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.

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

Numerical General Relativity is the art of solving Einstein’s Field Equations with computational methods. These lectures will review the formalism currently employed for astrophysical simulations in strong-gravity, notably comprising compact binaries, gravitational collapse and gravitational waves. They will cover the following topics: 3+1 formulation of Einstein’s equations, the initial data problem, the evolution problem, the gauge choice and the extraction of gauge-invariant quantities. A selection of breakthrough results for gravitational-wave astronomy will also be presented.Supported by the « 2021 Balzan Prize for Gravitation: Physical and Astrophysical Aspects », awarded to Thibault Damour

Numerical General Relativity is the art of solving Einstein’s Field Equations with computational methods. These lectures will review the formalism currently employed for astrophysical simulations in strong-gravity, notably comprising compact binaries, gravitational collapse and gravitational waves. They will cover the following topics: 3+1 formulation of Einstein’s equations, the initial data problem, the evolution problem, the gauge choice and the extraction of gauge-invariant quantities. A selection of breakthrough results for gravitational-wave astronomy will also be presented.Supported by the « 2021 Balzan Prize for Gravitation: Physical and Astrophysical Aspects », awarded to Thibault Damour

Seminar on  Quantum and Modularity ResurgenceThese are the first talks of the series of seminars on Resurgence and Quantum Modularity, and they are meant to be an introduction to the main topics of the series, namely resurgence and quantum modular forms. The first talk will introduce the notion of Borel and Laplace transforms, resurgent structures and the median resummation. The second talk will go through modular forms and their asymptotics leading to mock and then quantum modular forms.========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.

Exponential Networks are a useful tool to count BPS states in local Calabi-Yau 3-folds. In this talk we apply Exponential Networks to D0-D4 bound states in flat space. This leads us to an explicit correspondence between torus fixed points of the Hilbert scheme of points on ${mathbb C}^2$ and anomaly free finite webs attached to the quadratically framed pair of pants. This can be viewed as an A-model description of the ADHM construction.

Probability and analysis informal seminarIn this talk, we will consider the maximal edge-traversal time in First-passage percolation. This is the maximum value that optimal paths can take when traversing random weighted graphs. We will discuss our use of upper tail large deviation and the resampling argument as primary analytical tools. These methods have enabled us to determine the leading-order asymptotic of the maximal edge-traversal time for several Weibull distributions. This talk is based on two works: one with Clément Cosco and the other with Ryoki Fukushima.========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.

Soil undergoes numerous degradation processes, including compaction, sealing, salinization, acidification, impoverishment, contamination, and biodiversity loss. Among these, soil erosion stands out as the most critical in terms of both intensity and widespread impact. Although soil erosion is inherently a natural process, human activities, notably agriculture, deforestation, and urbanization, significantly accelerate it. With the continued growth of human populations, the strain on land resources intensifies, exacerbating soil erosion dynamics. This presentation aims to shed light on the nonlinear processes and mitigation strategies associated with soil erosion.The processes involved encompass the detachment, transportation, and deposition of soil particles, leading to adverse environmental, agricultural, and socio-economic consequences. On-site impacts include the loss of organic matter and nutrients from the topsoil, resulting in soil impoverishment, diminished biodiversity, and reduced crop yields. Off-site effects involve sedimentation in rivers and reservoirs, adversely affecting water quality, aquatic ecosystems, and infrastructure.Soil erosion is a dynamic phenomenon influenced by various factors such as rainfall, water flow, gravity, tillage, topography, vegetation cover, and land use. Three primary factors drive soil erosion: water, wind, and tillage. Water erosion further subdivides into sheet erosion, rill and gully erosion, and mass movements. Wind erosion entails the detachment and transportation of soil particles by the force of the wind. Tillage contributes to erosion through the force of gravity. Understanding these mechanisms is pivotal for devising effective soil conservation strategies.The susceptibility of an area to soil erosion is influenced by diverse factors, including climate, soil type, topography, vegetation cover, and land use practices. Successful soil erosion control needs implementing sustainable land management practices. Conservation tillage, cover cropping, associated cropping, contour plowing, and agroforestry represent examples of sustainable agricultural practices that aid in erosion reduction. Terracing, check dams, and vegetative buffers are additional solutions employed to mitigate water erosion, while windbreaks and cover crops prove effective measures against wind erosion.Addressing soil erosion necessitates a multidisciplinary approach that integrates community engagement, scientific knowledge, and policy development.========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 seminarIn 1986, Kardar, Parisi and Zhang introduced a model equation for a growing surface, in the form of a nonlinear partial differential equation with noise[1]. In the original paper they applied a dynamical renormalization group analysis to demonstrate its universal nature, which is one of the first identified non-equilibrium universality classes (KPZ universality class). Since then their equation (KPZ equation) has been accepted as a standard model in non-equilibrium statistical mechanics.  In this talk, we focus on its one dimensional version because it has attracted particular attention in the last decade or so. Mathematically there had been an issue of well-definendness of the equation itself, which was solved by a few different ideas. There is also a high precision experiment using liquid crystal. An important step was the discovery of an exact solution in 2010[2], which confirmed that the height fluctuation is of O(t^(1/3)) and its universal distribution is given by the Tracy-Widom distribution from random matrix theory. Since then there have been a large amount of studies on its generalizations, which now forms a field of “integrable probability”.  The activity still continues. Universal behaviors for general initial conditions can now be studied (“KPZ fixed point”). Very recently we have found a direct connection between KPZ systems and free fermion at finite temperature[3].  A remarkable aspect of one dimensional KPZ is its unexpectedly wide universality. For example, KPZ universality is expected to appear in long time behaviors of many one-dimensional Hamiltonian dynamical systems such as anharmonic chains [4]. This is surprising because time-evolution of such systems are deterministic and there are apparently no growing surface with noise. More recently people have observed appearance of KPZ behaviors in dynamical properties of quantum spin chains[5], first in numerical simulations but more recently in real experiments. These discoveries have been attracting considerable attention but theoretical foundations are not yet satisfactory. References[1] M. Kardar, G. Parisi, and Y. C. Zhang, Dynamic scaling of growing interfaces,Phys. Rev. Lett., 56, 889–892 (1986).[2] T. Sasamoto and H. Spohn, One-dimensional Kardar-Parisi-Zhang equation: an exactsolution and its universality, Phys. Rev. Lett., 104:230602 (2010);G. Amir, I. Corwin, and J. Quastel, Probability distribution of the free energy of the continuumdirected random polymer in 1+1 dimensions, Comm. Pure Appl. Math., 64, 466– 537 (2011).[3] T. Imamura, M. Mucciconi, T. Sasamoto, Solvable models in the KPZ class: approach throughperiodic and free boundary Schur measures, arxiv2204.08420.  [4] H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154,1191–1227 (2014).[5] M. Ljubotina, M. Znidaric, T. Prosen, Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet,Phys. Rev. Lett. 122, 210602 (2019).========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.

Historically, the synergy between physics and geometry, from the times of Archimedes and Newton to the era of Einstein, has repeatedly been the catalyst for pivotal breakthroughs in physics and mathematics. In this talk, I will introduce a new narrative demonstrating how physics and geometry intertwine, leading to unexpected and significant results in critical phenomena in physics. Specifically, I will elucidate how non-commutative geometry—a mathematical framework born from the insights of physicists—offers fresh perspectives on conformal field theory, a subject with profound applications across various physics domains, from condensed matter to quantum gravity, and string theory.  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.