Olivier Verdier

I want to show some simple heuristic calculations which show how monad rules stem from a functor adjunction.

Heuristic Calculations

Suppose we have some sort of duality product, and some "operators" $A$ and $A^*$.

Adjunctions means that \[ \langle y , A x \rangle \equiv \langle A^* y , x \rangle \]

We assume …

A natural derivation of the entropy from maximum likelihood.

The fundamental mathematical ideas behind thermodynamics

Some notes on the elementary properties of the exponential families

A proof of the divergence of the harmonic series with the Coq proof assistant.

A companion matrix is a matrix with a prescribed characteristic polynomial. I would like to show them from a broader perspective: companion matrices are the matrix version of a shift operator.

Type logic is the logic directly associated to types. It turns out that one can go quite far with regards to proving statements with Haskell. I show how to do that, and even how to prove statements in classical logic with Haskell.

My goal is to derive Maxwell's equations of electromagnetism with almost no effort at all. As often in mathematics, things look simpler when there is less structure. Here, as in mechanics, we do not assume any prior metric, so the geometry of the space at hand is very simple.