Fifty years of Mathematics with Masaki Kashiwara

This article accompanies the 10th Takagi Lectures, delivered by the author at RIMS, Kyoto, on May 26 2012. It contains an exposition of results, applications, and challenges of the Ribe program.

This work is a collection of old and new aplications of Galois cohomology to the clasification of algebraic and arithmetical objects.

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.

This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips) that are linked within.

This is a mainly expository article honoring my recently deceased friend and collaborator Krzysztof Galicki who died after a tragic hiking accident. I give a review of our recent work in Sasakian geometry. A few new results are also presented.

This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season of lockdown, I modestly try to contribute to scientific interaction at a distance. Therefore all comments and exchange of information are most welcome.

This is no longer available.

This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn Meeting of the Mathematical Society of Japan in September 2021.

In this report we've shown that the arguments, which the author of the Comment presents to prove his case, are either wrong or irrelevant.

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 stimulate readers to investigate them.