Related papers: Adventures in algebraic geometry
Recent advancements in gravitational wave astronomy hold the promise of a completely new way to explore our Universe. These lecture notes aim to provide a concise but self-contained introduction to key concepts of gravitational wave…
This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…
Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of S\~{a}o Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_\nu$, with…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
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.
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
These are lecture notes from a mini-course taught at Winterbraids XIII (Montpellier, 2024). The main character of these notes are curves in the complex projective plane, viewed from a topological perspective.
These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to "String Topology" and…
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
This short introduction to positive geometries, targeted at a mathematical audience, is based on my talk at OPAC 2022.
This survey is an invitation to recent developments in higher dimensional birational geometry.
We survey some ideas from the subject of Random Algebraic Geometry, a field that introduces a probabilistic perspective on classical topics in real algebraic geometry. This offers a modern approach to classical problems, such as Hilbert's…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
These are the notes from my courses on the arithmetic of quadratic forms.
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
These lecture notes are devoted to the recent progress in the geometric aspects of quantum integrable systems based on quantum groups solved using the Bethe ansatz technique. One part is devoted to their enumerative geometry realization…