|Workshop on Representation Theory and Analysis on Locally Symmetric Spaces|
|Topic:||Euler classes transgressions and Eistenstein cohomology of $GL(N)$|
|Affiliation:||Institut de Mathématiques de Jussieu-Paris Rive Gauche|
|Date:||Thursday, March 8|
|Time/Room:||4:00pm - 5:00pm/Simonyi Hall 101|
Abstract: In work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh we give a new construction of some Eisenstein classes for $GL_N (Z)$ that were first considered by Nori and Sczech. The starting point of this construction is a theorem of Sullivan on the vanishing of the Euler class of $SL_N$ (Z)-vector bundles and the explicit transgression of this Euler class by Bismut and Cheeger. Their proof indeed produces a universal form that can be thought of as a kernel for a regularized theta lift for the reductive dual pair $(GL_1 , GL_N )$. This suggests looking to reductive dual pairs $(GL_k, GL_N)$ with $k >1$ for possible generalizations of the Eisenstein cocycle. This leads to interesting arithmetic lifts.