The Legendre Transform: a Category Theoretic Perspective

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

He gave his talk on Wednesday May 27th. Afterwards we discussed it on the Category Theory Community Server, here:

https://categorytheory.zulipchat.com/#narrow/stream/229966-ACT.40UCR-seminar/topic/May.2027th.3A.20Simon.20Willerton

You can view or join the conversation there if you sign in.

You can see his slides here, or download a video here, or watch the video 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 $\overline{ \mathbb{R}}:=[-\infty,+\infty].$ 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.

The talk is based on this paper:

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

Also see his blog article:

• Simon Willerton, The nucleus of a profunctor: some categorified linear algebra, The n-Category Café.

2 Responses to The Legendre Transform: a Category Theoretic Perspective

1. M M says:

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• D says:

Please give some proof to show who owns Zoom, why it is not safe, and why people would usually adopt the new technology without question. Please do not hold prejudice or discrimination.

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