Riemannian Orbifolds with Non-Negative Curvature

Recent years have seen an increase in the study of orbifolds in connection to Riemannian geometry. We connect this field to one of the fundamental questions in Riemannian geometry, namely, which spaces admit a metric of positive curvature? We give a partial classification of 4 dimensional orbifolds with positive curvature on which a circle acts by isometries. We further study the connection between orbifolds and biquotients - which in the past was one of the main techniques used to construct compact manifolds with positive curvature. In particular, we classify all orbifold biquotients of SU(3). Among those, we show that a certain 5 dimensional orbifold admits a metric of almost positive curvature. Furthermore, we provide some new results on the orbifolds SU(3)//T^2 studied by Florit and Ziller

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 hat position on their head with the goal of both players guessing a white hat. We address the question of finding the optimal strategy, i.e., the one with the highest probability of winning, for this game. We provide an overview of prior work on this question, and describe several strategies that give the best known lower bound on the probability of winning. Upper bounds are also considered here