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Events happening on November 14, 2017

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Nov. 14, 2017 10am (Math 350)	Functional Analysis Leonard Huang (CU Boulder) X In a 1999 paper, Alex Kumjian and David Pask proved that if a discrete group $G$ acts freely on a directed graph $F$ , and if $α$ denotes the induced action of $G$ on the $C^{}$ -algebra $C(F)$ of the graph, then the reduced crossed-product $Cr(G,C(F),α)$ is strongly Morita-equivalent to the $C^{}$ -algebra $C(F/G)$ of the quotient graph. Very recently, Valentin Deaconu has been studying actions of discrete groupoids on Cuntz-algebra graphs, where the vertex set of such a graph is precisely the unit space of the acting groupoid. In this talk, I shall explain my observation that Jonathan Brown’s theory of proper groupoid dynamical systems may be used to prove an analog of the Kumjian-Pask Theorem for free actions of discrete groupoids on Cuntz-algebra graphs (in the sense of Deaconu). A Kumjian-Pask Theorem for Free Actions of Discrete Groupoids on Cuntz-Algebra Graphs
Nov. 14, 2017 11am (MATH 350)	Number Theory Scott Ahlgren (UIUC) X Kloosterman sums are ubiquitous in number theory. We estimate sums of Kloosterman sums of half-integral weight. Our estimates are uniform in all parameters in analogy with Sarnak and Tsimerman’s improvement of Kuznetsov's bound for the ordinary Kloosterman sums. As an application, we obtain an improved estimate for the classical problem of estimating the size of the error term in Rademacher's famous formula for the partition function. This is joint work with Nick Andersen (UCLA) Kloosterman sums, Maass cusp forms, and Rademacher’s formula
Nov. 14, 2017 12:10pm (Math …	Kempner Josh Grochow (CU Boulder) X Wildness is a phenomenon that grew up in representation theory, but has broad implications for classification problems, and turns out to be at the mathematical core of several major open problems in computational complexity. To give the flavor: Drozd's Dichotomy Theorem says that any finite-dimensional associative algebra over a field either has: (a) only finitely many indecomposable representations (e.g., finite groups in characteristic zero), (b) only finitely many 1-parameter families of indecomposable representations of each dimension (e.g., the polynomial ring k[x], where the 1-parameter families are given by choosing an eigenvalue for a Jordan block), or (c) is so complicated that it "contains" the representations of all other finite-dimensional algebras. The latter are called wild. This talk will provide a relatively gentle* introduction to wildness, and a few of the many places it arises in mathematics and computational complexity, including algorithms for testing isomorphism of finite groups, algorithms for multiplying matrices, and the only current approach to resolving major open questions such as P versus NP. * - In particular, by "gentle" I mean that I will not assume any background in representation theory. Wildness & geometry in representation theory & computational complexity
Nov. 14, 2017 1pm (MATH 220)	Athena Sparks (CU Boulder) Polynomial-time algorithm for PCSPs with majority polymorphisms
Nov. 14, 2017 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU) X We introduce a new class of polytopes generalizing chain polytopes of posets introduced by Stanley. More precisely, we define a polytope for each (non-reflexive) relation R on a finite set X. The vertices of the polytopes are indexed by the independent sets for the relation, which are natural generalizations of the notion of an antichain in a poset. Part of the motivation for studying this class of polytopes is the variety of polytopes that it encompasses. These include polytopes whose vertices are indexed by partitions, noncrossing partitions, nonnesting partitions. We describe the 1-skeletons of these polytopes and show that the 2-faces are either triangles or quadrilaterals. In the end, we define the Birkhoff R-polytope and describe its 1skeletons. R-Polytopes
Nov. 14, 2017 2pm (MATH 220)	Peter Mayr (CU Boulder) Promises and constraints 5
Nov. 14, 2017 3pm (MATH 350)	Topology Andy Riddle X Abstract: In the 1960’s Quillen developed model categories as a way to axiomatize homotopy theory. In this setup, a Quillen model category is a category with three special classes of morphism (weak equivalences, fibrations, and cofibrations) which satisfy a few axioms. These axioms then give a framework in which it is possible to setup the machinery of homotopy theory in a wide variety of contexts. In this talk I will give a gentle introduction to the definition of a model category and consider some of the model category structures which occur most frequently in algebraic topology. Introduction to Model Categories

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