Events
Differential Equations Seminar
- Events
- Differential Equations Seminar
Differential Equations and Nonlinear Analysis Seminar: Barbara Keyfitz, The Ohio State University, Hyperbolic Conservation Laws and Stability in L^2
ZoomRecently there has been considerable research into the stability of shocks in systems of conservation laws, with stability understood in some square-integrable sense. In this talk I will give some…
Differential Equations and Nonlinear Analysis Seminar: Terry Rockafellar, University of Washington, Augmented Lagrangian Methods and Local Duality in Nonconvex Optimization
ZoomAugmented Lagrangians were first employed in an algorithm for solving nonlinear programming problems with equality constraints. However, the approach was soon extended to inequality constraints and shown in the case…
Differential Equations and Nonlinear Analysis Seminar: Teemu Pennanen, King’s College London, Convex duality in nonlinear optimal transport
ZoomWe study problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of alarge class of related problems in…
Differential Equations and Nonlinear Analysis Seminar: Ivan Yotov, University of Pittsburgh, A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media
ZoomA nonlinear model is developed for fluid-poroelastic structure interaction with quasi-Newtonian fluids that exhibit a shear-thinning property. The flow in the fluid region is described by the Stokes equations and…
Differential Equations and Nonlinear Analysis Seminar: Juan Carlos, Centro de Modelización Matemática, Ecuador, Bilevel learning for inverse problems
ZoomIn recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A…
Differential Equations and Nonlinear Analysis Seminar: Stéphane Gaubert, École Polytechnique, France, What tropical geometry tells us about linear programming and zero-sum games
ZoomTropical convex sets arise as ``log-limits'' of parametric families of classical convex sets. The tropicalizations of polyhedra and spectrahedra are of special interest, since they can be described in terms of…
Differential Equations and Nonlinear Analysis Seminar: Bianchini Stefano, SISSA, ITALY, Properties of mixing BV vector fields
ZoomWe consider the density properties of divergence-free vector fields b in L^1(,BV(^2)) which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow X_t is an ergodic/weakly mixing/strongly mixing measure preserving map when evaluated…
Differential Equations and Nonlinear Analysis Seminar: Robin Neumayer, CMU, USA, Quantitative Faber-Krahn Inequalities and Applications
ZoomAmong all drum heads of a fixed area, a circular drum head produces the vibration of lowest frequency. The general dimensional analogue of this fact is the Faber-Krahn inequality: balls…
Differential Equations and Nonlinear Analysis Seminar: Francesca Bucci, Università degli Studi di Firenze, Italy, Riccati theory in the realm of PDE’s: state of the art and recent advances in the optimal control of evolution equations with memory
ZoomThe well-posedness of Riccati equations plays a central role in the study of the optimal control problem with quadratic functionals for linear partial differential equations (PDEs). Indeed, it allows the…
Differential Equations and Nonlinear Analysis Seminar: Jacopo Schino, NC State, Orbital stability of ground states to Schrödinger equations with mass constraint
ZoomI will discuss the existence and orbital stability of standing-wave solutions (i.e., with a specific time-dependence) with minimal energy (so-called ground states) to a non-linear Schrödinger equation where the L² norm is prescribed. I will…
Differential Equations Seminar: Paul Manns, TU Dortmund, Germany, On total variation regularization for PDE-constrained optimization with integer controls
ZoomWe study the effect of total variation regularization on PDE-constrained optimization problems, where the control input functions may only attain finitely many integer values. The regularization helps to avoid undesirable…
Differential Equations/Nonlinear Analysis Seminar: Michael Malisoff, LSU, Event-Triggered Control Using a Positive Systems Approach
SAS 4201Control systems are a class of dynamical systems that contain forcing terms. When control systems are used in engineering applications, the forcing terms can represent forces that can be applied…
Differential Equations/Nonlinear Analysis Seminar: Maria Teresa Chiri, Queen’s University, Controlling the spread of invasive biological species
ZoomWe consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. We…
Differential Equations/Nonlinear Analysis Seminar: Ryan Murray, NC State, Adversarially robust classification, non-local perimeters, and geometric flows
SAS 4201Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However,…
Differential Equations and Nonlinear Analysis Seminar: Alexei Novikov, PSU, USA, Long-time behavior of a randomly perturbed oscillator
ZoomWe consider a long-time behavior of a stochastically forced nonlinear oscillator. In a long-time limit the force converges to fractional Brownian motion, a process that has memory. In contrast, we…
Differential Equations and Nonlinear Analysis Seminar: Theodore D. Drivas, Stony Brook University, Remarks on the long-time dynamics of 2D Euler
ZoomWe will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations. Specifically, we discuss whether steady states can be isolated, wandering…
Differential Equations and Nonlinear Analysis Seminar: Michel De Lara, Cermics, École des Ponts ParisTech, France, Hidden Convexity in the l_0 Pseudonorm
ZoomThe so-called $l_0$ pseudonorm counts the number of nonzero components of a vector. It is standard in sparse optimization problems. However, as it is a discontinuous and nonconvex function, the…
Differential Equations and Nonlinear Analysis Seminar: Peter W. Michor, University of Vienna, Austria, Whitney manifold germs as source for manifolds of mappings
ZoomDuring the preparation of a foundational chapter on manifolds of mappings for a book on geometric continuum mechanics I found out that the following object behaves surprisingly well as source…
Differential Equations and Nonlinear Analysis Seminar: Guillaume Carlier, CEREMADE, Université Paris-Dauphine, A refined Fenchel-Young inequality and applications to optimal transport and convex duality
ZoomIn this talk, I will first present a very simple quantitative form of the Young-Fenchel inequality. I will then discuss some applications: a short proof of the Brøndsted-Rockafellar in Hilbert…