P-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 ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
Biological macromolecules such as DNA, RNA, proteins and cytoskeletal filaments are polymers. As such, they share a set of properties that are common to any polymer, which are the focus of this course. Details about the protein folding problem will be cove ...
Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prio ...
Ce cours propose une introduction à la mécanique analytique. Il introduit les formalismes lagrangien et hamiltonien, en insistant sur leur capacité à simplifier la description des systèmes contraints, des symétries et des lois de conservation. Il présente ...
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail. ...
Machine learning and data analysis are becoming increasingly central in many sciences and applications. This course concentrates on the theoretical underpinnings of machine learning. ...