Related papers: TASI 2004 Lectures: To the Fifth Dimension and Bac…
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
Recently, the HCI community has seen increased interest in the design of teaching augmentation (TA): tools that extend and complement teachers' pedagogical abilities during ongoing classroom activities. Examples of TA systems are emerging…
This is the written version of an invited review talk for the 13 Feb 2004 AAAS Meeting in Seattle. The talk's goal is to present a philosophical view of extragalactic astronomy as it applies to the sub-field of galaxy evolution. The talk is…
Elementary introduction to physics beyond the Standard Model. Lectures delivered at the 1995 European School of High-Energy Physics in Dubna, Russia.
In present work the generalization of Einstein's special theory of relativity on 5-dimentional space is considered, in which as fifth coordinates we consider the interval s of a particle. 5-dimentional vectors in this space are isotropic…
As the title indicates
The results of searches for several type of physics beyond the Standard Model using data from the four LEP experiments are presented. In the absence of any excess signal events seen in the data limits are placed on the existence of…
We give an introduction to conformal and superconformal algebras and their representations in various dimensions. Special emphasis is put on 4d $\mathcal{N}=2$ superconformal symmetry. This is the writeup of the lectures given at the Winter…
These are notes for some introductory lectures about microstate geometries and their construction. The first lecture considers BPS black holes in four dimensions as a way to introduce what one should expect from the BPS equations. The…
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
We give a short introduction to AdS/CFT and its plane wave limit.
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this review, we discuss the results of recent experimental…
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily…
These lectures discuss how the direct detection of gravitational waves can be used to probe the very early Universe. We review the main cosmological mechanisms which could have produced relic gravitational waves, and compare theoretical…
These notes are an expanded version of lectures given at the 2022 TASI summer school in Boulder, Colorado. One goal of these lecture notes is to (partially) bridge the gap between what one learns in typical introductory quantum field theory…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.