Eigenfunction concentration and Weyl Laws via geodesic beams Abstract. A broad spectrum of physical phenomena, including the localization of quantum particles, is governed by the behavior of Laplace eigenvalues and eigenfunctions. This behavior is intrinsically connected to that of the … Read more
On Liouville's theorem for conformal maps Abstract. A theorem of Liouville asserts that the simplest conformal transformations on Euclidean space---translations, dilations, reflections, and inversions---generate all conformal transformations when the dimension is at least 3. I will describe a new proof … Read more
Unbounded damped waves: backward uniqueness and polynomial stability Abstract. In this talk, we discuss the wave semigroup with an unbounded damping. In such a setting, there are explicit examples where the linear damped waves would go into finite-time extinction. We … Read more
Slice-Matching for Measure Transport: Approximation and Iterative Schemes Abstract: Transporting and estimating probability measures are fundamental tasks in various generative modeling methods like normalizing flows. An equally crucial aspect is having a suitable metric to gauge model performance and guide algorithm … Read more
Shape-morphing modes for solving PDEs with conserved quantities Abstract. I introduce shape-morphing modes for efficient and scalable approximation of solutions to time-dependent PDEs. Numerical methods typically assume the solution of a PDE as the linear combination of static modes, such as … Read more
Collatz map as a power-bounded non-singular transformation Ergodic Theory Seminar Website
Zoom link Syracuse maps as non-singular power-bounded transformations Ergodic Theory Seminar
Join us at the Tate-Turner-Kuralt Auditorium to experience five 15-minute presentations by the recipients of the Phillip and Ruth Hettleman Prizes for Scholarly Achievement. Among these presentations, one will be given by Yaiza Canzani, focusing on her research regarding … Read more
Some recent progress on integrable PDEs Abstract. Integrable PDEs arise as leading-order models in an astoundingly wide range of physical scenarios, such as fluid dynamics, ferromagnetism, and nonlinear optics. For rapidly decaying solutions, the inverse scattering method provides a powerful … Read more
Title: Hitchin WKB problem and Geometric P=W conjecture in rank 2 Abstract: After reviewing nonabelian Hodge and Riemann--Hilbert correspondences over curves, I state two closely related open problems concerning their large-scale behavior. I then propose an answer to these questions … Read more
Graduate students Kristen Giesbrect and Emma Crawford, have been selected as finalists for the Three Minute Thesis competition through the Graduate School (https://careerwell.unc.edu/programs/three-minute-thesis/). They will both compete on Wednesday, October 25, 4:00-5:00 in the Freedom Forum Center (305 Carroll Hall). One of … Read more
Join us for an informal meet-up where you can delve into the exciting world of research and the pursuit of advanced degrees in mathematics. Our discussion panel features experienced professors and postdocs associated with the NSF RTG project titled “Partial … Read more
