This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The Principal Investigator will conduct research on applications of algebro-geometric methods to Asymptotic Group Theory. The main goals of this project are twofold. One objective is to show that some group theoretic invariants (representation zeta functions) of arithmetic groups are motivic. The other objective is to study properties of these motives.
Group Theory is the mathematical field of inquiry that studies symmetry. Groups, which are the main object of focus, are usually analyzed by attaching numbers to them. The goal of this project is to show that, in some cases, these numbers have another interpretation. More precisely, the Principal Investigator will try to show that these numbers (representation zeta functions of arithmetic groups) are equal to the number of solutions of some polynomial equations. In this way, the different numbers attached to a group, as well as the numbers attached to different groups will be studied.
