Faculty Activities
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׳.

This minilecture series will be held 9:3012:30 on Mon, Feb 27.
9:30  Coffee
10:0010:50 Lecture I (at an introductory level)
11:0011:40 Lecture II
10:5012:30 Lecture III
Organizers: Amy NovickCohen and Nir Gavish
Type:  Seminar 

Name:  Applied Mathematics Seminar 
Title:  Stochastic origins of gradient flows: relation with modeling 
Speaker:  Mark Peletier 
Place:  Amado, 814, Technion 
Abstract:  
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׳.  This minilecture series will be held 9:3012:30 on Mon, Feb 27. 9:30  Coffee 10:0010:50 Lecture I (at an introductory level) 11:0011:40 Lecture II 10:5012:30 Lecture III Organizers: Amy NovickCohen and Nir Gavish 

SubmittedBy:  Shiri KaplanShabat, mathsec@tx.technion.ac.il 
EventLink:  Event № 432 
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 
Earlier and recent onedimensional estimates and asymptotic relations for the cosine and sine Fourier transform of a function of bounded variation are refined in such a way that become applicable for obtaining multidimensional asymptotic relations for the Fourier transform of a function with bounded Hardy variation.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Asymptotic relations for the Fourier transform of a function of bounded variation 
Speaker:  Elijah Liflyand, Bar Ilan University 
Place:  Amado 814, Technion 
Abstract:  
Earlier and recent onedimensional estimates and asymptotic relations for the cosine and sine Fourier transform of a function of bounded variation are refined in such a way that become applicable for obtaining multidimensional asymptotic relations for the Fourier transform of a function with bounded Hardy variation. 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 435 
In this talk we discuss asymptotic relations between sharp constants of approximation theory in a general setting. We first present a general model that includes a circle of problems of finding sharp or asymptotically sharp constants in some areas of univariate and multivariate approximation theory, such as inequalities for approximating elements, approximation of individual elements, and approximation on classes of elements. Next we discuss sufficient conditions that imply limit inequalities and equalities between various sharp constants. Finally, we present applications of these results to sharp constants in BernsteinV. A. Markov type inequalities of different metrics for univariate and multivariate trigonometric and algebraic polynomials and entire functions of exponential type.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Asymptotic Relations for Sharp Constants of Approximation Theory 
Speaker:  Michael I. Ganzburg, Hampton University, USA 
Place:  Amado 814, Technion 
Abstract:  
In this talk we discuss asymptotic relations between sharp constants of approximation theory in a general setting. We first present a general model that includes a circle of problems of finding sharp or asymptotically sharp constants in some areas of univariate and multivariate approximation theory, such as inequalities for approximating elements, approximation of individual elements, and approximation on classes of elements. Next we discuss sufficient conditions that imply limit inequalities and equalities between various sharp constants. Finally, we present applications of these results to sharp constants in BernsteinV. A. Markov type inequalities of different metrics for univariate and multivariate trigonometric and algebraic polynomials and entire functions of exponential type. 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 436 
Type:  Seminar 

Name:  Groups, Dynamics and Related Topics 
Title:  TBA 
Speaker:  Nadav Yesha (Imperial college) 
Place:  814, Technion 
SubmittedBy:  Uri Shapira, ushapira@tx.technion.ac.il 
EventLink:  Event № 431 
Type:  Seminar 

Name:  Nonlinear Analysis and Optimization Seminar 
Title:  Nonlinear rescaling in constrained optimization 
Speaker:  Roman Polyak (Technion) 
Place:  Room 814, Amado Mathematics Building, Technion 
Files:  Poster 1 
SubmittedBy:  Simeon Reich, sreich@tx.technion.ac.il 
EventLink:  Event № 428 
In his famous 1900 ICM address Hilbert proposed his famous list of problems for the 20th century. Among these was his 6th problem which was less clearly formulated than the others but dealt with a rigorous derivation of the macroscopic equations of continuum mechanics from the available microscopic theory of his time, i.e. statistical mechanics and specifically Boltzmann's kinetic theory of gases. The problem has drawn attention from analysts over the years and even Hilbert himself made a contribution. In this talk I will note how an exact summation of the ChapmanEnskog expansion for the Boltzmann equation due to Ilya Karlin ( ETH) and Alexander Gorban (Leicester) can be used to represent solutions of the Boltzmann equation and then show that these solutions CANNOT converge the classical balance laws of mass, momentum, and energy associated the Euler equation of compressible gas dynamics. Hence alas Hilbert's program (at least with respect to gas dynamics) has a negative outcome.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  The problem with Hilbert's 6th problem 
Speaker:  Marshall Slemrod, University of WisconsinMadison 
Place:  Amado 814, Technion 
Abstract:  
In his famous 1900 ICM address Hilbert proposed his famous list of problems for the 20th century. Among these was his 6th problem which was less clearly formulated than the others but dealt with a rigorous derivation of the macroscopic equations of continuum mechanics from the available microscopic theory of his time, i.e. statistical mechanics and specifically Boltzmann's kinetic theory of gases. The problem has drawn attention from analysts over the years and even Hilbert himself made a contribution. In this talk I will note how an exact summation of the ChapmanEnskog expansion for the Boltzmann equation due to Ilya Karlin ( ETH) and Alexander Gorban (Leicester) can be used to represent solutions of the Boltzmann equation and then show that these solutions CANNOT converge the classical balance laws of mass, momentum, and energy associated the Euler equation of compressible gas dynamics. Hence alas Hilbert's program (at least with respect to gas dynamics) has a negative outcome.


SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 434 
T.B.A
Reception will be held at 16:30
Faculty Lounge
Amado Mathematics Building, 8th floor
Type:  Lecture 

Name:  The 30th Elisha Netanyahu Memorial Lecture 
Title:  T.B.A 
Speaker:  Prof. Cedric Villani from Universite de Lyon 
Place:  T.B.A, Technion 
Abstract:  
T.B.A Reception will be held at 16:30 Faculty Lounge Amado Mathematics Building, 8th floor 

SubmittedBy:  Shiri KaplanShabat, mathsec@tx.technion.ac.il 
EventLink:  Event № 421 