Related papers: F-Theory, GUTs and Chiral Matter
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…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
This article contains a basic introduction to the local study of finite groups, including a brief perspective on the theory of fusion systems and $p$-local finite groups. -- Este art\'iculo contiene una introducci\'on b\'asica al estudio…
This paper is a very non-rigorous, loose, and extremely basic introduction to sheaves. This is meant to be a a guide to gaining intuition about sheaves, what they look like, and how they work, so that after reading this paper, someone can…
Some general considerations on the problem of non-perturbative definition of Chiral Gauge Theories are presented.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
This primer is an introduction to Conformal Field Theory in $D\geq3$. It is designed to introduce the reader to many of the important foundational concepts and methods in CFT. In it, pig picture ideas are prioritized over technical details,…
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.
The general framework and the present status of the low energy theory of the standard model are briefly reviewed. Recent applications to a few topic of interest for the determinations of Vud and of Vus are discussed
We provide the first evidence for a holographic correspondence between a gravitational theory in flat space and a specific unitary field theory in one dimension lower. The gravitational theory is a flat-space limit of topologically massive…
We discuss constraint structure of extended theories of gravitation (also known as f(R) theories) in the vacuum selfdual formulation introduced in ref. [1].
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.