Index Problem for Elliptic Operators Associated With Group Actions and NCG

Explore a 44-minute lecture on the index problem for elliptic operators associated with group actions and noncommutative geometry. Delve into the application of noncommutative geometry methods, including KK-theory and cyclic cohomology, to study operators arising from group actions on manifolds. Learn about the pseudodifferential uniformization technique, which reduces elliptic operators associated with group actions to elliptic pseudodifferential operators, enabling the use of the Atiyah-Singer formula for index problem solutions. Gain insights into the intersection of noncommutative geometry and mathematical physics, particularly in describing nonlocal phenomena. This talk, presented by Anton Savin at the Hausdorff Center for Mathematics, was part of the Hausdorff Trimester Program on Non-commutative Geometry and its Applications in December 2014.