24,476 research outputs found
Interview with John G. Thompson and Jacques Tits
No full textJohn G. Thompson and Jacques Tits are the recipients of the 2008 Abel Prize of the Norwegian Academy of Science and Letters. On May 19, 2008, prior to the Abel Prize celebration in Oslo, Thompson and Tits were jointly interviewed by Martin Raussen of Aalborg University and Christian Skau of the Norwegian University of Science and Technology. This interview originally appeared in the September 2008 issue of the Newsletter of the EuropeanMathematical Society.John G. Thompson and Jacques Tits are the recipients of the 2008 Abel Prize of the Norwegian Academy of Science and Letters. On May 19, 2008, prior to the Abel Prize celebration in Oslo, Thompson and Tits were jointly interviewed by Martin Raussen of Aalborg University and Christian Skau of the Norwegian University of Science and Technology. This interview originally appeared in the September 2008 issue of the Newsletter of the European Mathematical Society.</em
Interview with Srinivasa Varadhan
No full textS. R. S. Varadhan is the recipient of the 2007 Abel Prize of the Norwegian Academy of Science and Letters. On May 21, 2007, prior to the Abel Prize celebration in Oslo, Varadhan was interviewed by Martin Raussen of Aalborg University and Christian Skau of the Norwegian University of Science and Technology. This interview originally appeared in the September 2007 issue of the European Mathematical Society Newsletter.S. R. S. Varadhan is the recipient of the 2007 Abel Prize of the Norwegian Academy of Science and Letters. On May 21, 2007, prior to the Abel Prize celebration in Oslo, Varadhan was interviewed by Martin Raussen of Aalborg University and Christian Skau of the Norwegian University of Science and Technology. This interview originally appeared in the September 2007 issue of the European Mathematical Society Newsletter
Video of Christian Skau and Martin Raussen's interview with the Abel Prize Winner John Milnor
No full textThe television interview with Abel Laureate John Milnor that was broadcasted on Norwegian television in June is now available on the Abel Prize multimedia page. John Milnor received the Abel Prize «for pioneering discoveries in topology, geometry and algebra» to quote the Abel Committee. King Harald presented the Abel Prize to John Milnor at the award ceremony in Oslo, Norway on 24 May. Before the interview there is a short presentation of the award ceremony. John Milnor is interviewed by Martin Raussen and Christian Skau. The Abel Prize that carries a cash award of NOK 6 million (about EUR 765,000, USD 1 million), is awarded for outstanding scientific work in the field of mathematics. The video is produced by Intermedia, University of Oslo <br/
Interview with Abel Laureate Sir Andrew J. Wiles
No full textAndrew J. Wiles is the recipient of the 2016 Abel Prize of the Norwegian Academy of Science and Letters. The interview was conducted by Martin Raussen And Christian Skau in Oslo on May 23, 2016, in conjunction with the Abel Prize celebration
Deadlocks and dihomotopy in mutual exclusion models
Full text linkAlready in 1968, E.W. Dijkstra [Dij68] proposed to apply a geometric point of view in the consideration of coordination situations in concurrency. His progress graphs were the basis of the Higher Dimensional Automata (HDA) introduced by V. Pratt[Pra91] and developed in the thesis of É. Goubault[Gou95] and i
Reparametrizations with given stop data
Full text linkIn [1], we performed a systematic investigation of reparametrizations of continuous paths in a Hausdorff space that relies crucially on a proper understanding of stop data of a (weakly increasing) reparametrization of the unit interval. I am indebted to Marco Grandis (Genova) for pointing out tome that the proof of Proposition 3.7 in [1] iswrong. Fortunately, the statment of that Proposition and the results depending on it stay correct. It is the purpose of this note to provide correct proofs. [1] U. Fahrenberg and M. Raussen, Reparametrizations of continuous paths, J. Homotopy Relat. Struct. 2 (2007), no. 2, 93-117.In [1], we performed a systematic investigation of reparametrizations of continuous paths in a Hausdorff space that relies crucially on a proper understanding of stop data of a (weakly increasing) reparametrization of the unit interval. I am indebted to Marco Grandis (Genova) for pointing out tome that the proof of Proposition 3.7 in [1] iswrong. Fortunately, the statment of that Proposition and the results depending on it stay correct. It is the purpose of this note to provide correct proofs. [1] U. Fahrenberg and M. Raussen, Reparametrizations of continuous paths, J. Homotopy Relat. Struct. 2 (2007), no. 2, 93-117.</p
Simplicial models for trace spaces II: General higher dimensional automata
Full text linkHigher Dimensional Automata (HDA) are topological models for the studyof concurrency phenomena. The state space for an HDA is given as a pre-cubical complex in which a set of directed paths (d-paths) is singled out. The aim of this paper is to describe a general method that determines the space of directed paths with given end points in a pre-cubical complex as the nerve of a particular category.The paper generalizes the results from Raussen [19, 18] in which we had to assume that the HDA in question arises from a semaphore model. In particular, important for applications, it allows for models in which directed loops occur in the processes involved.Higher Dimensional Automata (HDA) are topological models for the studyof concurrency phenomena. The state space for an HDA is given as a pre-cubical complex in which a set of directed paths (d-paths) is singled out. The aim of this paper is to describe a general method that determines the space of directed paths with given end points in a pre-cubical complex as the nerve of a particular category.The paper generalizes the results from Raussen [19, 18] in which we had to assume that the HDA in question arises from a semaphore model. In particular, important for applications, it allows for models in which directed loops occur in the processes involved
Interview with Abel Laureate Sir Andrew Wiles
No full textThis interview is a translation of: Interview with Abel Laureate Sir Andrew Wiles Raussen, M. H. & Skau, C. 2016 In : Journal of the European Mathematical Society. 9, 101, p. 29-38 12 p
Interview with M. Gromov
No full textThis interview is a Chinese translation of: Interview with Mikhail Gromov Raussen, M. & Skau, C. 2010 In : American Mathematical Society. Notices. 57, 3, p. 391-403 13 p
Pair component categories for directed spaces
No full textThe notion of a homotopy flow on a directed space was introduced in \cite{Raussen:07} as a coherent tool for comparing spaces of directed paths between pairs of points in that space with each other. If all parameter directed maps preserve the homotopy type of path spaces, such a flow (and these parameter maps) are called inessential.For a directed space, one may consider various categories whose objects are pairs of reachable points and whose morphisms may be induced by these inessential d-maps. Localization with respect to subcategories with these inessential d-maps as morphisms can be combined with a path space functor into the homotopy category, the quotient pair component category has as objects pair components along which the homotopy type is invariant -- for a coherent and transparent reason.This paper follows up \cite{FGHR:04,GH:07,Raussen:07} and removes some of the restrictions for their applicability. If one uses homology equivalence instead of homotopy equivalence as the basic relation, it yields an alternative to computable versions of "natural homology" introduced in \cite{DGG:15} and elaborated in \cite{Dubut:17}. It refines, for good and for evil, the stable components introduced and investigated in \cite{Ziemianski:18}.The notion of a homotopy flow on a directed space was introduced in Raussen (Appl Categ Struct 15(4):355–386, 2007) as a coherent tool for comparing spaces of directed paths between pairs of points in that space with each other. If all directed maps along such a 1-parameter deformation preserve the homotopy types of path spaces, such a flow and the parameter maps are called inessential. For a directed space, one may consider various categories whose objects are pairs of reachable points to which a functor associates the space of directed paths between them. The monoid of all inessential maps acts on such a category by endofunctors leaving the associated path spaces invariant up to homotopy. We construct a pair component category as quotient category: it has as objects pair components along which the homotopy type is invariant—for a coherent and transparent reason. This paper follows up Fajstrup et al. (J Homotopy Relat Struct 12(1):81–108, 2004); Goubault and Haucourt (Appl Categ Struct 15(4):387–414, 2007); Raussen (Appl Categ Struct 15(4):355–386, 2007) and removes some of the restrictions for their applicability. At least in several examples, it gives reasonable results for spaces with non-trivial directed loops. If one uses homology equivalence instead of homotopy equivalence as the basic relation, it yields an alternative to computable versions of “natural homology” introduced in Dubut et al (in: Automata, languages, and programming. 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6–10, 2015. Proceedings. Part II, 171–183, Springer, Berlin 2015) and elaborated in Dubut (Directed homotopy and homology theories for geometric models of true concurrency. École normale supérieure Paris-Saclay 2017). It refines, for good and for evil, the stable components introduced and investigated in Ziemiański (Appl Categ Struct 27:217–244, 2019)
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