia; Brani Vidakovic, College of Engineering, Georgia Institute of Technology. There will be poster sessions. Anyone attending this symposium may present a poster. We especially encourage graduate students and postdocs to use this opportunity displaying their research results. Please register at the Symposium website.

Abstract: In this talk we will survey some recent developments in the scattering theory of complete, infinite-volume manifolds with ends modeled on quotients of hyperbolic space. The theory of scattering resonances for such spaces is in many ways parallel to the classical case of eigenvalues on a compact Riemann surface. However, it is only relatively recently that progress has been made in understanding the distribution of these resonances. We will give some introduction to the theory of resonances in this context and try to sketch this recent progress. We will also discuss some interesting outstanding conjectures and present numerical evidence related to these.

In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Statistical modeling amounts to specifying a set of candidates for what the probability distribution of an observed random quantity might be. Many models used in practice are of an algebraic nature in thatthey are defined in terms of a polynomial parametrization. The goal of this talk is to exemplify how techniques from computational algebraic geometry may be used to solve statistical problems thatconcern algebraic models. The focus will be on applications in hypothesis testing and parameter identification, for which we will survey some of the known results and open problems.