**Title:** On the geometric side of the trace formula for GL(N)

**Speaker:** Ali Altug

**Speaker Info:** Massachusetts Institute of Technology

**Brief Description:**

**Special Note**:

**Abstract:**

The Arthur-Selberg trace formula is one of the most fundamental and powerful tools in number theory and automorphic forms. For the general linear group GL(N), it gives a distributional identity I_spec(f) = I_geom(f) between a spectral and a geometric expansion of distributions on suitable functions f. The part that contribute discretely to the spectral side, I_disc, is central to the trace formula, and at the heart of I_disc is the so-called cuspidal part I_cusp(f). In many applications one is naturally lead to study I_cusp (or quantities related to Icusp) and hence it is fundamental to get an "explicit" (and, in a certain sense, geometric) expression for the difference I_geom(f) - (I_disc(f) - I_cusp(f)).In this talk I will talk about the problem of isolating the contribution of I_disc(f) - I_cusp(f) in I_geom(f). I will present a solution of this in the case GL(2) and talk about recent work of Arthur for G = GL(N). If time permits I will also say a few words about what kind of obstacles one encounters when one tries to execute the GL(2) strategy in higher rank, and possible directions one can pursue to overcome these.

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