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Title:   Log-concavity of random Radon partitions Speaker:   Natasha Ter-Saakov, Rutgers University
Abstract:
Over one hundred years ago, Radon proved that any set of d+2 points in R^d can be partitioned into two sets whose convex hulls intersect. I will talk about Radon partitions when the points are selected randomly. In particular, if the points are independent normal random vectors, let p_k be the probability that the Radon partition has size (k, d+2-k). Answering a conjecture of Kalai and White, we show that the sequence (p_k) is ultra log-concave and, as a consequence, a balanced partition is the most likely. Joint work with Swee Hong Chan, Gil Kalai, Bhargav Narayanan, and Moshe White.

Speaker:   Bernardo Araneda
Title:   Ernst equations, Kähler structures, and Einstein-Maxwell instantons
Abstract:   The Ernst formulation of the Einstein equations provides a solution-generating technique and leads to infinite-dimensional hidden symmetries encoded in the Geroch group. Other solution-generating methods are based on the existence of complex structures, such as the Gibbons-Hawking ansatz and Toda constructions. I will present a novel interplay between these two methods. As an application, the Einstein-Maxwell version of the Euclidean Black Hole Uniqueness Conjecture will be addressed. Based on joint work with Maciej Dunajski.