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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 the…
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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 this…

On Levine's notorious hat puzzle

It is proved that Vn, the optimal value of the joint success probability in the n-player game, is a strictly decreasing function of n.
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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. We…
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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 elements…
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Connectedness of two-sided group digraphs

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 elements…

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 underlying…
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Orbifold biquotients of SU(3)

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On a Certain Cooperative Hat Game

This work provides an overview of prior work on this question, and describes several strategies that give the best lower bound on the probability of victory, and generalizes the problem to consider the case of arbitrary color distribution.

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’s…
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