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Quasimorphisms are generalizations of homomorphisms to the real number. Groups with nice aciton on Gromov-hyperbolic spaces often have a large space of quasimorphisms, although such groups can have tr...
Shanghai Conference on Gauge/Gravity Duality and Its Applications will take place in Shanghai, China, from Aug.7-9,2016. This workshop aims to bring together a broad-wide range of colleagues on gauge/...
It was shown recently that entanglement of identical particles has a feature called dualism (Bose and Home 2013 Phys. Rev. Lett. 110 140404), which is funda-mentally connected with quantum indistingui...
We establish a character multiplicity duality for a certain natural class of nonlinear (nonalgebraic) groups arising as two-fold covers of simply laced real reductive algebraic groups. This allows us ...
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...
A dinner table seats k guests and holds n discrete morsels of food. Guests select morsels in turn until all are consumed. Each guest has a ranking of the morsels according to how much he would enjoy e...
We present a unified duality view of several recently emerged spectral methods for nonlinear dimensionality reduction, including Isomap, locally linear embedding, Laplacian eigenmaps, and maximum vari...
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. We consider approximate solutions obtained by solving ...
A strong stationary time for a Markov chain (X,) is a stopping time T for which XT is stationary and independent of T. Such times yield sharp bounds on certain measures of nonstationarity for X at...
We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Koszul duality for Operads     Koszul duality  Operads       2015/3/25
This is a copy of the article by the same authors published in Duke Math. J. (1994).
A Koszul duality for props     Koszul duality  props       2015/3/25
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszu...
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
During the summer of 1985, after the opening ceremony of Nankai Institute of Mathematics,a beautiful lecture of S.-S. Chern on Chern classes and the Atiyah-Singer index formula introduced me into the ...

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