Gigliola Staffilani, Massachusetts Institute of Technology
The Schrödinger equation as inspiration of beautiful mathematics
Lunedì 04 Luglio 2022, ore 17:00
Sala Consiglio 7 piano, Edificio La Nave | |
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Vojkan Jaksic, McGill University, Montreal, Canada
Approach to equilibrium in translation-invariant quantum systems: some structural results
Mercoledì 29 Giugno 2022, ore 17:00
Sala di Rappresentanza, 7 piano, Dip. di Matematica, via Bonardi 9 | |
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Giuseppe Ancona, Università di Strasburgo
Quadratic forms arising from geometry
Giovedì 16 Giugno 2022, ore 16:30
Sala di Rappresentanza del Dip. di Matematica, via C. Saldini 50 | |
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Andrea Malchiodi, Scuola Normale Superiore di Pisa
Prescribing scalar curvature in conformal geometry
Giovedì 19 Maggio 2022, ore 17:00
Sala Consiglio, 7 piano, Ed. La Nave, via Bonardi 9 | |
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Stefan Kebekus, University of Freiburg
The Minimal Model Program, and Extension Theorems for Differential Forms
Lunedì 04 Aprile 2022, ore 16:00
Sala di Rappresentanza, Via C. Saldini 50, Milano | |
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Marc Quincampoix, Université de Brest, France
Control of multiagent systems viewed as dynamical systems on the Wasserstein space
Mercoledì 23 Febbraio 2022, ore 17:00
Sala Consiglio 7 piano, Edificio La Nave e https://polimi-it.zoom.us/j/81969494860 |
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Abstract
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This talk is devoted to an overview of recent results on the optimal control of dynamical systems on probability measures modelizing the evolution of a large number of agents.
The system is composed by a number of agents so huge, that at each time only a statistical description of the state is available. A common way to model such kind of system is to consider a macroscopic point of view, where the state of the system is
described by a (time-evolving) probability measure on $R^d$ (which the underlying space where the agents move). So we are facing to a two-level system where the mascroscopic dynamic concerns probability measure while the microscopic dynamic - which describes the evolution of an individual agent - is a controlled differential equation on $ R^d$.
Associated to this dynamics on the Wasserstein space, one can associate a cost which allows to define a value function. We discuss the characterization of this value function through a Hamilton Jacobi Bellman equation stated on the Wasserstein space. We also discuss the problem of compatibility of state constraints with a multiagent control system. Since the Wasserstein space can be also viewed as the set of the laws of random variables in a suitable $L^2$ space, one can hope to reduce our problems to $L^2$ analysis. We discuss when this is possible.
This overview talk is based on several works in collaboration with I. Averboukh, P. Cardaliaguet, G. Cavagnari, C. Jimenez and A. Marigonda.
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