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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.