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:

• 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.

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2 Responses to The Legendre Transform: a Category Theoretic Perspective

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You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.

Zoom is owned by the Chinese. FBI says not safe to use, but as usual humans adopt the next technology without question.

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.