PDE and Applied Mathematics Seminar[ Edit ]
Lecture Series : Coffee 9:30, L1 10:0010:50 (intro), L2 11:0011:40, L3 10:5012:30. In equilibrium systems there is a long tradition of modelling systems by postulating an energy and identifying stable states with local or global minimizers of this energy. In recent years, with the discovery of Wasserstein and related gradient flows, there is the potential to do the same for timeevolving systems with overdamped (noninertial, viscositydominated) dynamics. Such a modelling route, however, requires an understanding of which energies (or entropies) drive a given system, which dissipation mechanisms are present, and how these two interact. Especially for the Wassersteinbased dissipations this was unclear until rather recently. In these talks I will discuss some of the modelling arguments that underlie the use of energies, entropies, and the Wasserstein gradient flows. This understanding springs from the common connection between large deviations for stochastic particle processes on one hand, and energies, entropies, and gradient flows on the other. In the first talk I will describe the variational structure of gradient flows, introduce generalized gradient flows, and give examples. In the second talk I will enter more deeply into the connection between gradient flows on one hand and stochastic processes on the other, in order to explain `where the gradientflow structures come from. Organizers: Amy NovickCohen and Nir Gavish
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Stochastic origins of gradient flows: relation with modeling 
Speaker:  Mark Peletier 
Place:  Amado 814, Technion 
Abstract:  
Lecture Series : Coffee 9:30, L1 10:0010:50 (intro), L2 11:0011:40, L3 10:5012:30. In equilibrium systems there is a long tradition of modelling systems by postulating an energy and identifying stable states with local or global minimizers of this energy. In recent years, with the discovery of Wasserstein and related gradient flows, there is the potential to do the same for timeevolving systems with overdamped (noninertial, viscositydominated) dynamics. Such a modelling route, however, requires an understanding of which energies (or entropies) drive a given system, which dissipation mechanisms are present, and how these two interact. Especially for the Wassersteinbased dissipations this was unclear until rather recently. In these talks I will discuss some of the modelling arguments that underlie the use of energies, entropies, and the Wasserstein gradient flows. This understanding springs from the common connection between large deviations for stochastic particle processes on one hand, and energies, entropies, and gradient flows on the other. In the first talk I will describe the variational structure of gradient flows, introduce generalized gradient flows, and give examples. In the second talk I will enter more deeply into the connection between gradient flows on one hand and stochastic processes on the other, in order to explain `where the gradientflow structures come from. Organizers: Amy NovickCohen and Nir Gavish 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 433 
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  The problem with Hilbert's 6th problem 
Speaker:  Marshall Slemrod 
Place:  Amado 814, Technion 
SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 434 