Skip to content Skip to navigation

MIGSAA Minicourse in honour of MARIA J. ESTEBAN June 19-20 2019

Heriot-Watt will award a honorary degree to Maria J. Esteban on June 21st, the current president of ICIAM and a world leader in the analysis of nonlinear PDES, variational methods and analytical methods in mathematical physics. Maria has been a frequent visitor to Heriot-Watt, particularly in the early nineties.

In conjunction with this event, Michela Ottobre, Beatrice Pelloni and John Ball have organised a Minicourse in honour of MARIA J. ESTEBAN  (June 2019)

Mini course in honour of MARIA J. ESTEBAN (19th - 20th June 2019)

Wednesday 19th     Venue:  G03, Ground Floor, Bayes Centre, 47 Potterrow, Edinburgh.

  • 9.15 – 11.30  M. J. Esteban - Functional inequalities, flows, symmetry and symmetry breaking
  • 11.30 – 12.00 Coffee break
  • 12.00 – 13.00  M. Loss -  Master Equation approach to kinetic theory
  • Social Lunch with speakers

Please note the change in venue

Thursday 20th          Venue:  ICMS Lecture Theatre, ICMS, Level 5, Bayes Centre, 47 Potterrow, Edinburgh

  • 9.15 – 11.30  M. J. Esteban  - Functional inequalities, flows, symmetry and symmetry breaking
  • 11.30 – 12.00 Coffee break
  • 12.00 – 13.00  G. Tarantello - Minimal immersions of closed surfaces in hyperbolic 3- manifolds

Titles and Abstracts

M. J. Esteban - Functional inequalities, flows, symmetry and symmetry breaking

Functional inequalities are an important component of the classical toolbox in the study of linear
and nonlinear partial differential equations, in order to obtain a priori estimates, to discuss
the long-time behavior of evolution equations and also to characterize the blow-up profile
of finite time blow-up solutions. They also play an important role in differential geometry and global analysis.
In this course I will discuss how a large class of such inequalities can be studied
using well adapted linear and nonlinear flows which allow us to find the best constants in the inequalities as well as the symmetry and other qualitative properties of their extremal functions.
Some cases where the flow methods do not seem easy to use will be also discussed,
showing that then the situation becomes often much more difficult. Various concrete cases will be considered in order to present different kinds of flows and their consequences.

M. Loss  - Master equation approach to kinetic theory

This talk is an overview on the master equation approach to kinetic theory pioneered by Mark Kac in 1956. This process

describes an ensemble of particles undergoing binary collisions. The talk will emphasize the problem of approach to equilibrium in the sense of entropy as well as through estimating the gap. Recent progress concerning three dimensional momentum preserving collisions will be discussed as well.

G. Tarantello - Minimal immersions of closed surfaces in hyperbolic 3- manifolds

Motivated by the the work of K. Uhlenbeck, we discuss minimal immersions of closed surfaces of genus larger than 1 on hyperbolic 3-manifold. In this respect we establish multiple existence for the Gauss –Codazzi equation and describe the asymptotic behaviour of the solutions in terms of the marked conformal structure on the surface and the (prescribed) second fundamental form relative to the minimal immersion. Joint work with Z. Huang and M. Lucia

 

 

SHARE