### Speaker

### Description

This is a report on joint work with Yonatan Harpaz and Denis Nardin.

Hermitian K-theory and motivic homotopy theory enjoy a fruitful relationship, in particular through the quadratic nature of morphisms in the latter, epistomized by the theorem of Morel relating the endomorphisms of the unit sphere with Milnor-Witt K-theory.

A recent definition of Hermitian K-theory in terms of stable infinity-categories and quadratic functors enables one to consider various flavours of Hermitian K-theory -- symmetric forms, quadratic forms, etc. -- related in a common framework. As required to distinguish these, the theory unfolds nicely without any invertibility of 2 assumption.

I'll discuss representability results of Hermtian K-theory in the stable homotopy category of schemes over a base, in a characteristic free manner.