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# Atiyah-Singer Index Seminar

**
Thu., Dec. 10, 2015 11:20 a.m.
**

**
Location: RIC 215
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**Speaker:**Asghar GhorbanpourElliptic differential operators as Fredholm operators II**Title:**

**Abstract:**With the Sobolev theory tools in hand, we are now ready to consider the theory ofelliptic differential operators and show how they define (bounded) Fredholm operatorson carefully chosen Sobolev spaces. To accomplish that, a pseudo-inverse of anelliptic operator will be constructed using the theory of pseudodifferential operators.Moreover, we will show that the index of all Fredholm operators defined by an ellipticoperator on different Sobolev spaces, are equal and it does make sense to look fora formula for the (Fredholm) index of elliptic operators.