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Author Archives: Fabrice Baudoin
An “elementary” problem
A few days ago, I was told the following problem: Let E a finite set of points in the plane with the property that any line containing two points of E contains at least a third one. Show that E … Continue reading
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Meet Cedric Villani
Cedric Villani is an extremely well-known mathematician in France, who was awarded the Fields medal in 2009. The following video shows well his personality and explains a little his conception about the work of mathematicians. As he points out, mathematics … Continue reading
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Lecture 12. The heat semigroup on a compact Riemannian manifold
In this section we shall consider a smooth and complete Riemannian manifold with dimension . The Riemannian measure will be denoted by . The Laplace-Beltrami of will be denoted by . Since is assumed to be complete, as we have … Continue reading
Lecture 11. The Laplace-Beltrami operator on a Riemannian manifold
In this lecture we extend the previous results in the framework of smooth manifolds. The main idea to extend those results is that, similar computations may be performed in local coordinates charts and then we use a partition of unity. … Continue reading
Posted in Curvature dimension inequalities
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How to write mathematics badly
It is not always clear how to write a mathematics paper but it is much more clear how not to write it ! This funny video by Jean-Pierre Serre shows some of the things one should avoid.
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Creativity in mathematics
Richard Feynman was obviously an extraordinary physicist and a charismatic lecturer. In the following video he discusses the differences and the interplay between mathematics and physics: His opening statement is: “Mathematicians only are dealing with the structure of the reasoning.” … Continue reading
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S.S. Chern
The following video contains interesting testimonies about the differential geometer Shiing-Shen Chern. Source
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Lecture 10. The distance associated to Laplace-Beltrami operators
In order to apply the diffusion semigroup theory developed in the first lectures and construct without ambiguity the semigroup associated to the Laplace-Beltrami operator L, we need to know if L is essentially self-adjoint. Interestingly, this property of essential self-adjointness … Continue reading
Lecture 9. Laplace-Beltrami operators on Rn
In this lecture we define Riemannian structures and corresponding Laplace–Beltrami operators. We first study Riemannian structures on Rn to avoid technicalities in the presentation of the main ideas and then, in a later lecture, will extend our results to the … Continue reading
Lecture 8. The heat semigroup on the circle
We now turn to a new part in this course. The first few lectures were devoted to the study of diffusion operators and the construction of associated semigroups. The goal of this new part of the course will be to … Continue reading
Research and Lecture notes 