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XIX SCHOOL OF MATHEMATICS ‹LLUIS SANTALӛ. INTERACTIONS BETWEEN PDE AND PROBABILITY

Información General

Código
63U5
Horas
30
Fecha
13 Ago 2018
17 Ago 2018
Precio
130 € Tarifa C
Tipo
Escuela
Temática
Ciencias y Tecnología
ECTS
1

Sede donde se gestiona

Santander

Lugar de impartición

Santander - Península de la Magdalena (Riancho)

Dirección

José Antonio Carrillo de la Plata
Professor
Department of Mathematics
Imperial College London


José Alfredo Cañizo Rincón
Investigador Ramón y Cajal
Departamento de Matemática Aplicada
Universidad de Granada


ORGANIZADO EN COLABORACIÓN CON


ORGANIZADO EN COLABORACIÓN CON

Descripción de la actividad

In the recent years a fruitful interaction has taken place between probability, functional inequalities and nonlinear partial differential equations (PDEs). Among others, there have been advances in entropy/entropy production inequalities for nonlinear aggregation-diffusion equations and transport inequalities and their links to the probability distribution of Fokker-Planck models. Some examples of current interest are the applications of variants of the Hardy-Littlewood-Sobolev inequality to understand Keller-Segel-type models and of Doeblin/Harris methods in integral kinetic equations.

On the other hand, the analysis of stochastic interacting particle systems, stochastic PDEs and related relevant questions such as mean-field limits and phase transitions is booming; in particular due to the important applications in life-sciences.

This summer school proposes five courses which give an advanced introduction to these topics and their applications in life sciences models, as well as six talks that present current related research problems.

 

Participantes

DIRECCIÓN

José Alfredo Cañizo Rincón
Investigador Ramón y Cajal
Departamento de Matemática Aplicada
Universidad de Granada

José Antonio Carrillo de la Plata
Professor
Department of Mathematics
Imperial College London

PARTICIPANTES

Matteo Bonforte
Professor
Departamento de Matemáticas
Universidad Autónoma de Madrid

Martin Hairer
Professor
Department of Mathematics
Imperial College London

Xue-Mei Li
Professor
Department of Mathematics
Imperial College London

Stephan Luckhaus
Professor
Institute of Mathematics
Universität Leipzig

Barbara Niethammer
Professor
Institute for Applied Mathematics
Universität Bonn

Grigorios Pavliotis
Professor
Department of Mathematics
Imperial College London

Benoît Perthame
Professor
Laboratoire Jacques-Louis Lions
Université Pierre et Marie curie

Dejan Slepcev
Professor
Department of Mathematical Sciences
Carnegie Mellon University

Angela Stevens
Professor
Institut für Numerische und Angewandte Mathematik
Fachbereich für Mathematik und Informatik
Universität Münster

Juan Luis Vázquez
Profesor Emérito
Departamento de Matemáticas
Universidad Autónoma de Madrid

Programa

Lunes, 13 Agosto 2018

09:00
The single neuron: slow-fast dynamics
Benoît Perthame
09:00
The single neuron: slow-fast dynamics
10:00
The Integrate-and-Fire model, role of noise
10:00
The Integrate-and-Fire model, role of noise
Benoît Perthame
11:30
Self-similarity in Smoluchowski's coagulation equation
11:30
Self-similarity in Smoluchowski's coagulation equation
Barbara Niethammer
12:30
Long time behaviour and phase transitions for the McKean- Vlasov equation
Grigorios Pavliotis
12:30
Long time behaviour and phase transitions for the McKean- Vlasov equation
15:00
Discrete variational problems in random settings and their continuum limits (I)
15:00
Discrete variational problems in random settings and their continuum limits (I)
Dejan Slepcev
16:00
Discrete variational problems in random settings and their continuum limits (II)
Dejan Slepcev
16:00
Discrete variational problems in random settings and their continuum limits (II)

Martes, 14 Agosto 2018

09:00
Discrete variational problems in random settings and their continuum limits (III)
Dejan Slepcev
09:00
Discrete variational problems in random settings and their continuum limits (III)
10:00
Discrete variational problems in random settings and their continuum limits (IV)
10:00
Discrete variational problems in random settings and their continuum limits (IV)
Dejan Slepcev
11:30
The BPHZ theorem for stochastic PDEs (I)
Martin Hairer
11:30
The BPHZ theorem for stochastic PDEs (I)
12:30
The BPHZ theorem for stochastic PDEs (II)
Martin Hairer
12:30
The BPHZ theorem for stochastic PDEs (II)
15:00
Analysis of the Integrate & Fire model
Benoît Perthame
15:00
Analysis of the Integrate & Fire model
16:00
Time elapsed models
16:00
Time elapsed models
Benoît Perthame
17:00
Poster session
17:00
Poster session
Matteo Bonforte
Martin Hairer
Xue-Mei Li
Barbara Niethammer
Juan Luis Vázquez

Miércoles, 15 Agosto 2018

09:00
The BPHZ theorem for stochastic PDEs (III)
Martin Hairer
09:00
The BPHZ theorem for stochastic PDEs (III)
10:00
The BPHZ theorem for stochastic PDEs (IV)
Martin Hairer
10:00
The BPHZ theorem for stochastic PDEs (IV)
11:30
Hessian estimates for Schrodinger equations
Xue-Mei Li
11:30
Hessian estimates for Schrodinger equations
12:30
Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains
12:30
Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains
Matteo Bonforte

Jueves, 16 Agosto 2018

09:00
Partial differential equations and interacting stochastic many-particle models for self-attraction and self-organization in biology.
Angela Stevens
09:00
Partial differential equations and interacting stochastic many-particle models for self-attraction and self-organization in biology.
10:00
Moderately interacting stochastic many particle systems
Angela Stevens
10:00
Moderately interacting stochastic many particle systems
11:30
Open problems at the interface between PDEs & probability
11:30
Open problems at the interface between PDEs & probability
Matteo Bonforte
Xue-Mei Li
Martin Hairer
Grigorios Pavliotis
Benoît Perthame
Dejan Slepcev
Juan Luis Vázquez
Moderación: José Alfredo Cañizo Rincón
15:00
The Harris-Meyn-Tweedie theorem in PDEs and kinetic theory
15:00
The Harris-Meyn-Tweedie theorem in PDEs and kinetic theory
José Alfredo Cañizo Rincón
16:00
Dislocations as finite size singularities and rigidity estimates
Stephan Luckhaus
16:00
Dislocations as finite size singularities and rigidity estimates

Viernes, 17 Agosto 2018

09:00
A PDE-ODE system and its connection to reinforced random walks
09:00
A PDE-ODE system and its connection to reinforced random walks
Angela Stevens
10:00
A hydrodynamic limit for chemotaxis in heterogeneous environments
10:00
A hydrodynamic limit for chemotaxis in heterogeneous environments
Angela Stevens
11:30
Aggregation-diffusion equations: stationary states, gradient flows, radial symmetry and metastability.
11:30
Aggregation-diffusion equations: stationary states, gradient flows, radial symmetry and metastability.
José Antonio Carrillo de la Plata
12:30
Degenerate Fractional Diffusion Equations. A review
Juan Luis Vázquez
12:30
Degenerate Fractional Diffusion Equations. A review

Sin fecha definida

Self-similarity in Smoluchowski's coagulation equation
Discrete variational problems in random settings and their continuum limits (I)
Discrete variational problems in random settings and their continuum limits (II)
Discrete variational problems in random settings and their continuum limits (III)
The BPHZ theorem for stochastic PDEs (I)
The BPHZ theorem for stochastic PDEs (II)
The Integrate-and-Fire model, role of noise
Time elapsed models
Partial differential equations and interacting stochastic many-particle models for self-attraction and self-organization in biology.
Discrete variational problems in random settings and their continuum limits (IV)
Analysis of the Integrate & Fire model
The BPHZ theorem for stochastic PDEs (IV)
A hydrodynamic limit for chemotaxis in heterogeneous environments
The single neuron: slow-fast dynamics
Long time behaviour and phase transitions for the McKean- Vlasov equation
Aggregation-diffusion equations: stationary states, gradient flows, radial symmetry and metastability.
A PDE-ODE system and its connection to reinforced random walks
Dislocations as finite size singularities and rigidity estimates
Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains
The BPHZ theorem for stochastic PDEs (III)
Hessian estimates for Schrodinger equations
Moderately interacting stochastic many particle systems
Open problems at the interface between PDEs & probability
Poster session
Degenerate Fractional Diffusion Equations. A review
The Harris-Meyn-Tweedie theorem in PDEs and kinetic theory