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.

The course is based on a minibook that will be published by Springer. The text below is a shortened preface  to this book.In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We  discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green’s functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green’s functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.

The course is based on a minibook that will be published by Springer. The text below is a shortened preface  to this book.In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We  discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green’s functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green’s functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.

The course is based on a minibook that will be published by Springer. The text below is a shortened preface  to this book.In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We  discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green’s functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green’s functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.

The course is based on a minibook that will be published by Springer. The text below is a shortened preface  to this book.In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We  discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green’s functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green’s functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.

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.