An Algorithm for Hecke Operators

Mark McConnell, Princeton University
Fine Hall 322

Hecke operators act on the cohomology of locally symmetric spaces for SL(n,R), and the Hecke eigenvalues are important in number theory and automorphic forms.  When n = 2, the case of classical modular forms, modular symbols (due to Manin) give an algorithm for computing the Hecke operators.  Ash and Rudolph extended the algorithm to all n, but only in the top non-vanishing degree of the cohomology--the virtual cohomological dimension, or vcd.  Gunnells found an algorithm for all n, but only in degree one less than the vcd.  This talk is on work in progress on an algorithm that computes the Hecke operators in all degrees.  This is joint work with Robert MacPherson.