Topics in flux compactifications of type IIA superstring theory

textRealistic four-dimensional model building from string theory has been a focus of the string theory community ever since its inception. Toroidal orientifold constructions have emerged as a technically simple class of candidate models. Novel ingredients, such as background fluxes, have been discovered and intensely studied over the past few years. They allow for a (partial) solution of several long standing problems associated with model building in this framework. In this thesis, I summarize progress that has been made in toroidal orientifold constructions in type IIA string theory.This includes a detailed discussion of moduli stabilization and (non-) supersymmetric AdS and Minkowski vacua. Furthermore I commence a systematic study of generalized NSNS, i.e., metric and non-geometric, fluxes. The emergence of novel D-terms is presented in detail. While most of the discussion applies to generic orientifolds of T⁶, most features are exemplified by and studied in terms of a certain orientifold of T⁶/ℤ₄ owing to its somewhat richer structure compared to simpler models studied before. It is also briefly reported on efforts of finding de Sitter vacua and inflation in this class of models.Physic

Approximation Theory XV: San Antonio 2016

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22\u201325, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation

Self-Dual Codes

Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page

Lectures on Higgs Boson Physics in the Standard Model and Beyond

These lectures focus on the structure of various Higgs boson theories. Topics in the first lectures include: mass generation in chiral theories, spontaneous symmetry breaking, neutrino masses, perturbative unitarity, vacuum stability, vacuum alignment, flavor changing neutral current solutions with multiple Higgs doublets, analysis of type I theory with Z2 symmetry, and rephasing symmetries. After an Essay on the Hierarchy Problem, additional topics are covered that more directly relate to naturalness of the electroweak theory. Emphasis is on their connection to Higgs boson physics. Topics in these later lectures include: supersymmetry, supersymmetric Higgs sector in the Runge basis, leading-order radiative corrections of supersymmetric light Higgs boson mass, theories of extra dimensions, and radion mixing with the Higgs boson in warped extra dimensions. And finally, one lecture is devoted to Higgs boson connections to the hidden sector.Comment: 71 pages, Delivered at Cambridge University and University of Liverpool, British Universities Summer School (BUSSTEPP 2008 & 2009

Kinetic theory and thermalization of weakly interacting fermions

Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations for the reduced density matrix of the fluid. We discuss here two related topics: the kinetic theory of the fermionic Hubbard model, in which conservation of total spin results in an additional Vlasov type term in the Boltzmann equation, and the relation between kinetic theory and thermalization.Comment: 19 pages, submitted to proceedings of the conference "Macroscopic Limits of Quantum Systems", Munich, Germany, March 20-April 1, 2017 (eds. D. Cadamuro, M. Duell, W. Dybalski, S. Simonella

Spiers Memorial Lecture: Interplay of theory and computation in chemistry—examples from on-water organic catalysis, enzyme catalysis, and single-molecule fluctuations

In this lecture, several examples are considered that illustrate the interplay of experiment, theory, and computations. The examples include on-water catalysis of organic reactions, enzymatic catalysis, single molecule fluctuations, and some much earlier work on electron transfer and atom or group transfer reactions. Computations have made a major impact on our understanding and in the comparisons with experiments. There are also major advantages of analytical theories that may capture in a single equation an entire field and relate experiments of one type to those of another. Such a theory has a generic quality. These topics are explored in the present lecture

An Introduction to Wishart Matrix Moments

These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments. Random matrix theory plays a central role in statistical physics, computational mathematics and engineering sciences, including data assimilation, signal processing, combinatorial optimization, compressed sensing, econometrics and mathematical finance, among numerous others. The mathematical foundations of the theory of random matrices lies at the intersection of combinatorics, non-commutative algebra, geometry, multivariate functional and spectral analysis, and of course statistics and probability theory. As a result, most of the classical topics in random matrix theory are technical, and mathematically difficult to penetrate for non-experts and regular users and practitioners. The technical aim of these notes is to review and extend some important results in random matrix theory in the specific context of real random Wishart matrices. This special class of Gaussian-type sample covariance matrix plays an important role in multivariate analysis and in statistical theory. We derive non-asymptotic formulae for the full matrix moments of real valued Wishart random matrices. As a corollary, we derive and extend a number of spectral and trace-type results for the case of non-isotropic Wishart random matrices. We also derive the full matrix moment analogues of some classic spectral and trace-type moment results. For example, we derive semi-circle and Marchencko-Pastur-type laws in the non-isotropic and full matrix cases. Laplace matrix transforms and matrix moment estimates are also studied, along with new spectral and trace concentration-type inequalities

QED in arbitrary linear media: amplifying media

Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium--media that give rise to absorption [Phys. Rev. A \textbf{75}, (2007) 053813]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media. To illustrate the theory, we present the electromagnetic-field correlation functions that determine the Casimir force in the presence of amplifying media.Comment: 11 pages, submitted for publication in the European Physical Journal Special Topics, related to the CEWQO 2007 conference (June 2007, Palermo