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        "event_title":"The Burau representation and shapes of polyhedra",
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        "description":"The Burau representation is a kind of homological representation of braid groups that has been around for around a century. It remains mysterious in many ways and is of particular interest because of its relation to quantum invariants of knots and links such as the Jones polynomial. In recent work, I came across a relationship between this representation and a moduli space of Euclidean cone metrics on spheres (think e.g. convex polyhedra) first examined by Thurston. After introducing the relevant definitions, I'll explain a bit about this connection and how I used the geometric structure on this moduli space to exactly identify the kernel of the Burau representation after evaluating its formal parameter at complex roots of unity. There will be many pictures!",
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        "event_title":"The Uniform Izumi-Rees Property and Improvements to the Uniform Chevalley Lemma",
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        "combined_title":"The Uniform Izumi-Rees Property and Improvements to the Uniform Chevalley Lemma: Thomas Polstra (University of Alabama)",
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        "description":"Let R be a Noetherian normal domain and P a prime ideal. The nth symbolic power P^(n) of P can be geometrically interpreted as the set of regular functions of R that vanish to order n at the generic point of V(P). With this geometric insight, if P\\subseteq Q are prime ideals within the non-singular locus of Spec(R), then the Local Zariski-Nagata Theorem states P^(n)\\subseteq Q^(n) and translates into a natural criterion for vanishing order along non-singular algebraic sets: functions vanishing to order n at the generic point of V(P) must vanish to order at least n at the generic point of V(Q).\r\n \r\nHowever, when Q is a singular prime, the behavior of vanishing orders becomes less intuitive. Huneke, Katz, and Validashti's Uniform Chevalley Lemma rectifies this scenario by providing a constant C, depending on Q, such that if a function vanishes to order Cn at the generic point of V(P), then it must vanish to order at least n at the generic point of V(Q).\r\n \r\nIn our exploration of uniformity in Noetherian rings, we introduce the Uniform Izumi-Rees Property, which eliminates the dependency of the constant C on Q in the Uniform Chevalley Lemma. Furthermore, we establish that normal domains essentially of finite type over a field enjoy the Uniform Izumi-Rees Property.",
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