Spring 2010 Special topics courses marked with * have additional information listed below. MWF TTH 9:30 MATH 674 (Margetis) MATH 742 (Novikov) 10 MATH 601 (Haines) STAT 741 (Smith) 11 MATH 713 (Kueker) 11 AMSC 667 (Levy) STAT 798K* (Kedem) MATH 748G (Goldman) MATH 608D* (Tamvakis) STAT 770 (Kagan) 12 MATH 608G (Ramachandran) 12:30 MATH 734 (Schafer) MATH 648M (Levy) 1 STAT 601 (Koralov) MATH 660 (Hamilton) 2 MATH 671 (Dogolpyat) 2 MATH 631 (Fitzpatrick) MATH 648N (Kaloshin) 3 Faculty meeting hour Monday 4-7 AMSC 661 (O'Leary) 5 STAT 701 (Yang) AMSC 612 (Nochetto) Titles and Info on special topics courses MATH 748G (Goldman) Geometric structures on manifolds MATH 648M (Levy) Advanced analytical methods with applications MATH 608D (Tamvakis) Algebraic combinatorics The aim of this course is to study the theory of symmetric functions and their many variations and extensions. The latter include the Schur and Hall-Littlewood functions, Macdonald polynomials, Schubert and Grothendieck polynomials, theta polynomials, etc. Some of these objects have been around for a very long time, but others have been defined only in the last few years, and there are plenty of open questions about them. The course will feature a new unified approach to many of the above topics, which relies on Young's raising operators. This material is quite beautiful and elegant on its own, but it is even more interesting because of its applications to other parts of mathematics, especially the representation theory of Lie groups G and the Schubert calculus in the cohomology of their homogeneous spaces G/P. There will be some discussion of the connections with these two subjects, although the plan is to keep the course as self contained as possible. The main prerequisite is a first year graduate course in algebra, especially rings and modules. We won't be following any particular textbook, but many of the topics we'll cover can be found in Macdonald's acclaimed monograph "Symmetric Functions and Hall Polynomials". MATH 608G (Ramachandran) Alg Geometry II -- Hodge theory MATH 648M (Levy) Advanced analytic methods and applications MATH 648N (Kaloshin) Topics in dynamics STAT 798K (Kedem) In the last 21 years or so, there has been a quiet revolution in statistics which started with the work of Art Owen cerca 1988. He introduced the extremely important notion of empirical likelihood. Building on Owen's work, a growing number of researchers further published fascinating papers containing both theoretical results and important statistical applications, using the empirical likelihood. This work regards likelihood considerations under constraints. It leads to a novel approach to semi-parametric statistics. Next Spring 2010, I am offering a special topics course STAT798K on this growing body of literature. I intend to show you, among other topics, how multivariate probability distributions "communicate" with each other given many data sources, and how to actually obtain these distributions by simple optimization. This idea revolutionizes the notions of regression and prediction. I intend to show you how to obtain powerful tests based on data from multiple sources. I intend to show you how to integrate data from numerous sources. I intend to show you all sorts of graphical ideas. The field is "hot" and there is room for a lot more research. My plan is to go through parts in Owen's 2001 book, and complement this by a review of the literature, particularly the work of our former colleague Jing Qin who has made a number of influential contributions. Since the ideas are novel, there is no need for "heavy" prerequisites, only that those who are interested come with an open mind.