Atiyah-Singer Index Seminar

Thu., Nov. 26, 2015 10:00 a.m.

Location: RIC 215

Speaker: Asghar Ghorbanpour
Title: Elliptic differential operators as Fredholm operators
Abstract:

With the Sobolev theory tools in hand, we are now ready to consider the theory of

elliptic differential operators and show how they define (bounded) Fredholm operators

on carefully chosen Sobolev spaces. To accomplish that, a pseudo-inverse of an

elliptic operator will be constructed using the theory of pseudodifferential operators.

Moreover, we will show that the index of all Fredholm operators defined by an elliptic

operator on different Sobolev spaces, are equal and it does make sense to look for

a formula for the (Fredholm) index of elliptic operators.