New Geometric Structures in the Langlands Program

Explore groundbreaking developments in the Langlands program through this illuminating conference talk by Laurent Fargues. Delve into the emergence of novel geometric structures over the past two decades, with a particular focus on Fargues' recent collaborative work with Scholze. Discover the innovative concept of the moduli space of G-bundles on the curve, a pivotal object introduced in their research. Gain insights into the curve Fargues defined and investigated alongside Fontaine. Examine how these new geometric structures are utilized to construct the semi-simple local Langlands correspondence. This hour-long presentation offers a comprehensive overview of cutting-edge advancements in mathematical research, providing valuable insights for those interested in number theory, algebraic geometry, and the Langlands program.