# Colloquium abstracts

**Girja Shanker Tripathi**

School of Mathematics, TIFR

September 15, 2011

**Representing hermitian K-theory by orthogonal Grassmannian in $A^1$-homotopy theory**: In this talk I will explain a joint work with Marco Schlichting on geometric representability of hermitian K-theory in the homotopy theory of schemes. After recalling some basic notions from the homotopy theory of schemes developed by Morel and Voevodsky, I will define an ind-scheme GrO, the orthogonal Grassmannian, and construct a map from GrO into hermitian K-theory KO. I will sketch a proof that this map is a homotopy equivalence and discuss some applications of the result.