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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Bourguignon-Gauduchon's variation formula for Dirac operators
Dirac算子 Bourguignon-Gauduchon 变分公式
2023/11/13
我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用，我们将计算Dirac算子沿Ricci flow的一阶变分。
Noncommutative circle bundles and new Dirac operators
Noncommutative circle bundles new Dirac operators
2011/1/21
We study the spectral triples over the total space of noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach we propose a definition of connection...
Spectral action for scalar perturbations of Dirac operators
spectral geometry noncommutative geometry
2011/2/22
We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function.
Bergman and Calderón projectors for Dirac operators
Bergman Calderón projectors Dirac operators
2010/12/8
For a Dirac operator D¯g over a spin compact Riemannian manifold with boundary (X, g), we give a natural construction of the Calder´on projector and of the associated Bergman projector on t...
We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra
of classical type. The Dirac operator is an element in the vector space clq(g) U q(g), where the first t...
Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional
Graph-Laplacians Dirac Operators Calculation the Connes-Distance-Functional
2010/11/1
We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of \tit{graph-Laplacians} and so-called \tit{graph-Dirac-o...
In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are ...