MATH-418: Heat kernel and analysis on manifoldsThis course develops the theory of the heat equation on Riemannian manifolds. We introduce the Laplace-Beltrami operator, the heat semigroup, and the heat kernel, study its fundamental properties, and explore how it "sees" the geometry of the underlying space.
MATH-750: K-stabilityThe topic is K-stability of Fano varieties, including (as time permits): the definitions, the equivalences of definitions, examples, the connection to the existence Kahler-Einstein metrics, and the construction of the moduli space.
MATH-467: Probabilistic methods in combinatoricsThe 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
PHYS-431: Quantum field theory IThe goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
PHYS-460: Nonlinear dynamics, chaos and complex systemsThe course provides students with the tools to approach the study of nonlinear systems and chaotic dynamics. Emphasis is given to concrete examples and numerical applications are carried out during the exercise sessions. ...
MATH-476: Optimal transportThe first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
PHYS-754: Lecture series on scientific machine learningThis lecture presents ongoing work on how scientific questions can be tackled using machine learning. Machine learning enables extracting knowledge from data computationally and in an automatized way. We will learn on examples how this is influencing the v ...
DH-405: Foundations of digital humanitiesThis course introduces the core concepts and methodologies of Digital Humanities, integrating both theoretical and practical perspectives. Students learn to work with large-scale cultural datasets, acquiring the tools and techniques required for their proc ...
COM-502: Dynamical system theory for engineersLinear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the qualitative analysis of nonlinear systems, both in discrete-t ...
PHYS-464: Solid state systems for quantum informationThis course will give an overview of the experimental state of the art of quantum technology for Quantum Information Processing (QIP). We will explore some of the most promising approaches for realizing quantum hardware and critically assess each approach' ...
CS-401: Applied data analysisThis course teaches the basic techniques, methodologies, and practical skills required to draw meaningful insights from a variety of data, with the help of the most acclaimed software tools in the data science world (pandas, scikit-learn, Spark, etc.) ...
MATH-511: Number theory II.b - Modular formsIn this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization. ...
MATH-494: Topics in arithmetic geometryP-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
MATH-680: Monstrous moonshineThe monstrous moonshine is an unexpected connection between the Monster group and modular functions. In the course we will explain the statement of the conjecture and study the main ideas and concepts leading to its proof. Our final goal is to study Borc ...
PHYS-817: SupersymmetrySupersymmetry is the unique quantum extension of the symmetry principles of relativity.
This course offers a first but broad introduction covering the role of Supersymmetry in our understanding of both physics beyond the Standard Model and non-perturbative ...
