Lectures on PDEs and Geometry

The next course will be held on March 12-15, 2018.
Find below the list of previous courses, together with the material (lecture notes, slides...)

Course 5. March 12-16, 2018
Monotonicity formulae, Liouville theorems, a priori estimates for singular/degenerate elliptic and parabolic equations

Professor Susanna Terracini
Università degli Studi di Torino, Torino, Italy.

Topics of the Lectures: [ Download Abstract in PDF ]

Lectures
The Lectures will take place in Departamento de Matemáticas
- Monday, March 12 2018 Aula 520,
  - 11:30-13:00 Terracini Lecture 1
- Tuesday, March 13 2018 Aula 520,
  - 11:30-13:00 Terracini Lecture 2
- Thursday, March 15 2018 Aula 520,
  - 11:30-13:00 Terracini Lecture 3

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Course 4. February 5-7, 2018
Parabolic equations with rough coefficients and singular forcing

Professor Felix Otto
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Topics of the Lectures: [ Download Abstract in PDF ]

Course 3. January 23-25, 2018
Stable solutions to some elliptic problems: minimal cones, the Allen-Cahn equation, and blow-up solutions

Professor Xavier Cabré
ICREA and Universitat Politécnica de Catalunya, Barcelona, Spain.

Topics of the Lectures: [ Download Abstract in PDF ]
Lecture Notes of the Lectures: [ Download Notes in PDF ]
Handwritten Notes of the Lectures: [ Download Notes in PDF ]
Video of Lectures at Columbia University, NYC, USA: [ Youtube Link ]

Course 2. November 23-24, 2017
Rectifiability, regular manifolds and differential forms in Carnot groups

Professor Bruno Franchi
Università degli Studi di Bologna, Bologna, Italy.

Topics of the Lectures: [ Download Abstract in PDF ]

Course 1. June 20-22, 2017
Symmetry and nonlinear diffusion flows

Professor Jean Dolbeault
CEREMADE, Université Paris Dauphine, Paris, France.

Notes of the Lectures: [ Download Notes in PDF ]
Topics of the Lectures
- Entropy methods in fast diffusion equations: the Bakry-
  Emery method on compact manifolds and on the Euclidean space
- Rényi entropy powers and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities
- Large time asymptotics, linearization and optimal constants
- Considerations on branches of solutions and bifurcations

Matteo Bonforte
Maria del Mar Gonzalez
both at UAM, Madrid, Spain

matteo.bonforteuam.es
mariamar.gonzaleznuam.es

The School will take place at
Departamento de Matemáticas
Facultad de Ciencias
Universidad Autónoma de Madrid
Google Maps Link

Sponsors
Universidad Autónoma de Madrid

Project supported by:
- 2016 BBVA Foundation Grant
for Researchers and
Cultural Creators

- Spanish research projects
MTM2014-52240-P
MTM2017-85757-P
MTM2014-53037-P
(MINECO, Spain).