I will report on work in progress with Radhika Ganapathy. One wishes to study irreducible `smooth' complex representations of symplectic and (split) orthogonal groups over local function fields, i.e., fields of the form F_q((t)). The theory of `

close local fieldsâ€™ proposes to do this by studying the representation theory of these groups over (varying) finite extensions of Q_p. We will discuss an approach to using this philosophy to study the local Langlands correspondence for these groups.

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Last updated: 09 Apr 2019