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Conformal Field Theory and Elliptic Cohomology
"... The purpose of the present paper is to address an old question (posed by Segal [37]) to find a geometric construction of elliptic cohomology. This question has recently become much more pressing due to the work of Mike Hopkins and Haynes Miller [19], who constructed exactly the “right”, or universal ..."
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Cited by 37 (9 self)
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The purpose of the present paper is to address an old question (posed by Segal [37]) to find a geometric construction of elliptic cohomology. This question has recently become much more pressing due to the work of Mike Hopkins and Haynes Miller [19], who constructed exactly the “right”, or universal, elliptic cohomology,
Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory
 Mem. Amer. Math. Soc
"... The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjun ..."
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Cited by 19 (8 self)
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The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this
QUASISYMMETRIC SEWING IN RIGGED TEICHMÜLLER SPACE
, 2005
"... Abstract. One of the basic geometric objects in conformal field theory (CFT) is the the moduli space of Riemann surfaces whose n boundaries are “rigged ” with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations to identify points. An alterna ..."
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Abstract. One of the basic geometric objects in conformal field theory (CFT) is the the moduli space of Riemann surfaces whose n boundaries are “rigged ” with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations to identify points. An alternative model is the moduli space of npunctured Riemann surfaces together with local biholomorphic coordinates at the punctures. We refer to both of these moduli spaces as the “rigged Riemann moduli space”. By generalizing to quasisymmetric boundary parametrizations, and defining rigged Teichmüller spaces in both the border and puncture pictures, we prove the following results: (1) The Teichmüller space of a genusg surface bordered by n closed curves covers the rigged Riemann and rigged Teichmüller moduli spaces of surfaces of the same type, and induces complex manifold structures on them. (2) With this complex structure the sewing operation is holomorphic. (3) The border and puncture pictures of the rigged moduli and rigged Teichmüller spaces are biholomorphically equivalent. These results are necessary in rigorously defining CFT (in the sense of G. Segal), as well
Contents..................................
, 2006
"... We present the PowerSetViewer visualization system for latticebased mining of powersets. Searching for items within the powerset of a universe occurs in many large dataset knowledge discovery contexts. Using a spatial layout based on a powerset provides a unified visual framework at three different ..."
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We present the PowerSetViewer visualization system for latticebased mining of powersets. Searching for items within the powerset of a universe occurs in many large dataset knowledge discovery contexts. Using a spatial layout based on a powerset provides a unified visual framework at three different levels: data mining on the filtered dataset, browsing the entire dataset, and comparing multiple datasets sharing the same alphabet. The features of our system allow users to find appropriate parameter settings for data mining algorithms through lightweight visual experimentation showing partial results. We use dynamic constrained frequentset mining as a concrete case study to showcase the utility of the system. The key challenge for spatial layouts based on powerset structure is in handling large alphabets, since the size of the powerset grows exponentially with the size of the alphabet. We present scalable algorithms for enumerating and displaying datasets containing between 1.5 and 7 million itemsets, and alphabet sizes of over 40,000. iii Contents Abstract.................................. ii
Contents
"... Chapter 1. Loop groups and positive energy representations 15 1.1. Loop groups 15 1.2. Central extensions 16 ..."
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Chapter 1. Loop groups and positive energy representations 15 1.1. Loop groups 15 1.2. Central extensions 16