相关论文: Geometry and the Imagination in Minneapolis

Lecture notes for the minicourse "Holonomy Groups in Riemannian geometry", a part of the XVII Brazilian School of Geometry, to be held at UFAM (Amazonas, Brazil), in July of 2012.

In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation…

We establish a precise relation between Galois theory in its motivic form with the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization). We identify, through a…

Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.

These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties,…

In this brief essay we succinctly comment on the historical origin of Hilbert geometry. In particular, we give a summary of the letter in which David Hilbert informs his friend and colleague Felix Klein about his discovery of this geometry.…

The recent progress of text-to-image generation has been recognized in architectural design. Our study is the first to investigate the potential of text-to-image generators in supporting creativity during the early stages of the…

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…

These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…

We present some episodes from the history of interactions between geometry and physics over the past century.

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…

In order to ask for future concepts of relativity, one has to build upon the original concepts instead of the nowadays common formalism only, and as such recall and reconsider some of its roots in geometry. So in order to discuss 3-space…

The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.

The paper presents a course on Combinatorial Algorithms that is based on the drafts of the author that he used while teaching the course in the Department of Informatics and Applied Mathematics of Yerevan State University, Armenia from…

This volume contains the proceedings of the Sixth International Workshop on Computing with Terms and Graphs (TERMGRAPH 2011). The workshop took place in Saarbruecken, Germany, on April 2nd, 2011, as part of the fourteenth edition of the…

Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So,…

This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.