Related papers: Stein structures: existence and flexibility
This note was written for the proceedings of the conference "Symplectic Geometry and Anosov Flows" held in Heideleberg in July 2024. It is meant as an invitation to the study of certain families of contact structures, centering around the…
We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…
We reprove and strengthen some old difficult theorems of 4-manifolds by the aid of recently discovered modern tools, which involve contact structures on 3-manifolds, compact Stein domains, etc.
These are notes of the lectures given during the Toric Topology Workshop at the Korea Advanced Institute of Science and Technology in February 2010. We describe several approaches to moment-angle manifolds and complexes, including the…
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…
This is the author's PhD thesis, published at the Universit\"at M\"unster, Germany in 2010. It contains a detailed description of the results of arXiv:0903.1989, arXiv:0905.0071 and arXiv:0908.2713.
These are the lecture notes for a short course in topological string theory that I gave at Uppsala University in the fall of 2004. The notes are aimed at PhD students who have studied quantum field theory and general relativity, and who…
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
Over the past decade, the class of Oka manifolds has emerged from Gromov's seminal work on the Oka principle. Roughly speaking, Oka manifolds are complex manifolds that are the target of "many" holomorphic maps from affine spaces. They are…
This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am…
These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…
This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…
Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…
These pages serve two purposes. First, they are notes to accompany the talk "Hyperbolic and projective geometry in constraint programming for CAD" by Walter Whiteley at the "Janos Bolyai Conference on Hyperbolic Geometry", 8--12 July 2002,…
These notes are adapted from two talks given at the 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology at the Alfred Renyi Institute. We will quickly review what we do and do not know about the…
These are expanded lecture notes for a minicourse taught at the "School on disordered media" at the Alfred Renyi institute in Budapest, January 2025.
This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.
The BRIDGES meeting in gauge theory, extremal structures, and stability was held June 2024 at l'Institut d'\'Etudes Scientifiques de Carg\`ese in Corsica, organized by Daniele Faenzi, Eveline Legendre, Eric Loubeau, and Henrique S\'a Earp.…
This collection of thirty two reviewed articles covers several fields of General Topology. Several contributions represent invited presentations at the Ninth Prague Topological Symposium.