Related papers: Introductory Lectures on Resurgence: CERN Summer S…

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series…

These lectures contain an introduction to the following topics: 1) Phenomenology of the hadron spectrum; 2) The static Wilson loop in perturbative and in lattice QCD. Confinement and the flux tube formation; 3) Non static properties:…

Using resurgent analysis we offer a novel mathematical perspective on a curious bijection (duality) that has many potential applications ranging from the theory of vertex algebras to the physics of SCFTs in various dimensions, to q-series…

This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various…

Many physics instructors aim to support student sensemaking in their classrooms. However, this can be challenging since instances of sensemaking tend to be short-lived, with students often defaulting to approaches based on answer-making or…

With the discovery of the Higgs boson the LHC experiments have closed the most important gap in our understanding of fundamental interactions. We now know that the interactions between elementary particles can be described by quantum field…

Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic sym- metries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism,…

These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of…

The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).

After recalling briefly the main physics issues beyond the Standard Model, the main physics objectives of experiments at CERN in the coming decade(s) are reviewed. These include the conclusion of the LEP programme during the year 2000, a…

We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the…

We introduce a non-perturbative continuum framework to study the dynamics of quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's theory of resurgent trans-series, combined with the physical principle of continuity,…

The aim of this paper is to derive new representations for the Hankel functions, the Bessel functions and their derivatives, exploiting the reformulation of the method of steepest descents by M. V. Berry and C. J. Howls (Berry and Howls,…

Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or…

This is an introductory course on fully developed turbulence. It discusses: in Lecture 1: the Navier Stokes equations, existence of solutions, statistical description, energy balance and cascade picture; in Lecture 2: the Kolmogorov theory…

1 First Lecture: Basics 1.1 Physical Derivation of the Master Equation 1.2 Some Simple Implications 1.3 Steady State 1.4 Action to the Left 2 Second Lecture: Eigenvalues and Eigenvectors of L 2.1 A Simple Case First 2.2 The General Case 3…

A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The…

In recent papers [1,2], a new method to cross the natural boundary has been proposed, and applied to Mordell-Borel integrals arising in the study of Chern-Simons theory, based on decompositions into {\it resurgent cyclic orbits}. Resurgent…

This series of lectures gives a pedagogical review of the subject of cosmological inflation. I discuss Friedmann-Robertson-Walker cosmology and the horizon and flatness problems of the standard hot Big Bang, and introduce inflation as a…

In this paper, we describe how we transformed our large-enrollment introductory physics sequence for life-science students to a Lecture/Studio format and aligned the physics concepts with authentic biological applications. We have reformed…