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It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact K¨ahler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of ...
We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if $A\subset\mathbb{R}^d$ is convex and the origin $0\in A$, then for any ball $B$ centered at the origin...
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...
We investigate when the space $\mathcal O_X$ of open subsets of a topological space $X$ endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of $X...
We develop a new definition of opetopic sets. There are two main technical ingredients. The first is the systematic use of fibrations, which are implicit in most of the approaches in the literature. ...
The distribution of distances in the star graph $ST_n$, ($1established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given...
The nerve of a strict omega-category is a simplicial set with ad-ditional structure, making it into a so-called complicial set, and strict omega-categories are in fact equivalent to complicial sets. T...
Planar Linkages and Algebraic Sets
The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with...

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