Related papers: An invitation to higher Teichm\"uller theory
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
This report provides my mathematical findings regarding the Mochizuki-Scholze-Stix controversy surrounding Mochizuki's Inter-Universal Teichm\"uller Theory.
This survey article gives an account of quasiconformal extensions of univalent functions with its motivational background from Teichm\"uller theory and classical and modern approaches based on Loewner theory.
The purpose of this note is threefold: (i) to recall (with some points made more explicit) the mathematical Weyl algebra model formulation, given before, of the Staruszkiewicz theory of quantum Coulomb field; (ii) to add some new elements…
The goal of this short article is to describe the local structure of the Teichm\"uller stack of [8] in the neighborhood of a K\"ahler point. In particular we show that at a generic K\"ahler point X, Catanese Kur=Teich question, when…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
This contribution has the aim to review the basics of existing knowledge on asteroid interiors and to explore the possibility of advancing the field by introducing into it some ideas from solid state physics.
This article is part introduction and part survey to the mathematical area centered around local cohomology.
This article presents an overview of neutrino physics research, with highlights on the physics goals, results and interpretations of the current neutrino experiments and future directions and program. It is not meant to be a comprehensive…
The notion of $\tau$-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite dimensional algebras. The…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.
This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this…
This article presents a list of open questions on higher rank Brill-Noether theory and coherent systems. Background material and appropriate references are included.
This is an introduction to some of the most probabilistic aspects of free probability theory.
I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness.
This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for…
The purpose of this book is two fold. (1) To give a systematic account of classical "zero theory" as developed by Jensen, P\'olya, Titchmarsh, Cartwright, Levinson and others. (2) To set forth developments of a more recent nature with a…