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INFO SHEET QUEEN’S UNIVERSITY AT KINGSTON Department of Mathematics and Statistics http://www.mast.queensu.ca November 10, 2015 CALENDAR Wednesday, November 11 Wednesday, November 11 Thursday, November 12 Remembrance Day Algebraic Geometry Seminar Time: 3:00 p.m. Place: Jeffery 319 Seminar on Free Probability and Random Matrices Friday, November 13 Time: 4:30 p.m. Place: Jeffery 110 Number Theory Seminar Friday, November 13 Time: 11:00 a.m. Place: Jeffery 422 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Classes cancelled from 10:30 am – 11:30 am for Remembrance Day Service Speaker: Owen Ren, Queen’s University Title: Vector bundles over the projective line Abstract Attached Speaker: Josué Daniel Vázquez Becerra, Queen’s University Title: Second order freeness: a free probability study of fluctuations of random matrices, Part III Abstract Attached Speaker: Peng-Jie Wong, Queen’s University Title: On Heilbronn characters Abstract Attached Speaker: Serdar Yüksel, Queen’s University Title: Convexity Properties, Existence and Approximation of Optimal Solutions in Decentralized Stochastic Control Abstract Attached Items for the Info Sheet should reach Anne ([email protected]) by noon on Monday. The Info Sheet is published every Tuesday. Wednesday, November 11, 3:00 p.m. Jeffery 319 Speaker: Owen Ren Title: Vector bundles over the projective line Algebraic Geometry Seminar Abstract: We will prove that every vector bundle over the complex projective line splits into a direct sum of line bundles and the isomorphism classes of the line bundles are (up to order) uniquely determined. Our proof will basically follow Grothendieck’s 1957 argument. Thursday, November 12, 4:30 p.m. Jeffery 110 Seminar on Free Probability and Random Matrices Speaker: Josué Daniel Vázquez Becerra Title: Second order freeness: a free probability study of fluctuations of random matrices, Part III Abstract: Second order freeness is a feature exhibited in the large limit by random matrix ensembles such as the orthogonal Gaussian random matrices and the orthogonal Wishart random matrices. Its main purpose is to help determine the asymptotic behaviour of the covariance of traces of products of random matrices; this is comparable to the description of the asymptotic behaviour of the expectation of the trace of products of random matrices that we get from freeness. Seminar website: http://www.mast.queensu.ca/~mingo/seminar/ Friday, November 13, 11:00 a.m. Jeffery 422 Speaker: Peng-Jie Wong Title: On Heilbronn characters Number Theory Seminar Abstract: In this talk, I will start by reviewing some aspects of number theory, and then discuss several properties of Heilbronn characters. If time allows, I will give an application to L-functions attached to elliptic curves. Friday, November 13, 2:30 p.m. Jeffery 234 Department Colloquium Speaker: Serdar Yüksel Title: Convexity Properties, Existence and Approximation of Optimal Solutions in Decentralized Stochastic Control Abstract: This talk is concerned with stochastic dynamic team problems and their optimal solutions. First, a brief review on information structures in decentralized control will be presented. To facilitate a convex analytical approach, strategic measures for team problems are introduced; these are probability measures induced by admissible team policies. Properties such as convexity, compactness and Borel measurability are studied. These lead to existence of and structural results for optimal policies. It is shown that the set of strategic measures for a team problem is in general non-convex unlike single decision maker control problems, but the extreme points of a relaxed set consist of deterministic team policies, which lead to their optimality. Characterizations for convexity of problems which include teams with a non-classical information structure will be presented. Finally, asymptotic optimality of finite model representations for a large class of dynamic team problems will be established. These lead to asymptotic optimality of quantized control policies, so that one can construct a sequence of finite models obtained through the quantization of measurement and action spaces whose solutions converge to the optimal cost. Witsenhausen's counterexample, an important problem considered in the literature, will be discussed as a special case. (Part of this is joint work with Naci Saldi and Tamas Linder).