We consider the random Cayley graphs of a sequence of finite nilpotent groups of diverging sizes G = G(n), whose ranks and nilpotency classes are uniformly bounded. For some k = k(n) such that 1 << log k << log |G|, we pick a random set of generators S = S(n) by sampling k elements…
We analyze a randomized preconditioned Cholesky-QR algorithm for computing the thin QR factorization of real matrices with full rank. Using a perturbation analysis that is transparent and identifies clearly all factors that contribute to error amplification, we identify steps of the algorithm that can be performed in lower precision while maintaining accuracy. The numerical experiments…
One of the main approaches to topological data analysis is to study discrete invariants of (multiparameter) persistence modules. In this talk, we discuss recent research which utilizes techniques from (relative) homological algebra to interpret classical examples of invariants and define new invariants. The Hilbert function and (generalizations of) the rank invariant serve as our main…
Finding combinatorial interpretations for the structure constants of Schubert polynomials is a long-standing open problem in algebraic combinatorics. In the case where one of the Schubert polynomials is a Schur polynomial, the structure constants are encoded in a poset called the “k-Bruhat order”. In studying the k-Bruhat order, Bergeron and Sottile were led to introduce…
In this talk we will first briefly review some geometric inverse problems we have studied for the one-dimensional heat, wave and Burgers equations. Then, we will consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. This is a preliminary simplified version of other more complicate and more realistic…
In this talk, we will investigate the acoustic transmission eigenvalue problem associated with an inhomogeneous media with a conductive boundary. These are a new class of eigenvalue problems that are not elliptic, not self-adjoint, and nonlinear, which gives the possibility of complex eigenvalues. The talk will consider the case of an Isotropic and Anisotropic scatterer.…
Quantum computers are physical machines that process information using the principles of quantum mechanics, which in turn is underpinned by linear algebra. The talk will start with a review of Lie algebras (consisting of matrices under the operation of commutator) and their role in quantum mechanics. The dynamical Lie algebra (DLA) of a quantum system…
A number of continuous interacting particle systems can be described as collections of Brownian particles on the real line whose collision dynamics are mediated by the local times associated with the gaps between adjacent particles. Examples of systems in this class include the ordered particle dynamics of rank-based diffusions and certain eigenvalue processes arising in…
Speaker's website: https://professeurs.uqam.ca/professeur/thomas.hugh_r/
How to use mathematics to see inside something that is too large or too precious to be opened up? Would you like to learn about the mathematical theory behind medical and seismic imaging? Attend Triangle Area Inverse Problems Weekend at NC State University from Friday October 4 thru Sunday October 6 to learn more. The event is…
Speaker's website: https://chinholee.github.io/
Speaker's website: https://www.dima.unige.it/~villa/ Zoom meeting: link
Event webpage: https://sites.google.com/ncsu.edu/conf-quantum-groups-rep2024/home?pli=1 This conference is in celebration of Kailash Misra's 70th birthday.
Speaker's website: https://sites.google.com/view/ritvikramkumar