Closure of Peter Markowich's Chair

Workshop : PDE Models in the Social Sciences

Social sciences pose significant challenges to mathematical modeling, in particular for devising predictive methods. Partial Differential Equations have become a major tool in this field by now.

This workshop presents several case studies of PDE modeling in the social sciences: opinion dynamics and achievment of consensus, crowd motion, economics and wealth distribution.

The event is organized by the Fondation Sciences Mathématiques de Paris as the closure of Peter Markowich's chair at LJLL and CEREMADE.

When: Friday January 24 2014
Where:  4, place Jussieu, Paris (metro Jussieu)
              Corridor 15-16, 3rd floor, room 309 (seminar room)
              Laboratoire Jacques-Louis Lions, UPMC



Scientific Program

9:30-10:20 : Laurent Boudin (LJLL, UPMC) Mathematical Models for Opinion Dynamics
10:20-10:40: Coffee Break
10:40-11:30: Marie-Therese Wolfram (KAUST, KSA) On the Mathematical Modeling and Simulation of Crowd Motion
11:30-12:20: Guillaume Carlier (CEREMADE Dauphine) Equilibria in Games with a Continuum of Agents and Transport

2:00 -2:50: Giuseppe Toscani (Universita’ di Pavia, Italy) Knowledge and Ingenuity: A Kinetic Approach
2:50-3:10: Coffee Break
3:10-4:00: Pierre-Emmanuel Jabin (University of Maryland, USA) Convergence to Consensus in Models with a Finite Range of Interactions
4:00-4:15: Peter Markowich (KAUST, KSA) Closing Remarks

Organisers

Jean Dolbeault (CEREMADE), Peter Markowich (KAUST) and Benoît Perthame (LJLL)

Lectures

Mathematical Models for Opinion Dynamics par Laurent Boudin
Abstract: About a decade ago mathematicians started to study opinion dynamics models. Various viewpoints have been proposed. In this talk, we shall mostly focus on kinetic models for opinion formation and discuss various phenomena which may affect the evolution of opinions inside a closed community.
Click here to find the slides of this lecture.
Video online soon.

 

On the Mathematical Modeling and Simulation of Crowd Motion par Marie Therese Wolfram
Abstract: Pedestrian crowds exhibit complex and coordinated behaviors, which result from the social interactions among individuals. The understanding of these microscopic interactions as well as the complex behavior on the macroscopic level pose challenging problems for the modeling, analysis and numerical simulations.
 In this talk we present mathematical modeling approaches for pedestrian motion on the microscopic level and discuss their mean field limit as the number of individuals tends to infinity. The resulting macroscopic models are in general highly nonlinear partial differential equations or systems thereof.
Hence we focus on particular analytic aspects and numerical simulations of the limiting equations to understand and capture the complex behavior of pedestrian crowds.
Click here to find the slides of this lecture.
Video online soon.


Equilibria in Games with a Continuum of Agents and Transport par Guillaume Carlier
Abstract: In this talk, I will describe several models with a continuum of agents where one can obtain equilibria by minimization arguments and in particular tools from optimal transport. I will address matching problems for teams  (joint with Ivar Ekeland) and Cournot-Nash equilibria (joint with Adrien Blanchet). Existence, uniqueness and characterization of equilibria will be discussed and some numerical simulations will also be presented.
Click here to find the slides of this lecture.
Video online soon


Knowledge and Ingenuity: A Kinetic Approach par Giuseppe Toscani
Abstract: In recent years the distribution of wealth in multi-agent societies has been investigated by resorting to classical methods of kinetic theory of rariefed gases. In analogy with the Boltzmann equation, the change of wealth in these models is due to microscopic binary tradings among agents. Surprisingly, other important aspects linked to dfferent types of human wealth, like knowledge (information) and ingenuity, have not been taken into consideration. In this lecture, we aim to present an effective model to study both the distribution of knowledge and ingenuity in a society of agents, based on microscopic rules of change, which include both the increase of information and the necessity to discard the unnecessary part of it. The so-obtained kinetic model is then studied in detail.
Click here to find the slides of this lecture.

Knowledge and Ingenuity: A Kinetic Approach par Giuseppe Toscani

 

Convergence to Consensus in Models with a Finite Range of Interactions par Pierre-Emmanuel Jabin
Abstract: We study the long time behavior of some opinion dynamics models. The evolution of the opinion  of one individual depends on the opinions of other individual through a given influence function. The models under consideration here are a generalization of the so-called Krause model which makes the interaction between individuals non symmetric. Because of this loss of symmetry, the long time behavior was essentially unknown in the realistic case of interactions with a finite range. We are able to show the convergence to an equilibrium consisting of several local consensus which do not interact anymore. This is a joint work with S. Motsch.

Convergence to Consensus in Models with a Finite Range of Interactions par Pierre-Emmanuel Jabin


Peter Markowich's closure speech


Socio


Economics at work