MenuEvents for 01/27/2023 from all calendars
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 302
Speaker: Gaik Ambartsoumian, University of Texas at Arlington
Title: On integral geometry using objects with corners
Abstract: 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 non-smooth trajectories. This talks will discuss some recent results about Radon-type 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).
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 302
Speaker: Ayah Almousa, University of Minnesota
Title: GL-equivariant resolutions over Veronese subrings
Abstract: We construct explicit GL-equivariant minimal free resolutions of certain (truncations of) modules of relative invariants over Veronese subrings in arbitrary characteristic. The free modules in the resolution correspond to certain skew Schur modules associated to "ribbon" or "skew-hook" diagrams, and the differentials at each step are surprisingly uniform. We then utilize the uniformity of these resolutions to explicitly compute information about tensor products, Hom, and Tor between these modules and show that they also have rather simple descriptions in terms of ribbon skew-Schur modules. I will emphasize the hidden role of symmetric function theory in detecting the answer to this question and guiding our intuition to build new tools to prove our results in arbitrary characteristic. This is joint work with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert.
Free Probability and Operators
Time: 4:00PM - 5:00PM
Location: BLOC 306
Speaker: Ken Dykema, TAMU
Title: On spectral and decomposable operators in finite von Neumann algebras.
Abstract: We describe spectral and decomposable operators on Hilbert spaces and then, in the case of operators belonging to finite von Neumann algebras, relate these properties to the Haagerup-Schultz subspaces of the operators. Finally, we will examine certain such operators arising naturally in free probability theory.
