Local Relative Langlands Conjecture - BunG Seminar LV

This seminar talk by Daniil Klyuev explores the Local Relative Langlands Conjecture, a mathematical framework proposed by Ben-Zvi, Sakellaridis, and Venkatesh. Delve into the concept of hyperspherical varieties for reductive groups and understand how dual hyperspherical varieties are constructed over Langlands dual groups. Learn about the local unramified relative Langlands conjecture, which predicts an equivalence between derived categories of G_{O}-equivariant sheaves on X_{F} and \check{G}-equivariant modules over cohomological shifts of k[\check{M}]. Discover the Plancherel algebra as an algebra object in the spherical Hecke category and its connection to the Braverman-Finkelberg-Nakajima definition of Coulomb branches. The talk provides insights into advanced mathematical concepts at the intersection of representation theory and algebraic geometry.