Multi-Variable Period Polynomials Associated to Cusp Forms

Abstract

My research centers on the cohomology of arithmetic varieties. More specifically, I am interested in applying analytical, as well as topological methods to gain better insight into the cohomology of certain locally symmetric spaces. An area of research where the intersection of these analytical and algebraic tools has historically been very effective, is the classical theory of modular symbols associated to cusp forms. In this context, my research can be seen as developing a framework in which to compute modular symbols in higher rank. An important tool in my research is the well-rounded retract for GLn . In particular, in order to study the cohomology of the locally symmetric space associated to GL3 more effectively I designed an explicit, combinatorial contraction of the well-rounded retract. When combined with the suitable cell-generating procedure, this contraction yields new results pertinent to the notion of modular symbol I am researching in my thesis.