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On the geometry of Riemannian manifolds with density
We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as theExpand
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Riemannian Orbifolds with Non-Negative Curvature
RIEMANNIAN ORBIFOLDS WITH NON-NEGATIVE CURVATURE Dmytro Yeroshkin Wolfgang Ziller Recent years have seen an increase in the study of orbifolds in connection to Riemannian geometry. We connect thisExpand
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Connectedness of two-sided group digraphs and graphs
Two-sided group digraphs and graphs, introduced by Iradmusa and Praeger, provide a generalization of Cayley digraphs and graphs in which arcs are determined by left and right multiplying by elementsExpand
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The Weighted Connection and Sectional Curvature for Manifolds With Density
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion-free connection introduced recently by the last two authors. WeExpand
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On a Certain Cooperative Hat Game
TLDR
We provide an overview of prior work on this question, and describe several strategies that give the best lower bound on the probability of victory. Expand
New Results in Exponential Families
We start this paper by giving a short crash course in generating functions, including a new result that can be used to simplify certain operations. Then, in sections 2 and 3 we introduce H.S.Wilf’sExpand
On Geometry and Topology of 4-Orbifolds
We prove an analogue of the result of Hsiang and Kleiner for 4-dimensional compact orbifolds with positive curvature and an isometric circle action. Additionally, we prove that when the underlyingExpand
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Holonomy of Manifolds with Density
In this paper we discuss some examples and general properties of holonomy groups of $\nabla^\varphi$ introduced by Wylie and the author, the connection corresponding to the $N=1$ Bakry-\'Emery RicciExpand
Computing optimal strategies for a cooperative hat game
We consider a `hat problem' in which each player has a randomly placed stack of black and white hats on their heads, visible to the other player, but not the wearer. Each player must guess a hatExpand