Related papers: Some Elements of Connes' Non-Commutative Geometry,…
In this essay we aim to explore the Geometric aspects of the Calabi Conjecture and highlight the techniques of nonlinear Elliptic PDE theory used by S.T. Yau [SY] in obtaining a solution to the problem. Yau proves the existence of a…
Withdrawn by the authors
Consistent Yang--Mills anomalies $\int\om_{2n-k}^{k-1}$ ($n\in\N$, $ k=1,2, \ldots ,2n$) as described collectively by Zumino's descent equations $\delta\om_{2n-k}^{k-1}+\dd\om_{2n-k-1}^{k}=0$ starting with the Chern character…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…
In a recent paper, Wang. et al. (2009) claim that Tsallis' nonadditivity of q-nonextensive statistical mechanics (Gell-Mann and Tsallis 2004, Tsallis 2009) is mathematically inconsistent and hence one should carefully review Tsallis' ideas…
This is the translation to appear in the "SUPERSYMMETRY 2000 - Encyclopaedic Dictionary" of the original paper, published in March 1980, (C.R. Acad. Sci. Paris, Ser. A-B, 290, 1980) in which basic notions of noncommutative geometry were…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.
This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.
We consider the mixed gravitational-Yang-Mills anomaly as the coupling between the $K$-theory and $K$-homology of a $C^*$-algebra crossed product. The index theorem of Connes-Moscovici allows to compute the Chern character of the $K$-cycle…
In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
Based on lectures delivered at (1) the AMS meeting at USC, Nov. 1992 (2) Conference on Quantum Aspects of Black Holes, ITP, UC- Santa %Barbara, %%June 1993. (3) 25th Summer Institute, Ecole Normale Superieure, % Paris, Aug. 1992. To appear…
This work provides a first step towards the construction of a noncommutative geometry for the quantum Hall effect in the continuum. Taking inspiration from the ideas developed by Bellissard during the 80's we build a spectral triple for the…
Studies of noncommutative gauge theory have mainly focused on noncommutative spacetimes with constant noncommutative structure, with little known about actions for noncommutative 4D Yang-Mills theory beyond this case. We construct an action…
We will survey some aspects of the smooth topology, algebraic geometry, symplectic geometry and contact geometry of anti-canonical pairs in complex dimension two.
In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…
This is a reply to "Comment on 'Noncommutative gauge theories and Lorentz symmetry,'" Phys. Rev. D 77 (2008) 048701 by Alfredo Iorio.