Breakthroughs in machine learning have led to impressive results in numerous fields in recent years. I will review some of the best-known results on the computer science side, provide simple ways to think about the associated techniques, discuss possible applications in string theory, and present some applications in string theory where they already exist. One promising direction is using machine learning to generate conjectures that are then proven by humans as theorems. This method, sometimes referred to as intelligible AI, will be exemplified in an enormous ensemble of F-theory geometries that will be featured throughout the talk.

It is a classical theorem of Magnus that the word problem for one-relator groups is solvable; its precise complexity remains unknown. A geometric characterization of the complexity is given by the Dehn function. I will present joint work with Daniel Woodhouse showing that one-relator groups have a rich collection of Dehn functions, including the Brady--Bridson snowflake groups on which our work relies.

We consider a collisionless kinetic equation describing the probability density of particles moving in a one-dimensional domain subject to partly diffusive reflection at the boundary. It was shown in 2017 by Mokhtar-Kharroubi and Rudnicki that for large times such systems either converge to an invariant density or, if no invariant density exists, exhibit a so-called “sweeping phenomenon” in which the mass concentrates near small velocities. This dichotomy is obtained by means of subtle arguments relying on the theory of positive operator semigroups. In this talk I shall review some of these results before discussing how, under suitable assumptions both on the boundary operators (which in particular ensure that an invariant density exists) and on the initial density, one may even obtain estimates on the rate at which the system converges to its equilibrium. This is joint work with Mustapha Mokhtar-Kharroubi (Besançon).

I will explain a new proof of the non-linear stability of the Minkowski spacetime as a solution of the Einstein vacuum equation. The proof relies on an iteration scheme at each step of which one solves a linear wave-type equation globally. The analysis takes place on a suitable compactification of $\mathbb{R}^4$ to a manifold with corners whose boundary hypersurfaces correspond to spacelike, null, and timelike infinity; I will describe how the asymptotic behavior of the metric can be deduced from the structure of simple model operators at these boundaries. This talk is based on joint work with András Vasy.

In this talk we will discuss non-Abelian T-duality as a solution generating technique in type II Supergravity, briefly reviewing its potential to motivate, probe or challenge classifications of supersymmetric solutions, and focusing on the open problem of providing the newly generated AdS brackgrounds with consistent dual superconformal field theories. These can be seen as renormalization fixed points of linear quivers of increasing rank. As illustrative examples, we consider the non-Abelian T-duals of AdS5xS5, the Klebanov-Witten background, and the IIA reduction of AdS4xS7, whose proposed quivers are, respectively, the four dimensional N=2 Gaiotto-Maldacena theories describing the worldvolume dynamics of D4-NS5 brane intersections, its N=1 mass deformations realized as D4-NS5-NS5’, and the three dimensional N=4 Gaiotto-Witten theories, corresponding to D3-D5-NS5. Based on 1705.09661 and 1609.09061.

The horizon conjecture, proved in a case by case basis, states that every supersymmetric smooth horizon admits an sl(2, R) symmetry algebra. However it is unclear how string corrections modify the statement. In this talk I will present the analysis of supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory, and show the conditions for the horizon to admit an sl(2, R) symmetry algebra. In the second part of the talk, I shall consider the inverse problem of determining all extreme black hole solutions associated to a prescribed near-horizon geometry. I will expand the horizon fields in the radial co-ordinate, the so-called moduli, and show that the moduli must satisfy a system of elliptic PDEs, which implies that the moduli space is finite dimensional.

The talk is based on arXiv:1605.05635 [hep-th] and arXiv:1610.09949 [hep-th].

My talk is based on joint work with Claire Debord (Univ. Auvergne).
We will explain why Lie groupoids are very naturally linked to Atiyah-Singer index theory.
In our approach -originating from ideas of Connes, various examples of Lie groupoids
- allow to generalize index problems,
- can be used to construct the index of pseudodifferential operators without using the pseudodifferential calculus,
- give rise to proofs of index theorems, 
- can be used to construct the pseudodifferential calculus.

I will present Vidit Nanda's paper "Local homology and stratification" (https://arxiv.org/abs/1707.00354), and briefly explain how in my master thesis I am applying ideas from the paper to study word embedding problems.

Abstract of the paper:  We outline an algorithm to recover the canonical (or, coarsest) stratification of a given regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a finite sequence of categories whose colimit recovers the canonical strata via (isomorphism classes of) its objects. The entire process is amenable to efficient distributed computation.
 

The Peter-Weyl idempotent of a parahoric subgroup is the sum of the idempotents of irreducible representations which have a nonzero Iwahori fixed vector. The associated convolution algebra is called a Peter-Weyl Iwahori algebra.  We show any Peter-Weyl Iwahori algebra is Morita equivalent to the Iwahori-Hecke algebra.  Both the Iwahori-Hecke algebra and a Peter-Weyl Iwahori algebra have a natural C*-algebra structure, and the Morita equivalence preserves irreducible hermitian and unitary modules.  Both algebras have another anti-involution denoted as •, and the Morita equivalence preserves irreducible and unitary modules for the • involution.   This work is joint with Dan Barbasch.