10:00 to 11:00 Andrei Negut (Massachusetts Institute of Technology)Categorified knot invariants and algebraic geometry In this talk, we will survey some recent progress in a broad and developing framework that seeks to connect categorified knot invariants, geometric representation theory, Hilbert schemes and matrix factorizations. The contributions discussed come from the work of many mathematicians, and I hope to also convey some interesting future perspectives on the topic. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Matthew Hogancamp (University of Southern California)Categorical diagonalization It goes without saying that diagonalization is an important tool in linear algebra and representation theory.  In this talk I will discuss joint work with Ben Elias in which we develop a theory of diagonalization of functors, which has relevance both to higher representation theory and to categorified quantum invariants.  For most of the talk I will use small examples to illustrate of components of the theory, as well as subtleties which are not visible on the linear algebra level.  I will also state our Diagonalization Theorem which, informally, asserts that an object in a monoidal category is diagonalizable if it has enough eigenmaps''.  Time allowing, I will also mention our main application, which is a diagonalization of the full-twist Rouquier complexes acting on Soergel bimodules in type A.  The resulting categorical eigenprojections categorify q-deformed Young idempotents in Hecke algebras, and are also important for constructing colored link homology theories which, conjecturally, are functorial under 4-d cobordisms. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 17:00 Free Afternoon 19:30 to 22:00 Formal Dinner at Christ's College