From the Langlands program to relative Langlands, with important new instances
The Langlands program, proposed more than 50 years ago, is often seen as the largest project in modern mathematics. Garnering the 2018 Abel prize, one of mathematics’ most prestigious awards, it is a grand unified theory of mathematics describing far-ranging connections between algebra, number theory and analysis. Functoriality is a central concept, describing deep relationships between the local and automorphic spectra of different groups. The relative Langlands program is a promising recent generalisation of the classical Langlands program. The EU-funded RELANTRA project intends to make fundamental contributions to the development of these concepts with a focus on the local setting, leading to significant new instances of relative Langlands correspondences/functorialities.
