Related papers: Recent Topics on Linear Dynamics
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas…
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…
Development of theory of dynamical systems admitting the normal shift in 1993-1999 is reviewed. Basics are given with complete proofs.
These lecture notes have been prepared as a course in fluid mechanics up to the presentation of the millennium problem listed by the Clay Mathematical Institute. At the end, a very modern aspect of fluid mechanics is covered concerning the…
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…
These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in…
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
This is a collection of notes for part of a short course on modal methods in fluid mechanics held at DAMTP, University of Cambridge, in the summer of 2019. These notes introduce the reader to resolvent analysis as it is currently used in…
These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent mathematical results about the long-time behaviour…
These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010. They serve to illustrate some techniques and results from the dynamics on…
This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…
This survey is on recent advancements in the intersection of physical modeling and machine learning. We focus on the modeling of nonlinear systems which are closer to electric motors. Survey on motor control and fault detection in operation…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
I developed the lecture notes based on my ``Linear Model'' course at the University of California, Berkeley over the past ten years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and…
We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.