• ## L'ouverture Écossaise

Il y a quelque temps que je suis avec une certaine régularité la chaîne Blitzstream, sur Youtube. Il s'agit d'une chaîne francophone sur les échecs, proposant un contenu très varié, et animée par Kévin Bordi, souvent accompagné du GM Fabien Libiszewski.

• ## Best of XKCD (and other comics)

This is a collection of the best XKCD comics, according to my personal taste.

• ## Holographic Duals of 3d S-fold CFTs

Some notes about the recent paper by Benjamin Assel and Alessandro Tomasiello, Holographic duals of 3d S-fold CFTs.

• ## Coulomb branches with complex singularities

Last week, Philip Argyres and Mario Martone published a very interesting paper, Coulomb branches with complex singularities. Some of the results are similar to those presented in my last publication, with Alessandro Pini and Diego Rodriguez-Gomez, The Importance of Being Disconnected, A Principal Extension for Serious Groups.

• ## Les neurosciences peuvent-elles éclairer l'éducation?

Conférence de Franck Ramus à l'ENS :

• ## Finite temperature holography

The $AdS/CFT$ correspondence is one of the central discoveries of the last decades in high-energy physics. As we know, in one of its incarnation it relates a certain supergravity theory on $AdS_5 \times S^5$ with $\mathcal{N}=4$ SYM with gauge group $SU(N)$ in the large $N$ limit and large 't Hooft coupling. But what's the relation to the real world? $\mathcal{N}=4$ SYM is an elegant theory, but certainly very different from what we find in experiments, so it seems holography (at least in this restricted sense) allows us to gain little if not no knowledge about the real world.

• ## Exact correlators on the Wilson Loop in $\mathcal{N}=4$ SYM

I'm talking here about the paper which appeared last week, by Simone Giombi and Shota Komatsu.

• ## Vandermonde Gaussian Integral

This is just to signal the formula for an integral that is useful in many matrix model computations: $$\int_{\mathbb{R}^n} \mathrm{d} \Lambda |\Delta (\Lambda)|^{\beta} \mathrm{exp} \left( - \frac{\mathrm{Tr} \, \Lambda^2 }{g^2}\right) = \frac{g^{n+ \beta n(n-1)/2} \pi^{n/2}}{2^{\beta n(n-1)/4}} \prod\limits_{j=1}^n \frac{\Gamma \left(1+ j \frac{\beta}{2} \right)}{\Gamma \left(1+ \frac{\beta}{2} \right)} \, .$$ In this formula, $\beta = 1,2,4$ determines which Gaussian ensemble is used (respectively Orthogonal, Unitary and Symplectic), $\Lambda = \mathrm{diag} (\lambda_1 , \dots , \lambda_n)$ is a diagonal matrix, the measure is $\mathrm{d} \Lambda = \mathrm{d} \lambda_1 \dots \mathrm{d} \lambda_n$ and $$\Delta (\Lambda) = \prod\limits_{1 \leq i < j \leq n} (\lambda_i - \lambda_j)$$ is the Vandermonde determinant.

• ## Matrix Integrals

Our aim in this note will be to say something about integrals of the form $$Z = \int_E \mathrm{d}M \, e^{-\mathrm{Tr} V (M)} \, ,$$ where for simplicity we will consider $V(M)$ to be a polynomial in $M$. We will follow closely the excellent review by Bertrand Eynard, Taro Kimura and Sylvain Ribault called Random matrices, available here.

• ## Homology and Volumes of compact Lie groups

In this post, I would like to show a nice relation between some Lie groups and products of spheres of odd dimensions. This can be made precise in the context of homology, and is useful to compute the volumes of compact Lie groups.