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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Carrillo José Antonio, University of Oxford
Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications
Giovedì 02 Dicembre 2021, ore 17:00
https://polimi-it.zoom.us/j/85300866421 |
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Abstract
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This talk will be devoted to an overview of recent results understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics and financial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear diffusion Keller-Segel type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under suitable assumptions on the Fourier modes of the interaction potential. The analysis is based on linear stability in the right functional space associated to the regularity of the problem at hand. While in the case of linear diffusion, one can work in the L2 framework, nonlinear diffusion needs the stronger Linfty topology to proceed with the analysis based on Crandall-Rabinowitz bifurcation analysis applied to the variation of the entropy functional. Explicit examples show that the global bifurcation branches can be very complicated. Stability of the solutions will be discussed based on numerical simulations with fully explicit energy decaying finite volume schemes specifically tailored to the gradient flow structure of these problems. The theoretical analysis of the asymptotic stability of the different branches of solutions is a challenging open problem. This overview talk is based on several works in collaboration with R. Bailo, A. Barbaro, J. A. Canizo, X. Chen, P. Degond, R. Gvalani, J. Hu, G. Pavliotis, A. Schlichting, Q. Wang, Z. Wang, and L. Zhang. This research has been funded by EPSRC EP/P031587/1 and ERC Advanced Grant Nonlocal-CPD 883363. |
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Kestutis Cesnavicius, Institut de Mathématique d'Orsay, Université Paris-Saclay
The perfectoid approach to purity questions
Lunedì 15 Novembre 2021, ore 16:00
Sala di Rappresentanza, Via C. Saldini 50, Milano e ON LINE | |
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