Related papers: An invitation to higher Teichm\"uller theory
The purpose of this article is to provide a version of Bloch-Wigner theorem over the class of rings with many units.
I give a theory motivation for future measurements in quark flavour physics, trying to identify observables, which are less familiar, but nevertheless interesting and promising.
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
The overarching goal of this thesis is to demonstrate that complementarity is at the heart of quantum information theory, that it allows us to make (some) sense of just what information "quantum information" refers to, and that it is useful…
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
In this paper, we propose a novel approach that aims: to facilitate the building of teams relying on notions of skills, of motivation or of potential; identify the requested upgrade effort to improve his own knowledge and join a team; or…
In this article, we describe the geography of the Teichm\"uller stack of \cite{LMStacks} and of one of its variants we introduce here, giving some answers to questions as: which points are orbifold points? What are the different local…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
The aim of this article is to draw attention towards various natural but unanswered questions related to the lower central series of the unit group of an integral group ring.
This introduction to higher category theory is intended to a give the reader an intuition for what $(\infty,1)$-categories are, when they are an appropriate tool, how they fit into the landscape of higher category, how concepts from…
Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperk\"ahlerian manifolds as stated by Verbitsky. The initial purpose of this document (which was prepared for a seminar talk) was to extract the…
Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…
Lipman Bers' universal Teichm\"uller space, classically denoted by $T(1)$, plays a significant role in Teichm\"uller theory, because all the Teichm\"uller spaces $T(G)$ of Fuchsian groups $G$ can be embedded into it as complex submanifolds.…
This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied…
I review the theoretical motivation for the axion and present an update of the experimental status of axion searches. I finally comment on some aspects of the physics of axion-like particles.