We improve Cheeger's lower bound for the first nonzero eigenvalue of the Laplacian on compact Riemannian manifolds with Ricci curvature bounded from below. Zoom link: https://ncsu.zoom.us/j/8027642791?pwd=d1lNaWZyUW4zeUFvaTA5VmlsTWtjdz09
Are you a math undergrad or grad student and interested in doing an internship related to math? This event is for you! The Graduate Training Module for Friday, October 8th is titled, "What is an Internship?" and consists of a panel of current graduate students who have done several different types of internships, and are ready and…
We review randomized algorithms for the numerical solution of least squares/regression problems, with a focus on algorithms that row-sketch from the left, or column-sketch from the right. These algorithms tend to be efficient and accurate on matrices that have many more rows than columns. We present probabilistic bounds for the amount of sampling required to…
I will tell you about my dissertation work on two variants of stable Grothendieck polynomials and their combinatorics. Relevant combinatorial objects include crystals (edge-labelled directed digraphs from representation theory), tableaux (numbers in boxes with rules), decreasing factorizations (numbers in parentheses), and insertion algorithms (how to put numbers in boxes). Background in algebraic combinatorics is helpful…
We consider an optimal control problem subject to a poro-visco-elastic model with applications to fluid flows through biological tissues. Our goal is to optimize the fluid pressure and solid displacement using distributed or boundary control. We discuss an application of this problem to a tissue in the human eye. Previous literature on well- posedness of…
In this talk, I will present our recent numerical methodology studies for unsteady moving interface problems and applications to dynamic fluid-structure interaction (FSI) problems. Our numerical methodologies include the body-fitted mesh method (arbitrary Lagrangian−Eulerian (ALE) method), the body-unfitted mesh method (fictitious domain (FD) method), combining with the mixed finite element approximation, as well as the…
Broadly speaking, there are two classes of inverse problems — those that are concerned with the analysis of PDEs, and those that are geometric in nature. In this talk, I will introduce the audience to these classes by highlighting two classical examples: Calderón’s problem for the PDE setting, and the boundary rigidity problem in the…
One of the major open problems in homogenization of Hamilton-Jacobi equations is to under deep properties of the effective Hamiltonian. In this talk, I will present some recent progress. In particular, consider the effective Hamiltonian associated with the mechanical Hamiltonian H(p,x)=(|p|^2)/2+V(x). We can show that for generic V, the effective Hamiltonian is piecewise 1d in…
In a non-local game, two non-communicating players cooperate to convince a referee about a strategy that does not violate the rules of the game. A quantum strategy for such a game enable players to determine their answers by performing joint measurements on a shared entangled state. In this talk we will concentrate on non-local games…
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyperparameters that define the distribution law of the model parameters is crucial. We show…
Time-delayed feedback control, attributed to Pyragas (1992 Phys. Lett. 170), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form dx/dt=f(x) has an additional term G(x(t)-x(t-T)) introduced where G is some 'gain matrix' and T a time delay. This form of the delay term is such…
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…