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Events happening on March 13, 2018

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Mar. 13, 2018 11am (MATH 350)	Number Theory Number Theory Lab X Carly will tell us about the Arizona Winter School. Number Theory Lab Meeting
Mar. 13, 2018 12:10pm (Math …	Kempner Dmitry Kaledin (Steklov Mathematics Institute and Independent University of Moscow) X Witt vectors were first introduced eighty years ago, but they still come up in different questions of commutative and homological algebra, algebraic geometry, and even algebraic topology. I will try to give a general introduction to this remarkable subject, and show both its classical parts and some recent discoveries. Witt vectors, commutative and non-commutative
Mar. 13, 2018 1pm (MATH 220)	Nik Ruskuc (St Andrews) X It is known that subdirect products of groups can be pretty wild even if the factors are reasonably tame. For instance, Baumslag and Roseblade showed that there are uncountably many non-isomorphic subdirect products of two copies of the free group F_2. However, this wild behaviour cannot occur for subdirect products of finitely generated abelian groups as a consequence of the fundamental theorem for finite abelian groups: they are all finitely generated, finitely presented, and there are only finitely many up to isomorphism. Finitely generated commutative semigroups often behave similarly to the abelian groups: e.g. they are finitely presented, have a solvable word problem, the subsemigroups of N (the natural numbers, the free monogenic semigroup) are essentially arithmetic progressions, etc. So we ask: How many subsemigroups (up to isomorphisms) does the direct product NxN (two copies of the semigroup of natural numbers) contain? This is joint work with my student Ashley Clayton. Subdirect products involving the semigroup of natural numbers Sponsored by the Meyer Fund
Mar. 13, 2018 2pm (MATH 350)	Lie Theory Nantel Bergeron (York University (Canada)) X I will define hypergraphs and explain a Hopf structure on them. Using orientations on hypergraphs we provide an explicit bijection between acyclic orientations on them and faces of hypergraphic polytopes. This allows us to obtain a geometric interpretation of the coefficients of the antipode map in this Hopf algebra. This interpretation differs from similar ones for a different Hopf structure on hypergraphs provided recently by Aguiar and Ardila. (Joint with C. Benedetti and J. Machacek). Hypergraphical polytope: Orientations and antipode Sponsored by the Meyer Fund
Mar. 13, 2018 3pm (Math 350)	Algebraic Geometry Dori Bejleri (Brown University) X A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher. Stable pair compactifications of the moduli space of degree one del Pezzo surfaces via elliptic fibrations Sponsored by the Meyer Fund
Mar. 13, 2018 4pm (MATH 350)	Algebraic Geometry Morgan Brown (University of Miami) X The essential skeleton is an invariant of a degeneration that appears in both Berkovich geometry and minimal model theory. I will show that for degenerations with a semistable model, the essential skeleton of a product of degenerations is the product of their skeleta. As an application, we are able to describe the homeomorphism type of some degenerations of hyperkähler varieties, both for a Hilbert scheme of degenerating K3 surfaces and for a Kummer variety associated to a degeneration of an abelian surface. This is joint work with Enrica Mazzon. The Skeleton of a Product of Degenerations

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