Related papers: Perspectives on geometric analysis
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
This is an extended version of a talk given at the conference "Algebra and Topology in Interaction" on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…
This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of…
This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya,…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)--to Klein. We will see that they are not rivalling but are tied (by…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
The theme of this book chapter is to discuss algorithms for identifying and reconstructing groups and clusters of galaxies out of the general galaxy distribution. I review the progress of detection techniques through time, from the very…
To commemorate the 100th anniversary of general relativity, the International Society on General Relativity and Gravitation (ISGRG) commissioned a Centennial Volume, edited by the authors of this article. We jointly wrote introductions to…
This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
This article is intended as a kind of precursor to the document Geometry for Post-primary School Mathematics, part of the Mathematics Syllabus for Junior Certicate issued by the Irish National Council for Curriculum and Assessment in the…