Related papers: Lectures on K\"{a}hler Geometry
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
The first goal of this article is to survey recent progress in Brill--Noether theory, including both the study of the moduli space of maps from a curve to projective space and the geometry of the resulting curves in projective space. The…
This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…
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…
These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
This is an introductory text to differential geometry (written in Polish) aimed for high-school students.
We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields,…
This document contains notes from the graduate lecture course, "Symmetries in QFT" given by J.F.Wheater at Oxford University in Hilary term. The course gives an informal introduction to QFT.
In this paper we study a generalization of K\"ahler differentials, which correspond to the secondary Hochschild homology associated to a triple $(A,B,\varepsilon)$. We establish computations in low dimension, while also showing how this…
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…