Related papers: Introduction to complex dynamics in one dimension
This contribution to the XXVII Symposium on Multiparticle Dynamics held in Frascati, Italy, September, 1997 consists of the following subject matter: (1) Introductory generalities. (2) Brief mention of some of the contributions to the…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.
This is an expanded version of the notes for the two lectures at the 2004 International Mathematics Conference (Chonbuk National University, August 4-6, 2004). The first lecture discusses the origins of cluster algebras, with the focus on…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
Notes on exact S-matrices in 1+1 dimensions, based on lectures given at the 1996 Eotvos Graduate School, Budapest, and at the Institut Henri Poincare, Paris.
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 course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
We discuss the motivation and the phenomenology of models with either flat or warped extra dimensions. We describe the typical mass spectrum and discovery signatures of such models at the LHC. We also review several proposed methods for…
This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
We introduce our experiment of research-oriented teaching mainly in Nanjing University and Tsinghua University, China. The great population and enrollment in China makes it worth to concern. It lasts 20 years and involves thousands of…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
This contribution is relative to the opening lectures of the ISSAOS 2001 summer school and it has the aim to provide the reader with some concepts and techniques concerning chaotic dynamics and transport processes in fluids. Our intention…
Lectures on the construction on the moduli space of principal bundles, given in the Mini-School on Moduli Spaces at the Banach center (Warsaw) 26-30 April 2005.
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
In this paper we investigate complex dynamics in infinite dimensions.
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
This is a broad-brush introduction to the theory of spin in quantum field theory, presented at the 1993 SLAC Summer Institute. It may be useful for beginning students.