Short Course

Reza Pakzad, University of Pittsburgh
Rigidity in Geometry and PDEs

‎In geometry, analysis and PDEs, the term "rigidity" can describe a situation where a local constraint on a given mathematical object,  such as a mapping or a manifold, leads to a restricted global behavior. The most known example of such a statement is perhaps Liouville's theorem, which states that any conformal smooth mapping on a domain of ${\mathbb R}^n$, $n\ge 3$, must be a Möbius transformation. 
‎In this short course, I will review the history of some of the  most  known rigidity statements, beginning with the Liouville's theorem, and describe some of the many manifestations, applications and ramifications of this type of statements  in  nonlinear analysis. Among others, I will discuss quantitative rigidity statements, rigidity of Sobolev deformations and rigidity and flexibility for Monge-Ampère equations.  I will occasionally sketch a proof in order to highlight the underlying structures, but the main objective will be  to avoid the most difficult technicalities and to increase the general knowledge of students about an active field in contemporary analysis.

Date & Time: 
‎Sunday‎, ‎July 31‎, ‎2016‎, ‎15:30 - 17:00
‎Monday‎, ‎August 1‎, ‎2016‎, ‎15:30 - 17:00
‎Tuesday‎, ‎August 2‎, ‎2016‎, ‎13:30 - 15:00 & 15:30 - 17:00
Room 221, Dept. Math. Sci., Sharif University of Technology