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Texas A&M University
Mathematics

Events for 01/24/2025 from all calendars

Algebra and Combinatorics Seminar

iCal  iCal

Time: 3:00PM - 3:50PM

Location: BLOC 302

Speaker: Frank Sottile, TAMU

Title: The phase limit set of linear spaces and discriminants

Abstract: As an amoeba is the set of lengths of points in a variety, its coamoeba is the set of angles (arguments) of its points. The set of limiting arguments forms its phase limit set. This combinatorial backbone of the coamoeba reflects the structure of the corresponding tropical variety. We give a recursive description of the phase limit set of a linear space/hyperplane complement in terms of the flats of the hyperplane arrangement. We use this to study the phase limit set of a reduced discriminant, showing that it is a union of prisms over discriminants of lower dimension. We conjecture that in dimension at least three the discriminant is a subset of its phase limit set, which implies that that coamoeba discriminant has a polyhedral structure.


Departmental Colloquia

iCal  iCal

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Genming Bai

Title: On the convergence of parametric finite element methods for geometric flows

Abstract: In this talk, we present our recent major progress in parametric finite element methods by providing the first-ever convergence proof for two long-standing open problems using a novel framework of projection error. Dziuk’s method and the Barrett–Garcke–Nurnberg (BGN) method are the two most fundamental finite element methods for discretizing geometric flows, including mean curvature flow, surface diffusion, and two-phase flow, among others. However, the rigorous justification of their convergence has remained open since they were first proposed in 1990 and 2007 respectively. The main difficulty in Dziuk’s method for mean curvature flow lies in the loss of H1 parabolicity structure in the error equation. Surprisingly, within the framework of projection error, the intrinsic orthogonality structure helps us recover H1 positive definiteness, thereby ensuring overall convergence. This framework is expected to be a new powerful tool which would help to design and analyse robust and convergent algorithms where our analysis of a stabilized version of the BGN method is the first example of this kind. We will also discuss applications such as shape optimization, simulations of bubbles and biomembranes, and front tracking of a surface in complex fluid environments. The methodologies and treatments developed in this series of works are hopeful to become standard in the future.


Free Probability and Operators

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Carl Pearcy, Texas A&M University

Title: Does the existence of nontrivial invariant subspaces imply that of nontrivial hyperinvariant subspaces for operators on Hilbert space?

Abstract: In this lecture I will discuss the status of my conjecture that operators with n.i.s. have n.h.s. and various sufficient conditions that imply that the conjecture is true