**Title:** Categorical Diagonalization

**Speaker:** Ben Elias

**Speaker Info:** University of Oregon

**Brief Description:**

**Special Note**:

**Abstract:**

Suppose you have an operator f and a collection of distinct scalars $\kappa_i$ such that $\prod (f - \kappa_i) = 0$. Then Lagrange interpolation gives a method to construct idempotent operators $p_i$ which project to the $\kappa_i$-eigenspaces of f. We think of this process as diagonalization, and we categorify it: given a functor F with some additional data (akin to the collection of scalars), we construct a complete system of orthogonal idempotent functors P_i. We will give some simple but interesting examples involving modules over the group algebra of $\mathbb{Z}/2\mathbb{Z}$. The categorification of Lagrange interpolation is related to the technology of Koszul duality.Diagonalization is incredibly important in every field of mathematics. I am a representation theorist, so I will briefly indicate some of the important applications of categorical diagonalization to representation theory.

This is all joint work with Matt Hogancamp.

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