Given a non-zero square-integrable function $g$ and $\Lambda=\{(a_k, b_k)\}_{k=1}^N \subset \mathbb{R}^2$ let $\mathcal{G}(g, \Lambda)=\{e^{2\pi i b_k \cdot}g(\cdot - a_k)\}_{k=1}^N.$ The Heil-Ramanathan-Topiwala (HRT) Conjecture is the question of whether $\mathcal{G}(g, \Lambda)$…
We consider the problem of inferring the basal sliding coefficient field for an uncertain Stokes ice sheet forward model from surface velocity measurements. The uncertainty in the forward model stems from unknown (or…
I give an introductory talk about geometric inverse problems and ray transforms (no proofs are involved). I mainly focus on the Euclidean X-ray transform of scalar fields and vector fields,…
Quasiconvex functions, a major generalization of convex functions, naturally arise in calculus of variations, optimal control and differential games in L-infinity. This connection with HJ equations, representation formulas, obstacle problems,…
Organizer: Seth Sullivant smsulli2@ncsu.edu
Let $U_1,\ldots,U_n$ be independent random vectors which are uniformly distributed on the unit sphere. The random hyperplanes $U_1^\perp,\ldots,U_n^\perp$ dissect the space into a collection of random cones. A uniform random…
In this talk I will present a Bayesian approach to quantify the uncertainty of model parameters and hemodynamic predictions in a one-dimensional fluid-dynamics model of the pulmonary system by integrating…
In this talk, we will discuss a recent global existence result on the Poiseuille flow of nematic liquid crystals via full Ericksen-Leslie model. The existing results on the Ericksen-Leslie model…
I will discuss recent progress on dimension-free estimates for the Hardy--Littlewood maximal functions in the continuous and discrete settings. Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili pivanis@ncsu.edu
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only…
Organizer: Seth Sullivant smsulli2@ncsu.edu
We will discuss Marstrand's classical theorem concerning the interplay between density of a measure and the Hausdorff dimension of the measure's support in the context of finite-dimensional Banach spaces. This…
Free-boundary problems are partial differential equations in which the unknown function and its domain must be simultaneously determined. They arise ubiquitously as mathematical models for phenomena in many fields, most…
A central question in machine learning theory is whether an algorithm enjoys good generalization, which is the ability to correctly predict new examples from prior observations. While classical wisdom advocates…
Thin liquid films flowing down vertical fibers exhibit complex and interesting interfacial dynamics, including droplet formation and traveling wave patterns. Such dynamics play a crucial role in the design of…
Not even influence inequalities for Boolean functions can escape the long arm of stochastic processes. I will present a (relatively) natural stochastic process which turns Boolean functions and their derivatives…
We hope this email finds you well. Given the uniqueness of this academic year, the Triangle Area Graduate Mathematics Conference (TAGMaC) will be happening differently than usual. We’d like to…
We hope this email finds you well. Given the uniqueness of this academic year, the Triangle Area Graduate Mathematics Conference (TAGMaC) will be happening differently than usual. We’d like to…
We hope this email finds you well. Given the uniqueness of this academic year, the Triangle Area Graduate Mathematics Conference (TAGMaC) will be happening differently than usual. We’d like to…
Computerized tomography techniques, which are used for visualizing the interior structure of an object of interest in a non-invasive manner, have played a central role in medical imaging, industrial non-destructive…