A Workshop on
Spectral Reciprocity Laws with

In recent decades, many formulas have been found relating one sum of L-functions to a different sum of L-functions. These are what we call spectral reciprocity formulas. These spectral reciprocity formulas have found interesting applications in analytic number theory, and they are related to the theory of periods of automorphic forms as well as topics of classical representation theory such as the 3j and 6j symbols. The goal of the workshop is to discuss spectral reciprocity formulas and look at their relationship with these and other topics.

In particular, a large part of the workshop will study the paper “The Tetrahedral (or 6j) Symbol” (available on the arXiv https://arxiv.org/abs/2602.14908v1) of Akshay Venkatesh and X. Griffin Wang. The paper develops a broad local-field generalisation of the classical 6j symbol, an object arising from the representations of SO₃ and traditionally connected with angular momentum, Racah coefficients, and hypergeometric functions. A central theme of the paper is the discovery of a hidden symmetry governed by the Weyl group of type D₆, together with a remarkable connection to the half-spin representation and the pure-spinor cone for Spin₁₂. The paper also interprets tetrahedral symbols as an interface in relative harmonic analysis and relates the associated integral transform to spectral reciprocity in automorphic forms. The workshop will introduce the classical 6j symbol, explain the main constructions and results of the paper, and discuss their significance for representation theory, special functions, and the relative Langlands programme.

The four-day workshop will feature a series of engaging lectures by eminent mathematicians, offering participants an opportunity to explore a diverse range of mathematical ideas on the theme of the workshop, and interact with mathematicians.