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

Heriot-Watt will award a honorary degree to Maria 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 ESTEBAN  (June 2019)

Wednesday 19th

  • 9.15 – 11.30  M. Esteban 2 hours with 15 min break in between - Functional inequalities, flows, symmetry and symmetry breaking
  • 11.30 – 12.00 Coffee break
  • 12.00 – 13.00  M. Loss - TBA
  • Social Lunch with speakers

Thursday 20th

  • 9.15 – 11.30  M. Esteban 2 hours with 15 min break in between - 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

Register through this link if you would like to attend https://www.smartsurvey.co.uk/s/MinicourseEstebanJune/

Titles and abstracts

M. 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   TBA

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

 

 

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