## Lecturer:

Abstract: Hermitian K-theory can be described as the "real" analogue of algebraic K-theory, and plays a motivic role similar to the role played by real topological K-theory in classical stable homotopy theory. However, the abstract framework surrounding and supporting Hermitian K-theory is less well understood than its algebraic counterpart, especially in the case when 2 is not assumed to be invertible in the ground ring.

In this talk we will describe an on going project with Baptiste Calmès and Denis Nardin whose goal is to obtain a formulation of Hermitian K-theory in the setting of quadratic ∞-categories.

This formulation encompasses, on the one hand, several different forms of Hermitian K-theory, and enjoys, on the other, a suitable universal characterization, which is analogous to the one established for algebraic K-theory by Blumberg, Gepner and Tabuada.