Abstract: The Paley graph is a classical number-theoretic construction of a graph that is believed to behave "pseudorandomly" in many regards. Accurately bounding the clique number of the Paley graph is a long-standing open problem in number theory, with applications to several other questions about the statistics of finite fields. I will present recent results…

Abstract: Sampling from high-dimensional probability distributions is a fundamental and challenging problem encountered throughout science and engineering. One of the most popular approaches to tackle such problems is the Markov chain Monte Carlo (MCMC) paradigm. While MCMC algorithms are often simple to implement and widely used in practice, analyzing the rate of convergence to stationarity,…

Abstract: In this talk I will propose new tools for the exploratory data analysis of data objects taking values in a general separable metric space. First, I will introduce depth profiles, where the depth profile of a point ω in the metric space refers to the distribution of the distances between ω and the data objects. I will describe…