Related papers: Report on GRG18, Session A3, Mathematical Studies …
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
The talks given in parallel session D4 at the 20th International Conference on General Relativity and Gravitation (Warsaw 2013) are summarized.
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
This paper is the write-up of a rapporteur talk given by the author at the 33rd International Cosmic Ray Conference in Rio de Janeiro, Brazil, in 2013. It attempts to summarize results and developments in ground-based gamma-ray observations…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
During the five days of this conference a very dense scientific program has enlighted our research fields, with the presentation of large number of interesting lectures. I will try to summarize the theoretical aspects of some of these new…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
This article is the write-up of a rapporteur talk given at the 34th ICRC in The Hague, Netherlands. It attempts to review the results and developments presented at the conference and associated to the vibrant field of ground-based gamma-ray…
This is the contribution representing Parallel Session A3, on Modified Gravity, in the Proceedings of the GR 20 Conference (July 2013, Warszawa, Poland). It consists of three invited chapters, selected by the Session Chair (P.H.) to…
We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
Lecture notes on selected topics in the theory of gravitation.
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
We summarize the talks presented at the QG4 session (loop quantum gravity: cosmology and black holes) of the 13th Marcel Grossmann Meeting held in Stockholm, Sweden.
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…
This paper contains the material discussed in the series of three lectures that I gave during the workshop of the ICRA 2018 in Prague. I will introduce the reader to some of the techniques used in the study of the geometry of quiver…