The colloquium typically meets Mondays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall.
The colloquium is preceded by tea starting at 3:30 in the Faculty Lounge, adjacent to Room 617. Click on title for abstract.
Martin J. Gander, University of Geneva, Switzerland
Nick Higham, University of Manchester, UK
Abdelhamid Meziani, Florida International University
Donatella Danielli, Purdue University
Francis Bonahon, USC
The convenient formula (X+Y)^n = X^n + Y^n is (unfortunately) frequently used by our calculus students. Our more advanced students know that this relation does hold in some special cases, for instance in prime characteristic n or when YX=qXY with q a primitive n-root of unity. I will discuss similar ``miraculous cancellations’’ for 2-by-2 matrices, in the context of the quantum group U_q(sl_2).
Eduardo Teixeira, University of Central Florida
The development of modern free boundary theory has promoted major knowledge leverage across pure and applied disciplines and in this talk I will provide a panoramic overview of such endeavor. The goal of lecture, however, will be to explicate how geometric insights and powerful analytic tools pertaining to free boundary theory can be imported to investigate regularity issues in nonlinear diffusive partial differential equations. This new systematic approach has been termed non-physical free boundaries, and in the past few years has led us to a plethora of unanticipated results.
Phil Gressman, University of Pennsylvania
In the 1970s, E. Stein and other mathematicians studying fundamental questions related to pointwise convergence of Fourier series discovered surprising new links between this very old problem and the geometry of submanifolds of Euclidean space. These discoveries paved the way for many of the questions at the forefront of modern harmonic analysis. A common element in many of these areas is the role of a strange sort of curvature condition which arises naturally from Fourier-theoretic roots but is poorly understood outside the extreme cases of curves and hypersurfaces. In this talk, I will discuss recent work which combines elements of Geometric Invariant Theory, Convex Geometry, Signal Processing, and other areas to shed light on this problem in intermediate dimensions.
John Voight, Dartmouth College
A Belyi map is a finite, branched cover of the complex projective line that is unramified away from 0, 1, and infinity. Belyi maps arise in many areas of mathematics, and their applications are just as numerous. They gained prominence in Grothendieck's program of dessins d'enfants, a topological/combinatorial way to study the absolute Galois group of the rational numbers.
In this talk, we survey computational methods for Belyi maps, and we exhibit a uniform, numerical method that works explicitly with power series expansions of modular forms on finite index subgroups of Fuchsian triangle groups. This is joint work with Jeroen Sijsling and with Michael Klug, Michael Musty, and Sam Schiavone.
Jose Maria Diego Rodriguez, Instituto de Fisica de Cantabria
Dark matter is arguably one of the main mysteries in modern physics. We know how much is there, we know where it is but we don't know what it is. Despite the numerous (and expensive) efforts on Earth to directly detect the alleged and elusive dark matter particle, experimental evidence remains as elusive as the dark matter particle itself. As of today, the strongest (and only) experimental evidence for dark matter still comes from astrophysical probes. One of such probes is gravitational lensing that can be used to map the distribution of dark matter on cosmological scales. I will briefly review the most popular candidates for dark matter and focus on our research that uses gravitational lensing to rule out some of these candidates.