Paata Ivanisvili, North Carolina State University, Enflo’s problem
ZoomA 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…
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…
This work explores the recovery stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs,…
In my talk, I will explain the approach of finding solutions to nonlinear PDEs via tug-of-war games. I will focus on the context of p-Laplacian and the non-local geometric p-Laplacian.…
In a Hilbert space, for convex optimization, we report on recent advances regarding the acceleration of first-order algorithms. We rely on inertial dynamics with damping driven by the Hessian, and…
We survey the known results concerning the minimal Riesz energy on sufficiently smooth sets, and present some new results on fractal sets, which are the key examples of non-rectifiable sets.…
A popular method to approximate a fixed point of a non-expansive map is C is the Krasnoselskii-Mann iteration. This covers a wide range of iterative methods in convex minimization, equilibria,…
Mesh-free methods for boundary value problems (BVPs) can be convenient on manifolds where generating a mesh may be difficult or when the manifold is not known explicitly but is determined…
Mean field game PDE systems were introduced by J-M. Lasry and P.-L. Lions to describe Nash equilibria in multi-agents dynamic optimization. In the simplest model, those are forward-backward systems coupling…
High intensity (focused) ultrasound HIFU is used in numerous medical and industrial applications ranging from lithotripsy and thermotherapy via ultrasound cleaning and welding to sonochemistry. The relatively high amplitudes arising in…
Counterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. Block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other failures…
In this talk we present well posedness of Measure Differential Equations, i.e. evolution equations in the Wasserstein space of probability measures driven by dissipative probability vector fields. We take inspiration…
Iterative Bregman projections is a classical method to compute Bregman projections onto an intersection of affine sets. In statistics it was applied to the adjustment of distributions to a priori…
In this joint ongoing work with Nicolas Forcadel (INSA Rouen) we study traffic flows models with a bifurcation. The model consists in a single incoming road divided after a junction…
In 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…
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
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…
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…
In this talk, we first propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of…
In this talk we consider the pressureless Euler system in dimension greater than or equal to two. Several works have been devoted to the search for solutions which satisfy the…
Zoom meeting: Link