Motivated by work of Krasnov and Schlenker on the renormalized volume of hyperbolic 3-manifolds, we construct a Lorentzian version of the theory. This defines a (possibly infinite) invariant of positive curves in flag varieties. This is joint work with François Labourie and Yilin Wang.
 

Séminaire de géométrie arithmétique
Let U be a smooth variety over an algebraically closed field k of characteristic p > 0 and let X be a smooth compactification of U where D := X – U is an effective Cartier divisor. To an l-adic local system L on U, Abbes and Saito attached a conductor c(L) measuring the wild ramification of L at the generic points of D. In this talk, we will advertise the existence of a polynomial P depending only on X such that the Betti numbers of every l-adic local system L on U are bounded by rk(L) P(c(L)). We will underline the role played by Saito’s characteristic cycle and explain how these bounds can be extended to constructible complexes on arbitrary schemes of finite type over k. If time permits, we will explain some arithmetic and geometric consequences for the étale fundamental group. This is joint work with Haoyu Hu. 
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Séminaire de géométrie arithmétique
The Torelli locus — the image of the moduli space of curves (Mg) in the moduli space of abelian varieties (Ag) — is much-studied but still mysterious. In characteristic p, Ag has a beautiful stratification by the isomorphism type of the p-torsion A[p], and examples show that Mg is far from transverse to this stratification. In an ongoing project, we develop tools to understand (and perhaps make principled conjectures about) which strata of Ag meet Mg. In this talk, we explain some of the structures involved and then give some new results about them. Parts of this are joint work with Bryden Cais and Rachel Pries. 
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I will explain the implementation of a bootstrap method that combines Schwinger-Dyson equations, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, to determine finite temperature observables. I will show plots of these observables (determined using the bootstrap) that interpolate between available analytic results in the low and high temperature limits respectively as well as bounds on thermal phase transitions. Finally, I will show preliminary results in the ungauged two-matrix quantum mechanics.
 
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Probability and analysis informal seminar
The Solid on Solid model is a mainstay of the modelisation of 2D interfaces in the physics literature and it has also received extensive attention in mathematics. In particular a major work of Frölich and Spencer showed that it exhibits a roughening transitions where at low temperature, the interface is extremely localized with O(1) fluctuations at the microscopic scale while at high temperature it delocalize with logarithmic variance.However, almost all the existing literature focuses on the case where the interface is parallel to the main axis of the underlying lattice, as in a crystal facet, but of course this cannot be the case globally everywhere. We will show that, at least for a model with a small added potential, whenever the interface has a tilt the phenomenology changes completely : at low enough temperature prove that the behavior of the interface is rough (like the high temperature usual case) and provide a full scaling limit for the fluctuations. The main approach is a comparison to the zero-temperature case which can be described as lozenge tilings and a renormalization procedure to understand the asymptotic of an interacting tiling model.
  
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Probability and analysis informal seminar
After a brief historical review, I will explain how to pick a (uniform) random hyperbolic surface of genus g. After that, we will focus on the length spectrum. More specifically, we will examine short closed geodesics on a random hyperbolic surface of genus g. It turns out that, when g is big, the lengths of these geodesics are distributed just like the short cycles in a large random graph. This is a joint work with Simon Barazer and Alessandro Giacchetto.
 
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Although the high-energy limit of gauge theory amplitudes in an old and well-studied subject, comparatively little is known about gravity.  Many basic questions remain about graviton Reggeization and graviton Regge physics more broadly.  More confusingly, the high-energy limit in gravity is known to coincide with the classical limit.  In this talk, I will address these questions using an effective field theory for high energy scattering in gravity.  In particular, I clarify the role of Regge physics in gravity and more generally address the question of resummability of large logs.  Lastly, I explain the interplay between classical and Regge physics, and how one may use this to calculate large logs appearing in classical amplitudes to high loop orders. 
 
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Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

The different types of genes mutations in cancer genomes, the selection of driver mutations and the possibility of epistasis networks in cancer will be discussed.