## Derived Structures in the Langlands Program

In Winter 2019, I co-organized the London Number Theory Study Group with Pol van Hoften, Alice Pozzi, and Carl Wang-Erickson. The topic of the study group was the work of Akshay Venkatesh, in particular his work on derived structures in the Langlands program, specifically his joint work Derived Galois Deformation Rings with Soren Galatius and the paper Derived Hecke Algebras.

The study group followed two tracks: a *Galois* track, following the first paper, and a *Hecke* track, which followed the second. In the last few talks, the comparison between the derived Galois deformation ring and the spherical derived Hecke algebra was discussed.