Events
Kailash Misra, NC State, Affine Lie Algebras and Crystals
SAS 1102Affine Lie algebras, also sometimes called current algebras, are infinite-dimensional analogs of finite-dimensional semisimple Lie algebras. The representation theory of affine Lie algebras has applications in many areas of mathematics (number theory, combinatorics, group theory, geometry, topology, etc.) and physics (conformal field theory, integrable systems, statistical mechanics, etc.). To study the combinatorial properties of affine Lie algebra…
Juan Villarreal Montoya, NC State, Logarithmic vertex algebras
ZoomFirst, I will make a general introduction to vertex algebras. Then, I will mention some results of recent work with Bojko Bakalov on Logarithmic vertex algebras. Jointly in person in SAS 4201 or virtually on Zoom. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to…
Ben Daniel, NC State, Analyzing a Randomized Algorithm for Rank-Revealing QR Factorizations
ZoomA rank-revealing QR factorization (RRQR) of an mxn matrix A can be an efficient alternative to the singular value decomposition. Given 1≤k<n, the problem of computing an RRQR is selecting k linearly independent columns of A. In this talk, we discuss the RRQR and present an efficient two-staged randomized algorithm to compute one. We analyze…
Cashous Bortner, NC State, Identifiabiity of Linear Compartmental Tree Models
ZoomA linear compartmental model is a linear ODE model which can be visualized by a directed graph. Identifiability is the study of determining whether a model's parameter values can be inferred from the defining "input-output equation" under perfect conditions. In this talk, I present a novel combinatorial formula for the computation of the coefficients of these…
Longfei Li, University of Louisiana at Lafayette, Numerical methods for fourth-order PDEs on overlapping grids with application to Kirchhoff-Love plates
ZoomWe propose novel numerical methods for solving a class of high-order hyperbolic PDEs on general geometries, which involve 2nd-order derivatives in time and up-to 4th-order derivatives in space. These PDEs are widely used in modeling thin-walled elastic structures such as beams, plates and shells, etc. High-order spatial derivatives together with general geometries bring a number…
Irina Kogan, NC State, Group Actions, Invariants, and Applications
ZoomI will overview some important milestones in the development of the Invariant Theory from its classical times to modern days, leading into a discussion of the current progress in theory, computation, and applications. The highlights include Hilbert's basis theorem, geometric invariant theory, differential algebra of invariants, the moving frame approach, Lie's work on symmetries of…
Differential Equations and Nonlinear Analysis Seminar: Riccardo Sacco, Politecnico di Milano, Italy, A Nonlinear Heterogeneous Transmission Model for Organic Polymer Retinal Prostheses
ZoomIn this talk we propose a model for the simulation of retinal prostheses based on the use of organic polymer nanoparticles (NP). The model consists of a nonlinearly coupled system of elliptic partial differential equations accounting for: (1) light photoconversion into free charged carriers in the NP bulk; (2) charge transport in the NP bulk…
Joseph Hoisington, University of Georgia, Calibrations and Harmonic Mappings of Rank-1 Symmetric Spaces.
ZoomWe will prove lower bounds for the p-energies of mappings of real, complex and quaternionic projective spaces to arbitrary Riemannian manifolds. The equality cases of the results for real and complex projective space give strong characterizations of some families of energy-minimizing harmonic mappings of these spaces. If we have enough time, we will also describe…
Differential Equations and Nonlinear Analysis Seminar: Gian Paolo Leonardi, University of Trento, Italy, A refined form of Cheeger’s inequality
ZoomWe 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
Cashous Bortner, NC State, “What is an Internship” Panel
ZoomAre 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…
Ilse Ipsen, NC State Randomized Algorithms for Least Squares/Regression Problems
ZoomWe 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…
Jianping Pan, NC State, Crystals, Stable Grothendieck Polynomials, and Putting Numbers In Boxes
ZoomI 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…
Sarah Strikwerda, NC State, Optimal Control in Fluid Flows through Deformable Porous Media
ZoomWe 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…
Pengtao Sun, University of Nevada, Las Vegas, Numerical Studies for Unsteady Moving Interface Problems and Applications to Fluid-Structure Interactions (FSI)
SAS 4201In 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…
CANCELLED: Tracey Balehowsky, University of Calgary, Determining a Riemannian Metric from Least-Area Data
ZoomBroadly 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…
Differential Equations and Nonlinear Analysis Seminar: Yifeng Yu, University of California – Irvine, High Degeneracy of Effective Hamiltonian in Two Dimensions
ZoomOne 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…
Ilse Ipsen, CVs and Cover Letters
SAS 4201Carlos M. Ortiz Marrer, Pacific Northwest National Laboratory/ NC State, Non-Local Games on Graphs
ZoomIn 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…
Michael Merritt, NC State, Efficient Global Sensitivity Analysis for Rare Event Simulation
ZoomBy 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…