Seminar on Quantum Modularity and ResurgenceQuantizing the mirror curve of a toric Calabi-Yau threefold gives rise to quantum-mechanical operators. Their fermionic spectral traces produce factorially divergent power series in the Planck constant and its inverse, which are conjecturally captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss a general conjecture on the resurgence of these dual asymptotic series, and I will present a proven exact solution in the case of the first spectral trace of local $P^2$. A remarkable number-theoretic structure underpins the resurgent properties of the weak and strong coupling expansions and paves the way for new insights relating them to quantum modular forms. Finally, I will mention how these results fit into a broader paradigm linking resurgence and quantum modularity. This talk is based on arXiv:2212.10606 and further work with V. Fantini (available soon).========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.

Dark compact objects are nowadays routinely observed through multiple experimental schemes. Measurements of their vibrational spectra offer unprecedented opportunities to investigate the highly dynamical regime of General Relativity, search for signs of new physics, and increase the evidence for their « black hole nature ». After an introduction to the topic, I will review recent achievements of this scientific program enabled by gravitational-wave observations, and current efforts to extend it through the inclusion of nonlinear effects and generic orbital configurations of binary mergers. Prospects for high-precision measurements through next-generation interferometric detectors will also be briefly discussed.[1] https://drive.google.com/file/d/1OcfmyL0KBUAZrXfi9N7dhiOaALbyEgxj/view?usp=sharing 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.

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.

Seminar on  Quantum and Modularity ResurgenceIn this talk, I will review the exact WKB approach used in the QFT/ODE correspondence related to the NS phase of the Ω-background. By AGT correspondence, those QFT’s are related to c = ∞ CFTs. In particular, I will focus on the Stokes graph, also known as the spectral network in physics. The spectral network plays an essential role in the exact WKB and the nonabelianization of SL(N,C) flat connections. We find that the very same structure also exists at the self dual phase of the Ω-background, which is the c = 1 Liouville CFT by AGT correspondence. I will introduce our work on nonabilianization of the Virasoro conformal blocks using Heisenberg conformal blocks with the key ingredient of spectral networks. This is analogous to the nonabelianization of SL(2, C) flat connections by the GL(1, C) connections. This is a joint work in progress with Andrew Neitzke.========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.

Einstein’s path to the discovery of General Relativity, from 1907 to November 1915, will be described. A particular emphasis will be given to the multi-pronged character of Einstein’s strategy.Supported by the « 2021 Balzan Prize for Gravitation: Physical and Astrophysical Aspects », awarded to Thibault Damour