On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with vanishing boundary trace leads to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify the rate of convergence to this profile uniformly in relative error, showing the rate is either exponentially fast (with a rate constant predicted by…
AMS is hosting a workshop on Mental Health and Neurodivergence next Friday, October 22, 1:55-2:45pm. During the workshop, someone from the Counseling Center will give a presentation on diagnoses and disorders that are common among graduate students. They'll cover common symptoms, treatments, as well as if/how students with the diagnoses can be supported by the university, both within…
Beginning with the solution of the classical Plateau problem—the problem of finding an area-minimizing disk whose boundary is a prescribed simple closed curve in Euclidean 3-space—we will survey some applications of Calculus of Variations to solve geometric extremal problems. Particular emphasis will be placed on the problem of finding a smooth surface in 3-space with…
The totally positive flag variety is the subset of the complete flag variety Fl(n) where all Plücker coordinates are positive. By viewing a complete flag as a sequence of subspaces of polynomials of degree at most n-1, we can associate a sequence of Wronskian polynomials to it. I will present a new characterization of the…
Many computational problems depend on solving systems of linear equations. The Conjugate Gradient method (CG) is a widely used iterative method that solves systems of linear equations. Early termination of CG sacrifices accuracy to save computational resources. The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of CG that solves systems of linear equations…
Incommensurate stacked 2D materials have gained significant attention after the recent discovery of a new mechanism of superconductivity in systems with small twist angles. Theoretically, the electronics of such systems are studied through tight-binding models. These models can be studied in several different spaces, though momentum space is often the leading favorite for physicists because…
Presentations by: Andy Sageman-Furnas and Fatma Terzioglu During each 50-minute First Year Research Seminar, two faculty give our new graduate students a short (~20-25 minute), accessible talk about their research or research area
In general relativity, in the absence of special symmetries, there is no reasonable, nontrivial notion of mass-energy density accounting not only for all source fields but also for gravity itself. Nevertheless there are good definitions, such as the ADM mass, of the mass of an entire isolated system, modelled as an asymptotically flat space-time. Numerous…
In this talk, we first propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. To this end we introduce a dynamical system for which we prove that its trajectories asymptotically converge…
Are you interested in continuing in academia after you finish your degree? You should consider the Preparing the Professoriate program and/or the Teaching and Communications Certificate offered by NCSU! This week in the Graduate Training Module, GIST is excited to host Vanessa Doriott Anderson, Director of the Teaching and Communication Programs and Organizer of the Preparing…
Are you an undergraduate that has heard of LaTeX, but don't know how to use it? This event is for you! LaTeX is the typesetting software used by the majority of mathematicians (and several other fields) for everything from CV's, to research papers to exams. If you plan on continuing in academia, it is almost necessary…
The AMS Student Chapter and MGSA are co-hosting a Trivia Night for graduate students on Friday, October 29, 5-6:30pm. Free pizza, chips, and soda will be provided in the 4th floor lounge. We'll form teams based on MentoRings as possible, though you do not need to be in a MentoRing (or have a team already formed)…
We consider the shallow water magnetohydrodynamic (SWMHD) equations, in which multiscale phenomena appear in geophysics, astrophysics, and energy production applications. However, capturing both large and small scales numerically requires an exact treatment of the physically-observed divergence-free condition of the magnetic field and typically a very fine spatial grid. An alternative to requiring a fine spatial…
When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases…
In this talk we will introduce a new stability theory for implicit-explicit (IMEX) time integration schemes—which treat some terms in a differential equation implicitly (for stability) and others explicitly (for efficiency). Our focus will be on devising new efficient stable schemes for several fluid equations ranging from the incompressible Navier-Stokes equations, nonlinear diffusion equations, and…
The talk will begin with the reconstruction of three-dimensional bodies from their two-dimensional projections. Then I analyze the induced action of the Euclidean group on the body's projected outlines using moving frames, leading to a complete classification of the outline differential invariants and the associated outline signature of the body. Zoom invitation is sent to…
In this talk we consider the pressureless Euler system in dimension greater than or equal to two. Several works have been devoted to the search for solutions which satisfy the following adhesion or sticky particle principle: if two particles of the fluid do not interact, then they move freely keeping constant velocity, otherwise they join…
Are you an undergraduate interested in mathematical research and/or going to grad school? Doing a Research Experience for Undergraduates (REU) is an excellent opportunity to try undergraduate research and add to your CV! UUG is hosting the "What is an REU?" presentation and panel, with panelists including several previous REU attendees and an REU organizer to answer…
We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by…
There are several challenges associated with inverse problems in which the unknown parameters can be modeled as piecewise constant functions. We model the unknown parameter using multiple level sets to represent the piecewise constant function. Adopting a Bayesian approach, we impose prior distributions on both the level set functions that determine the piecewise constant regions…