Related papers: Model spaces: a survey
This is a slightly modified version of the survey article. Minor changes to the text and the references have been made.
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is…
This is a concise foreword to, rather than a review of D-brane physics.
In [1], Y. Belov, K. Seip, and the author studied the Carleson measures for certain spaces of analytic functions of which the de Branges spaces and the model subspaces of the Hardy space H2 are the prime examples. In this paper, we continue…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
These notes have been prepared as reading material for the mini-course that the author gave at IMS, National University of Singapore, as part of the "Summer school on the moduli space of Higgs bundles".
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
We characterize invariant subspaces of Brownian shifts on vector-valued Hardy spaces. We also solve the unitary equivalence problem for the invariant subspaces of these shifts.
A concise introduction to the Standard Model of fundamental particle interactions is presented.
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…
A short review of phenomenological and experimental aspects of extra spatial dimensions at colliders is presented.
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.