Topology Seminar Series: Daniel Ruberman, Brandeis

Daniel Ruberman, Brandeis

Title: End-Periodic Index Theory
Speaker: Daniel Ruberman, Brandeis
Date: Thursday, April 25, 2013
Time: 11:30am – 12:30pm
Place: Lecture Hall 102, Simons Center




Abstract: The Atiyah-Patodi-Singer index theorem calculates the index of anelliptic differential operator on a manifold with boundary, subject to
certain boundary conditions that arise naturally in geometry and topology.
In many circumstances, these give rise to an index problem on a manifold
with product ends. I will discuss joint work with Tom Mrowka and Nikolai
Saveliev on a generalization to the setting of manifolds with periodic ends
and the connection with problems in 4-dimensional topology. I will also
discuss the simplest version of the periodic index theorem, namely the
Gauss-Bonnet theorem, where the difference between the periodic and product
settings is already evident.