Variational Methods for Evolving Objects

Contents

Outline

Schedule:
July 30 - August 3, 2012
Venue:
Room 3-309, Faculty of Science Building #3, Hokkaido University, Sapporo
Organizers:
L. Ambrosio (Pisa), Y. Giga（Tokyo）, P. Rybka (Warsaw）, Y. Tonegawa (Sapporo)
Course Lecturers:
L. Ambrosio (Pisa)
Y. Brenier (Nice)
R. Jerrard (Toronto)
Invited Speakers:
A. Chambolle (Palaiseau)
W. Gangbo (Atlanta)
P. Guidotti (Irvine)
P. Mucha (Warsaw)
M. Novaga (Padova)
D. Pallara (Lecce)
N. Wickramasekera (Cambridge)
Program:
Course Lecturers & Main Themes:
Luigi Ambrosio: Gradient flows in metric spaces and in the space of probability measures » Abstract
Yann Brenier: Optimal Transport
Robert Jerrard: Dynamics of vortices and other topological defects in nonlinear field theories
July 30 (Monday)
09:00-09:50 Registration
09:50-10:00 Opening
10:00-10:50 Luigi Ambrosio (Scuola Normale Superiore)
(Lecture I) Metric formulations of gradient flows: Energy Dissipation Inequalities and Evolution Variational Inequalities
11:10-12:00 Yann Brenier (Université de Nice)
(Lecture I) Optimal transport of densities
14:00-14:50 Robert Jerrard (University of Toronto)
(Lecture I) Overview, and parabolic equations
15:10-16:10 Diego Pallara (Università del Salento)
Bounded variation functions in Hilbert spaces and related semigroups
16:30- Poster Session
July 31 (Tuesday)
10:00-10:50 Luigi Ambrosio (Scuola Normale Superiore)
(Lecture II) Convergence of the Euler scheme and existence results
11:10-12:00 Yann Brenier (Université de Nice)
(Lecture II) Optimal incompressible transport
14:00-14:50 Robert Jerrard (University of Toronto)
(Lecture II) Wave equations and timelike minimal surfaces
15:10-16:10 Wilfrid Gangbo (Georgia Institute of Technology)
A variational problem involving a polyconvex integrand » Abstract
16:30-17:30 Matteo Novaga (University of Padova)
Variational problems in infinite dimensional spaces » Abstract
18:00- Get-together at Common Space
August 1 (Wednesday)
10:00-11:00 Antonin Chambolle (Ecole Polytechnique)
Some non-local curvature evolutions
11:30-12:30 Patrick Guidotti (University of California, Irvine)
Nonlinear Diffusions and Image Processing
12:30- Free Time (Excursion: optional)
August 2 (Thursday)
10:00-10:50 Luigi Ambrosio (Scuola Normale Superiore)
(Lecture III) The theory of gradients in metric measure spaces
11:10-12:00 Yann Brenier (Université de Nice)
(Lecture III) Optimal transport of divergence-free vector fields
14:00-14:50 Robert Jerrard (University of Toronto)
(Lecture III) Vortex dynamics in nonlinear Schrodinger equations
15:10-16:10 Piotr Mucha (Warsaw University)
TBA
16:30-17:30 Neshan Wickramasekera (University of Cambridge)
Higher multiplicity in minimal submanifolds
18:00-20:00 Reception Party
August 3 (Friday)
10:00-10:50 Luigi Ambrosio (Scuola Normale Superiore)
(Lecture IV) Heat flow and gradient flow of the entropy in metric measure spaces
11:10-12:00 Yann Brenier (Université de Nice)
(Lecture IV) Perspectives and open problems
14:00-14:50 Robert Jerrard (University of Toronto)
(Lecture IV) Stability of binormal curvature flow
15:10-15:50 Discussion
15:50- Closing
Poster:
» poster.pdf (9.4MB)
Co-sponsorship:
RCIM Research Center for Integrative Mathematics in Hokkaido University
http://www.math.sci.hokudai.ac.jp/center/en/