Publications

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• Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state

  Vladimir V. Skokov

  SciPost Phys. Lect. Notes 91 (2025) · published 7 March 2025 | Toggle abstract · pdf

  These lecture notes, prepared for the 2024 XQCD PhD, provide an introduction to the analytic structure of an equation of state near a second-order phase transition and its most prominent landmark: the Yang-Lee edge singularity. In addition to discussing general properties, the notes review recent theoretical progress in locating the QCD critical point by tracking the trajectory of the Yang-Lee edge singularity.

  1 citation

• High-dimensional random landscapes: From typical to large deviations

  Valentina Ros

  SciPost Phys. Lect. Notes 102 (2025) · published 13 October 2025 | Toggle abstract · pdf

  We discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms: low-rank matrix estimation (case 1) and low-rank tensor estimation (case 2). We show how to map the inference problem onto the optimization problem of a high-dimensional landscape, which exhibits distinct geometrical properties in the two cases. We discuss methods for characterizing typical realizations of these landscapes and their optimization through local dynamics. We conclude by highlighting connections between the landscape problem and large deviation theory.

  1 citation

• An introduction to large deviations with applications in physics

  Ivan N. Burenev, Daniël W. H. Cloete, Vansh Kharbanda, Hugo Touchette

  SciPost Phys. Lect. Notes 104 (2025) · published 23 October 2025 | Toggle abstract · pdf

  These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications," held in July 2024 at Les Houches in France. They present the basic definitions and mathematical results that form the theory of large deviations, as well as many simple motivating examples of applications in statistical physics, which serve as a basis for the many other lectures given at the school that covered more specific applications in biophysics, random matrix theory, nonequilibrium systems, geophysics, and the simulation of rare events, among other topics. These notes extend the lectures, which can be accessed online, by presenting exercises and pointer references for further reading.

  1 citation

• Lecture notes on large deviations in non-equilibrium diffusive systems

  Bernard Derrida

  SciPost Phys. Lect. Notes 106 (2025) · published 29 October 2025 | Toggle abstract · pdf

  These notes are a written version of lectures given in the 2024 Les Houches Summer School on Large deviations and applications. They are are based on a series of works published over the last 25 years on steady properties of non-equilibrium systems in contact with several heat baths at different temperatures or several reservoirs of particles at different densities. After recalling some classical tools to study non-equilibrium steady states, such as the use of tilted matrices, the Fluctuation theorem, the determination of transport coefficients, the Einstein relations or fluctuating hydrodynamics, they describe some of the basic ideas of the macroscopic fluctuation theory allowing to determine the large deviation functions of the density and of the current of diffusive systems.

  1 citation

• A somewhat random walk through nuclear and particle physics

  Thomas D. Cohen, Nicholas R. Poniatowski

  SciPost Phys. Lect. Notes 34 (2021) · published 20 September 2021 | Toggle abstract · pdf

  These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of symmetry. The basic philosophy is to introduce many of the fundamental ideas in nuclear and particle physics using relatively sophisticated mathematical tools -- but to do so in as a simplified a context to explain the underlying ideas. Thus, for example, the Higgs mechanism is discussed in terms of an Abelian Higgs model. The emphasis is largely, but not entirely theoretical in orientation. The goal is for readers to develop an understanding of many of the underlying issues in a relatively sophisticated way.

  1 citation

• Field theory of collinear and noncollinear magnetic order

  Oleg Tchernyshyov

  SciPost Phys. Lect. Notes 85 (2024) · published 5 September 2024 | Toggle abstract · pdf

  These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.

  1 citation

• A brief tutorial on information theory

  Tarek Tohme, William Bialek

  SciPost Phys. Lect. Notes 87 (2024) · published 23 September 2024 | Toggle abstract · pdf

  At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial, lightly edited. It covers basic definitions and context rather than detailed calculations. We hope to have maintained the informality of the presentation, including exchanges with the students, while still being useful.

  1 citation

• Introduction to string theory

  Carlo Maccaferri, Fabio Marino, Beniamino Valsesia

  SciPost Phys. Lect. Notes 90 (2025) · published 29 January 2025 | Toggle abstract · pdf

  These are lecture notes of the introductory String Theory course held by one of the authors for the master program of Theoretical Physics at Turin University. The world-sheet approach to String Theory is pedagogically introduced in the framework of the bosonic string and of the superstring.

• Les Houches lectures on non-perturbative topological strings

  Marcos Mariño

  SciPost Phys. Lect. Notes 112 (2026) · published 27 January 2026 | Toggle abstract · pdf

  In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the non-perturbative sectors of the theory as unveiled by the theory of resurgence. I give a self-contained derivation of recent results on non-perturbative amplitudes, and I explain the conjecture relating the resurgent structure of the topological string to BPS invariants. In the second part of the lectures I introduce the topological string/spectral theory (TS/ST) correspondence, which provides a non-perturbative definition of topological string theory on toric Calabi–Yau manifolds in terms of the spectral theory of quantum mirror curves.

• Population genetics: An introduction for physicists

  Andrea Iglesias-Ramas, Samuele Pio Lipani, Rosalind J. Allen

  SciPost Phys. Lect. Notes 89 (2024) · published 10 December 2024 | Toggle abstract · pdf

  Population genetics lies at the heart of evolutionary theory. This topic forms part of many biological science curricula but is rarely taught to physics students. Since physicists are becoming increasingly interested in biological evolution, we aim to provide a brief introduction to population genetics, written for physicists. We start with two background chapters: chapter 1 provides a brief historical introduction to the topic, while chapter 2 provides some essential biological background. We begin our main content with chapter 3 which discusses the key concepts behind Darwinian natural selection and Mendelian inheritance. Chapter 4 covers the basics of how variation is maintained in populations, while chapter 5 discusses mutation and selection. In chapter 6 we discuss stochastic effects in population genetics using the Wright-Fisher model as our example, and finally we offer concluding thoughts and references to textbooks in chapter 7.