The Legendre Transform: a Category Theoretic Perspective

In the ninth talk of the ACT@UCR seminar, Simon Willerton will tell us about a categorical approach to the Legendre transform, and its connection to tropical algebra.

He will give his talk on Wednesday May 27th at 5 pm UTC, which is 10 am in California, or 1 pm on the east coast of the United States, or 6 pm in the UK. It will be held online via Zoom, here:

https://ucr.zoom.us/j/607160601

You can see his slides here:

• Simon Willerton, The Legendre–Fenchel transform from a category theoretic perspective.

Abstract. The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this talk I’ll show how it arises in the context of category theory using categories enriched over the extended real numbers It turns out that it arises out of nothing more than the pairing between a vector space and its dual in the same way that the many classical dualities (e.g. in Galois theory or algebraic geometry) arise from a relation between sets.

I won’t assume knowledge of the Legendre-Fenchel transform.