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.