Related papers: Introduction to evolution equations in geometry
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
Awfully idiosyncratic lecture notes from CMI summer school in arithmetic geometry July 31-August 4, 2006. Does not include: rationality problems, techniques of the minimal model problem and much of the rest. Includes: Lecture 0: geometry…
The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.
We describe the gauge-theoretic approach to transformations in integrable geometry through discussion of two classical examples: surfaces of constant negative Gauss curvature and isothermic surfaces. These are purely expository notes…
In this series of lectures I review recent observational progress in constraining models of galaxy formation and evolution highlighting the importance advances in addressing questions of the assembly history and origin of the Hubble…
This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
These lectures are a brief introduction to supersymmetry.
This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009,…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the particle and its characteristic…
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 an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
This file, provided as bibliographical information, contains the table of contents and editors' foreword from the proceedings of the July 1996 Warwick EuroConference on Algebraic Geometry.
Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays,…
The evolution of complexity has been a central theme for Biology and Artificial Life (Bonner, 1988; Bedau et al., 2000). Complexification has been interpreted in different ways: as a process of diversification between evolving units…
These notes are an expanded version of the author's lectures at the graduate workshop "Noncommutative Algebraic Geometry" at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular…