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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Benjamin Schlein, University of Zurich
Landau–Pekar equations and quantum fluctuations for the dynamics of a polaron
Lunedì 20 Settembre 2021, ore 17:00
https://polimi-it.zoom.us/j/82145408841?pwd=VTZxUVJrYVRjQUltTC9ISnNBbzg3QT09 | |
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Jean Dolbeault, Université Paris Dauphine
Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results
Martedì 06 Luglio 2021, ore 17:00
https://polimi-it.zoom.us/j/81798558580 | |
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Jacopo De Simoi, University of Toronto
Dynamical rigidity of convex billiards
Lunedì 21 Giugno 2021, ore 17:00
https://zoom.us/j/91544493126?pwd=cHVlNEFkZ1lHWjNONG9kWHdoaGwxQT09 | |
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Leszek Demkowicz, Oden Institute, The University of Texas at Austin
The DPG Method for Convection-Reaction Problems
Lunedì 10 Maggio 2021, ore 17:00
https://us02web.zoom.us/j/81021076857 | |
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