| Abstract: The Arthur Trace Formula (ATF) is an equality of two distributions of nice test function on adelic groups and it has played a central role in the modern Number Theory and Automorphic Forms in the las 50 years or so. Arthur established the first iteration of the ATF, called the non-invariant trace formula, using complicated geometric/combinatorial and analytical techniques, with further iterations, such as invariant, stable, weighted, twisted, weighted, trace formulae to follow. In a joint work with Kiumars Kaveh (University of Pittsburgh) we explicate the geometric/combinatrial aspects of the development of the non-invariant ATF by recasting it in the language of convex polytopes and fans, making the geometric and combinatorial aspects more transparent and natural. In this talk I will report on this work. I will not assume prior knowledge of the trace formula for this talk. |