Mathematical Physics and Harmonic Analysis Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

01/27 1:50pm 
BLOC 302 
Gaik Ambartsoumian University of Texas at Arlington 
On integral geometry using objects with corners
Integral geometry is dedicated to the study of integral transforms mapping a function (or more generally, a tensor field) defined on a manifold to a family of its integrals over certain submanifolds. A classical example of such an operator is the Radon transform, mapping a function to its integrals over hyperplanes. Generalizations of that transform integrating along smooth curves and surfaces (circles, ellipses, spheres, etc) have been studied at great length for decades, but relatively little attention has been paid to transforms integrating along nonsmooth trajectories. This talks will discuss some recent results about Radontype transforms that have a “corner” in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc). 

02/03 1:50pm 
BLOC 302 
Patricia Ning TAMU 
Mosco Convergence of Dirichlet Forms on Machine Learning Gibbs Measures
The MetropolisHastings (MH) algorithm as the most classical MCMC algorithm, has had a great influence on the development and practice of science and engineering. The behavior of the MH algorithm in highdimensional problems is typically investigated through a weak convergence result of diffusion processes. In this paper, we introduce Mosco convergence of Dirichlet forms in analyzing the MH algorithm on large graphs, whose target distribution is the Gibbs measure that includes any probability measure satisfying a Markov property. The abstract and powerful theory of Dirichlet forms allows us to work directly and naturally on the infinitedimensional space, and our notion of Mosco convergence allows Dirichlet forms associated with the MH Markov chains to lie on changing Hilbert spaces. Through the optimal scaling problem, we demonstrate the impressive strengths of the Dirichlet form approach over the standard diffusion approach. 

02/24 1:50pm 
BLOC 302 
Eitan Tadmor University of Maryland 


03/03 1:50pm 
BLOC 302 
Alejandro Aceves SMU 


03/03 4:00pm 
TBA 
Lim Yen Kheng Xiamen University Malaysia 
Solving physics problems from the perspective of (tropical) algebraic geometry
In the first part of the talk, it will be shown how the partition function in statistical mechanics can be interpreted as an algebraic variety. In accordance to earlier literature, the zerotemperature limit is equivalent to taking the tropical limit of the algebraic variety. Previous literature have also generalised the temperature parameter to an nvector. Here, we show that in the case of n=2, the two components of this generalised quantity are the inverse temperature and inverse temperature times chemical potential, respectively. Other values of n can also be similarly interpreted as various intensive thermodynamic parameters.
The second part of the talk concerns null geodesics in four dimensional spacetimes. In particular, we observe that the condition for null circular orbits defines an Adiscriminantal variety. A theorem by Rojas and Rusek for Adiscriminants leads to the interpretation that there are two branches of null circular orbits for certain classes of spacetimes. A physical consequence of this theorem is that light rings around generic black holes with nondegenerate horizons are unstable. [Joint work with Mounir Nisse]


03/31 1:50pm 
BLOC 302 
Terry Harris Cornell University 
TBA 

04/07 1:50pm 
BLOC 302 
Nestor Guillen Texas State University 
TBA 

04/14 1:50pm 
BLOC 302 
Yulia Yershova TAMU 
TBA 
The organizers for this seminar are
Bob Booth
and
Rodrigo Matos.
Email them with talk suggestions and to request the Zoom link.