相关论文: Lectures on the three--dimensional non--commutativ…

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely…

The motion of three-dimensional (3D) solitary waves and solitons in nonlinear crystal-like structures, such as photonic materials, is studied. It is demonstrated that collective excitations in these systems can be tailored to move in…

These are the lecture notes from a five-hour mini-course given at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. Their aim is to give an overview of Serre's modularity conjecture and of its proof…

These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.

In [5], Connes and Chamseddine defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensioanl manifolds. We propose a way to study the Connes-Chamseddine cycle from the…

These are the expanded notes of a course given at the Summer school "Geometric, topological and algebraic methods for quantum field theory" held at Villa de Leyva, Colombia in July 2015. We first give an introduction to non-commutative…

The scattering is studied using moduli space metric for well-separated vortices of non-Abelian vortices in (2+1)-dimensional U(N) gauge theories with N Higgs fields in the fundamental representation. Unlike vortices in the Abelian-Higgs…

We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete description of noncommutative three-dimensional…

Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".

This note summarizes some recently published results, that are reported in cond-mat today. Its aim is twofold. First, I believe that it is worthwhile to clarify the theoretical interpretation of a series of x-ray scattering experimental…

We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient conditions on sequences x = x_1,x_2,...,x_n, y = y_1,y_2,...,y_n of positive integers, for existence of 2-dimensional…

These notes form an extended version of a minicourse delivered in Universite de Montreal (June 2002) within the framework of a NATO workshop ``Normal Forms, Bifurcations and Finiteness Problems in Differential Equations''. The focus is on…

We realize a nonlinear acoustic lens composed of a two-dimensional array of sphere chains interfaced with water. The chains are able to support solitary waves which, when interfaced with a linear medium, transmit compact pulses with minimal…

We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we…

Contribution to the Proceedings in honour of C.N. Yang, editor S-T Yau. To

We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-St\"ackel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the…

We explore algebraic properties of noncommutative frames. The concept of noncommutative frames is due to Le Bruyn, who introduced it in connection with noncommutative covers of the Connes-Consani arithmetic site.

We present results of numerical simulations for pure U(1) gauge theory in a non-commutative space. The theory is mapped onto a dimensionally reduced matrix model, which renders its numerical treatment feasible. New data on large lattices…

Talk given at Orbis Scientiae Conference, Coral Gables, FLA, Dec. 16-19, 1999. Talk surveys some recent three-neutrino models of neutrino masses and mixings.

This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of…