K-theoretic aspects of the nearby Lagrangian conjecture

Appears in collection : Giroux 60 - Convexity in contact and symplectic topology

It was recently shown by M. Abouzaid, S. Courte, S. Guillermou and T. Kragh that every nearby Lagrangian admits a so-called twisted generating function of tube type, thereby establishing a connection between the nearby Lagrangian conjecture and Waldhausen's algebraic K-theory of spaces. I will discuss several aspects of this connection, including a joint work in progress with M. Abouzaid, S. Courte and T. Kragh which finds new restrictions on the smooth structure of nearby Lagrangians.