Jacek Brodzki
University of Southampton
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Publication
Featured researches published by Jacek Brodzki.
Communications in Mathematical Physics | 2008
Jacek Brodzki; Varghese Mathai; Jonathan Rosenberg; Richard J. Szabo
We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant
IEEE Transactions on Power Systems | 2014
Rubén J. Sánchez-García; Max Fennelly; Sean Norris; Nick Wright; Graham A. Niblo; Jacek Brodzki; Janusz Bialek
Comptes Rendus De L Academie Des Sciences Serie I-mathematique | 1999
Jacek Brodzki; Roger Plymen
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Journal of Topology and Analysis | 2012
Jacek Brodzki; Graham A. Niblo; Piotr Nowak; Nick Wright
Geometry & Topology | 2012
Jacek Brodzki; Graham A. Niblo; Nick Wright
-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.
Bulletin of The London Mathematical Society | 2002
Jacek Brodzki; Roger Plymen
A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology to reveal the internal connectivity structure of such a network. Spectral clustering uses the eigenvalues and eigenvectors of a matrix associated to the network, it is computationally very efficient, and it works for any choice of weights. When using line admittances, it reveals the static internal connectivity structure of the underlying network, while using power flows highlights islands with minimal power flow disruption, and thus it naturally relates to controlled islanding. Our methodology goes beyond the standard k-means algorithm by instead representing the complete network substructure as a dendrogram. We provide a thorough theoretical justification of the use of spectral clustering in power systems, and we include the results of our methodology for several test systems of small, medium and large size, including a model of the Great Britain transmission network.
Journal of the European Mathematical Society | 2012
Jacek Brodzki; Graham A. Niblo; Nick Wright
Abstract Relying on properties of the inductive tensor product, we construct cyclic type homology theories for certain nuclear algebras. In this context, we establish continuity theorems. We compute the periodic cyclic homology of the Schwartz algebra of p-adic GL(n) in terms of compactly supported de Rham cohomology of the tempered dual of GL(n).
Archive | 2006
Jacek Brodzki; Graham A. Niblo
We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a point our result reduces to a classic theorem of B.E. Johnson characterising amenability of groups. In the case when the compact space is the Stone-\v{C}ech compactification of the group we obtain a cohomological characterisation of exactness for the group, answering a question of Higson.
arXiv: High Energy Physics - Theory | 2008
Jacek Brodzki; Varghese Mathai; Jonathan Rosenberg; Richard J. Szabo
We introduce the notion of an asymptotically invariant mean as a coarse averaging operator for a metric space and show that the existence of such an operator is equivalent to Yu’s property A. As an application we obtain a positive answer to Higson’s question concerning the existence of a cohomological characterisation of property A. Specifically we provide coarse analogues of group cohomology and bounded cohomology (controlled cohomology and asymptotically invari- ant cohomology, respectively) for a metric space X, and provide a cohomological characterisation of property A which generalises the results of Johnson and Ringrose describing amenability in terms of bounded cohomology. These results amplify Guentner’s observation that property A should be viewed as coarse amenability for a metric space. We further provide a generalisation of Guentner’s result that box spaces of a finitely generated group have property A if and only if the group is amenable. This is used to derive Nowak’s theorem that the union of finite cubes of all dimensions does not have property A.
Journal of Noncommutative Geometry | 2009
Jacek Brodzki; Graham A. Niblo; Nick Wright
Let G denote the p-adic group GL(n), and let S(G) denote the Schwartz algebra of G. We construct a Chern character from the K-theory of the reduced C*-algebra of G to the periodic cyclic homology of S(G) which becomes an isomorphism after tensoring over Z with C.