Related papers: Classifying N-Extended 1-Dimensional Super Systems
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…
This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological…
In this report we summarize the work performed at Snowmass 2001 on the physics of extra dimensions. We divide these analyses into the following classes: searches for extra dimensional phenomena, identification of specific new physics…
In these lectures I will discuss the following topics: (1) Twistors in 4 flat dimensions: Massless particles; constrained phase space (x,p) versus twistors; Physical states in twistor space. (2) Introduction to 2T-physics and derivation of…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
These notes are based on the lecture courses given at the Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul Sabatier (Toulouse, 08-12.01.1996).
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
The Shatters relation and the VC dimension have been investigated since the early seventies. These concepts have found numerous applications in statistics, combinatorics, learning theory and computational geometry. Shattering extremal…
We construct a class of nonabelian superconformal (1,0) hypermultiplet theories in six dimensions by introducing an abelian auxiliary field. The gauge fields of this class of theories are non-dynamical, and this class of theories can be…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Talk presented at Strings '99 in Potsdam, Germany (July 19 - 24, 1999).
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…
L-Infinity structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of $L_n$ and $L_{\infty}$ structures on…
The Semiclassical Expansion of the t-J model. Lectures in the Jerusalem Winter School on Strongly Correlated Electrons, Dec. 1991, by Assa Auerbach, Physics Dept., Technion, Israel. LateX. Tech-102.