**Title:** P-adic interpolation in representation theory and arithmetic

**Speaker:** Professor Matthew Emerton

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

We will explain a rather simple construction of certain infinite dimensional representations of groups of invertible matrices whose entries are p-adic numbers. These representations occur on the cohomology groups of certain manifolds (arithmetic quotients of symmetric spaces) which one constructs out of the corresponding group of invertible matrices with real coefficients. An important feature of these representations is that they occur in p-adic analytic families.These representations are of interest because, as we will explain, one expects that they correspond to certain objects of great number-theoretic interest: p-adic analytic families of representations of the absolute Galois group of the field of rational numbers.

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