Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Explicit Arithmetic Cohomology Computations over Quadratic Number Fields

Speaker: **Jonathan Hanke**, Rutgers University

Date: Thursday, November 14, 2013 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In recent years a great deal of progress has been made in computing explicit Voronoi reduction theories for positive definite quadratic forms, primarily through the use of computers and improved algorithms for dealing with the very large stabilizer symmetry groups that can arise. Recently, in joint with with H. Gangl, P. Gunnells, A. Schürmann, M. Dutour-Sikiri', and D. Yasaki, these techniques have been applied to compute the group cohomology of GL_n and SL_n over the ring of integers of various small discriminant (real and imaginary) quadratic number fields when n < = 4, and also to compute some associated K groups. In this talk we describe the basics of the Voronoi reduction algorithm and how such computations are carried out explicitly. The talk is meant to be friendly, and accessible to both graduate students and researchers.