Over the last decades, the study of unitary representations of reductive Lie groups has progressed through a fruitful interaction between algebraic, geometric, and computational methods.
For real groups, the Atlas software for Lie groups and Representations makes it possible to parametrize representations and answer deep structural questions about them. Initiated in 2002 by J. Adams, F. du Cloux, and D. Vogan, its primary goal was the computation of the unitary dual of real reductive Lie groups using computer-based methods. The software has now matured to the point where it can determine whether a given irreducible representation is unitary. Its capabilities also facilitate the systematic study of Arthur-packets and broader aspects of endoscopic theory.
In parallel, computational methods for groups defined over p-adic fields are advancing, with algorithms now available to compute Arthur packets and related number-theoretic and structural properties of representations, such as theta lifts and the Aubert–Zelevinsky dual.
Atlas has become a fundamental tool for the study of real reductive groups, while computational approaches for p-adic groups are rapidly emerging. These parallel developments makes the present moment particularly suitable for organizing a summer school and conference that brings these two directions together.
The summer school will take place from June 28 to July 2, 2027, and will be followed by a three-day conference from July 5 to July 7, 2027. Both events will be held at CY Advanced Studies (CYAS) at CY Cergy Paris Université.
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