This is a synergistic, intra-disciplinary symposium that will focus on new and developing links between operator K-theory and representation theory.

The meeting will consider the following threads:

*Recent advances in operator K-theory and representation theory for affine Hecke algebras and p-adic groups (including the local Langlands correspondence).* In a series works, Plymen and collaborators have constructed a conjectural, and partly proven, bridge (known as the ABPS conjecture) between the K-theory of the reduced group C*-algebra of a p-adic group G and the parametrization (a la Bernstein) of the tempered dual of G. This conjecture relates intimately to the Langlands parameters and thus is of relevance to a wide group of researchers.

*New constructions linking K-theory, trace formula and automorphic forms.* In recent works, Mesland and Sengun constructed a KK-theoretic counterpart of the Hecke ring of Shimura. This contruction endowed many K-groups associated to arithmetic groups (such as group C*-algebras and boundary cross product algebras) with the action of the Hecke ring. Could these new K-theoretic Hecke modules play a role similar to that of the cohomology of arithmetic groups in the theory of automorphic forms?

*New approaches to tempered representation theory for real Lie groups via operator algebras and noncommutative geometry. *In recent works, Higson and collaborators have pioneered approaches to parabolic induction in the tempered representation theory of reductive groups via Hilbert C*-modules, and approaches to the tempered dual in full via the Mackey bijection.

*Emerging approaches to the topological aspects of harmonic analysis on reductive symmetric spaces.* Given a quotient X=G/H of a real reductive group by the fixed points of an involution on that group, the spectrum of L^{2}(X) as a G-representation is well-understood by harmonic analysis as a measure space. The recent interactions indicated that there is a promising possibility to study the spectrum topologically, using C*-algebras and K-theory.

We plan to push further the synergistic aspects of the meeting by bringing together a balance of experts who work in representation theory and harmonic analysis, with experts in noncommutative geometry and operator K-theory. Speakers will be encouraged to present open problems accessible across boundaries, and touch on possible new points of contact between the above research threads.