In my previous talk, on 9/4/24, I set Stark’s Conjectures in the more general context of Hilbert’s 12th Problem, highlighting the special complex functions used by number-theorists to study various cases in recent decades. I also surveyed the remarkable way that the same special functions have cropped up recently in Quantum and Statistical Physics, as indeed have SICs themselves in the case of the first order Stark Conjecture over real quadratic fields.In this second, more number-theoretic, talk I will focus on the latter case. After recalling the necessary details, I will motivate and explain some ongoing work which sets SICs in the context of the Heisenberg group over ${mathbb Z}_p$ (the p-adic integers), `Theta-pairings’ of p-adic measures and Coleman’s power series. This in turn motivates the search for `special measures’ to replace the complex functions mentioned above, in a possible p-adic theory of real-multiplication.Although this will necessarily be a more technical talk than the previous one, I shall still aim to make it largely accessible to non-number-theorists.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We show that holographic CFTs with a global U(1) symmetry that contain particles satisfying a form of the weak gravity conjecture, contain states that thermalize much slower than the typical thermalization time set by the black hole temperature. In the eikonal limit, these states correspond to metastable bulk configurations containing charged particles hovering outside the horizon of a Reissner–Nordström black hole in AdS. More generally, we study slow thermalization by computing the quasinormal modes of black holes due to charged scalar perturbations. We find that these states persist a finite distance away from the critical point in the EFT parameters, contrary to the ‘critical slowing down’ behavior expected near a phase transition. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarWe present an introduction to the theory of hydrodynamic limit for interacting particle systems; focused on jump and spin processes on a lattice. This theory is born in the 1970s but the first quantitative results were only obtained in the last decade. We will review recent advances on quantitative methods in the parabolic scaling, and present a recent joint work. ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Nahm sums (a class of q-hypergeometric series) appear in several contexts of mathematics: As characters of VOAs, as knot invariants, and as generating functions for certain partitions.Their modularity is known to be connected to the vanishing of elements in the Bloch group.I will present some applications of Nahm sums and work in progress concerning this connection. ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Seminar on Quantum Modularity and ResurgenceIn my talk I discuss examples of functions that are not quite modular forms but still exhibit nice symmetries. I am, as application, in particular interested in their asymptotic growth.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarConsider a Coulomb gas restricted to a Jordan domain in the complex plane. How does the asymptotic expansion of the free energy depend on the geometry of the domain, as the number of particles tends to infinity? I will explain how this problem is related to the Grunsky operator — a classical tool in complex analysis — and how this in turn reveals a close connection to the Loewner energy and other interesting domain functionals. I will further discuss the effect of corners,  which turns out to be universal in a certain sense. Most main players will be introduced in the talk. This is joint work with Kurt Johansson (KTH).========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of d=1+1 CFTs. We investigated three examples of increasing complexity: the deformed Ising, Tricritical-Ising, and non-unitary minimal model M(3,7). The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The M(3,7) CFT deformed by its Z2-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the M(3,5)CFT. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

For hyperbolic manifolds, we study two quantifications of being a homology 3-sphere, one geometric and the other topological: the spectral gap for the Laplacian on coclosed 1-forms and the size of the first torsion homology group.We first produce different examples of sequences of hyperbolic homology 3-spheres with volume going to infinity and with a uniform spectral gap on coclosed 1-forms.This answers a question of Lin-Lipnowski which they asked as a step towards constructing infinitely many examples of hyperbolic 3-manifolds that do not admit any irreducible solutions to the Seiberg-Witten equations.We then focus on the relation between a sequence having a uniform spectral gap, and exponential growth of torsion homology in that sequence. For arithmetic towers the work of Bergeron-Sengun-Venkatesh conjecturally suggests a precise such relation.We show that for any sequence of closed hyperbolic rational homology 3-spheres that converges to a tame manifold with at least one end, if the sequence has a uniform spectral gap for coexact 1-forms, then the torsion homology grows exponentially.This is based on joint work with Anshul Adve, Vikram Giri, Ben Lowe and Jonathan Zung. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

One of the celebrated outcomes of the modern conformal bootstrap is that most likely the 3D Ising model is an (extremal) conformal field theory (CFT) that saturates the bound in a certain optimization problem. However, numerically, we don’t see the different families of operators predicted from the lightcone analysis of a single crossing equation. This raises questions about whether extremal CFTs have a sparser spectrum than predicted or if numerics in the derivative basis face challenges in capturing these additional operators. This motivates us to seek an alternative basis of functionals acting on a single correlator crossing equation. These functionals are constructed using a class of 1D functionals that are dual to generalized free-field solutions. We took the first modest step to implement these functionals to numerically bootstrap higher-dimensional CFTs, demonstrating their efficiency, especially in two dimensions, where they outperform the traditional approach. Additionally, we have identified a series of new kinks in our plot that have gone unnoticed so far. In three dimensions, we reproduced the known bound, and although it is efficient, we require better control over the evaluation of these functionals to progress further. Notably, the convergence of these bounds is also better for large external dimensions in this functional basis. In this talk, I will provide an overview of this framework and discuss the general outlook.  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We consider a finitely generated, Zariski dense, Anosov subgroup of SL(d,R), d>2. We discuss results and problems about the dimension of the unique minimal set for the action of the group on partial flag spaces.

The notion of Hp,q-convex cocompact representations was introduced by Danciger, Guéritaud, and Kassel and provides a unifying framework for several interesting classes of discrete subgroups of the orthogonal groups SO(p,q+1), such as holonomies of convex cocompact hyperbolic manifolds or maximal globally hyperbolic anti-de Sitter spacetimes of negative Euler characteristic. By recent works of Seppi-Smith-Toulisse and Beyrer-Kassel, we now know that any Hp,q-convex cocompact representation of a group Γ of cohomological dimension p admits a unique invariant maximal spacelike p-dimensional manifold inside the pseudo-Riemannian hyperbolic space Hp,q, and that the space of Hp,q-convex cocompact representations of Γ forms a union of connected components in the associated SO(p,q+1)-character variety.In this talk, I will describe some recent joint work with Gabriele Viaggi in which we provide various applications for the existence of invariant maximal spacelike submanifolds. These include a rigidity result for the pseudo-Riemannian critical exponent (which answers affirmatively a question of Glorieux-Monclair), a comparison between entropy and volume, and several compactness and finiteness criteria in this framework.