Related papers: Classifying N-Extended 1-Dimensional Super Systems
Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…
A new class of noncommutative $k$-algebras (for $k$ an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first order theory is assigned describing models of a…
I review my results about noncommutative gauge theories and about the relation of these theories to M(atrix) theory following my lecture on ICMP 2000.
Invited talk at European Workshop on the QCD Structure of the Nucleon (QCD-N\'02), Ferrara, Italy, 3--6 Apr 2002
These are (not updated) notes from the lectures I gave at the NATO ASI ``Symmetric Functions 2001'' at the Isaac Newton Institute in Cambridge (June 25 -- July 6, 2001). Their goal is an informal introduction to asymptotic combinatorics…
Invited talk delivered at the International Conference on General Relativity and Cosmology (ICGC), Ahmedabad, India; 13 - 18 December 1991. To appear in its proceedings.
Introductory lectures on Extra Dimensions delivered at TASI 2004. The emphasis is on basic mechanisms rather than specific models.
Condensed account of the Lectures delivered at the Meeting on {\it Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20, 2005.
This is an extended version of the talk given by the author at the NATO Advanced Study Institute "Supersymmetry and Trace Formulae" (Isaac Newton Institute, Cambridge, UK, 8-19 Septemebr 1997). Contains the following sections: 1.…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
A carefully constructed explanation of my connection of the real normed division algebras to the particles, charges and fields of the Standard Model of quarks and leptons provided to an interested group of attendees of the 2nd Mile High…
The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the…
The phenomenology of large, warped, and universal extra dimensions is reviewed. Characteristic signals are emphasized rather than an extensive survey. This is the writeup of lectures given at the Theoretical Advanced Study Institute in…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.
Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and…
The first part of these notes gives an introduction to noncommutative projective geometry after Artin--Zhang. The second part provides an overview of the work of Polishchuk that reconciles noncommutative two-tori having real multiplication…
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…
An overview is given of the application of twistor geometric ideas to supersymmetry with particular emphasis on the construction of superspaces associated with four-dimensional spacetime. Talk given at Leuven conference, July 1995.