Algebra and Number Theory Seminar: Chapman Howard

Title: Epsilon Dichotomy and a Conjecture of Prasad and Takloo-Bighash

Abstract: The philosophy of using L-functions (analytic invariants) to study algebraic objects has produced many important results in the last century. We’ll discuss how this philosophy can be refined to a more interesting invariant (the epsilon factor or local root number), which in our case completely determines the representations we will study. With the importance of the local root number well understood, we’ll move toward the conjecture, explain previously proven cases, what work we have done so far, and how one might prove our case.