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Events happening on September 11, 2018

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Sep. 11, 2018 1pm (MATH 350)	Ulam D. Kaledin X This is a continuation of my talk on Sep. 4. although it should be understandable by itself. I will give a precise derivator-style definition of an enhanced category and explain the main points of the theory. On the notion of an enhanced category, II
Sep. 11, 2018 1pm (MATH 220)	Peter Mayr X Constraint Satisfaction Problems (CSP) include a wide variety of classical decision problems, like satisfiability of Boolean formulas, colorability of graphs, solvability of systems of linear equations,... and real-life problems, like scheduling, database queries. The Dichotomy Conjecture by Feder & Vardi states that every CSP is either solvable in polynomial time or NP-complete. It has just been verified independently by Bulatov and by Zhuk using two different algebraic approaches. We give an introduction to CSP, the algebraic formulation of the Dichotomy Conjecture and, time permitting, a broad overview of Zhuk's algorithm. See https://arxiv.org/abs/1704.01914 More details of the solution will be filled in throughout the semester. Constraint Satisfaction Problems
Sep. 11, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) X The concept of a Cofinality Spectrum Problem (CfSP) was introduced recently by M. Malliaris and S. Shelah (J. Amer. Math. Soc., 2016), and was used to obtain spectacular results in model theory and set theoretic topology. In model theory the Malliaris-Shelah results on CfSPs shed new light on Keisler’s order -- a notion from the 1960’s to classify first order theories. In set theoretic topology these results were used to prove that the cardinals p and t related to the continuum are equal (in ZFC), although for decades, this equality was expected to be independent of ZFC. Overview of the Malliaris--Shelah paper, Part 1
Sep. 11, 2018 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between groups. A supercharacter theory is a framework for simplifying the character theory of a finite groups, while ideally not losing all important information. This talk examines one such theory that straddles the gap between retaining valuable group information while reducing the above questions to more combinatorial lattice constructions. Joint with Aliniaeifard. The structure of normal lattice supercharacter theories
Sep. 11, 2018 3pm (MATH 220)	Topology Sam Nariman (Northwestern University) Topology Seminar Pretalk Sponsored by the Meyer Fund
Sep. 11, 2018 3pm (MATH 350)	Algebraic Geometry Zheng Zhang (CU Boulder) X The period map is a powerful tool for studying moduli spaces, and has been applied successfully to abelian varieties, K3 surfaces, cubic threefolds/fourfolds, and hyper-Kahler manifolds. However, for some interesting moduli problems (e.g. moduli spaces for pairs of varieties) there might be no obvious way to construct periods. Joint with R. Laza and G. Pearlstein, we construct a period map for cubic pairs consisting of a cubic threefold and a transverse hyperplane using a variation of the construction by Allcock, Carlson and Toledo (which allows us to encode a cubic pair as a “lattice polarized” cubic fourfold). The main result is that the period map induces an isomorphism between a GIT model of the moduli of cubic pairs and the Baily-Borel compactification of some locally symmetric domain. On the moduli space of pairs consisting of a cubic threefold and a hyperplane
Sep. 11, 2018 4pm (MATH 350)	Topology Sam Nariman (Northwestern University) X There are at least three different approaches to construct characteristic invariants of a flat symplectic bundle. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. For surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes. In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic surface bundles. As an application, we give a homotopy theoretic description of Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes. On the moduli space of flat symplectic surface bundles Sponsored by the Meyer Fund

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