# ULL Topology Seminar, Spring 2010

February 5th: "Kan complexes and $\infty$-categories," Daniel.
February 19th: "$\infty$-categories and composition through horns," Daniel.
March 19th: " 'Composition' and joins for $\infty$-categories," Daniel.
April 30th: "$A^1$-Representability of Hermitian $K$-theory," Girja Shanker Tripathi (graduate student, LSU). Here are the notes (in "Beamer format") for Girja's talk. Abstract: I will discuss my result that in the $A^1$-homotopy category of smooth schemes over a field of characteristic not equal to 2, the Hermitian $K$-theory is representable by "orthogonal Grassmannians." This result is the Hermitian analogue of the corresponding result for algebraic $K$-theory. I will introduce some ideas (parallel to the ones in topology) from the $A^1$-homotopy theory developed by Morel and Voevodsky (1999). (Note that the location is different from usual: MDD 208.)