Related papers: The Limits of Mathematics

This is more or less the content of a 5-hour mini-course that I have given at KTH in the program ``Master class in low-dimensional dynamics'' during May 1-5, 2023. It was not intended to be exhaustive but to give the students a grasp of…

These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…

This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institute of Mathematics, Nankai University, Tianjin, China. July…

This is the Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, which was held in Montreal, QU, August 18-20, 1995

This is the Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, which was held in Stockholm Sweden, July 30 - August 1, 1999

I give a brief, non-technical, historical perspective on numerical analysis and optimization. I also touch on emerging trends and future challenges. This content is based on the short presentation that I made at the opening ceremony of…

These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…

These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled…

This volume of the Electronic Proceedings in Theoretical Computer Science (EPTCS) contains extended abstracts of talks to be presented at the Seventh International Conference on Computability and Complexity in Analysis (CCA 2010) that will…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might…

This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift…

In joint work with Adam Black and Reuben Drogin, we develop a new approach to understanding the diffusive limit of the random Schrodinger equation based on ideas taken from random matrix theory. These lecture notes present the main ideas…

The 10th Asia-Europe workshop in "Concepts in Information Theory and Communications" AEW10 was held in Boppard, Germany on June 21-23, 2017. It is based on a longstanding cooperation between Asian and European scientists. The first workshop…

In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion…

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.

This is the Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence, which was held in Stanford, CA, July 17-19, 1992

This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…

This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…

This volume contains the proceedings of the International Workshop on Developments in Implicit Computational complExity (DICE 2010), which took place on March 27-28 2010 in Paphos, Cyprus, as a satellite event of the Joint European…