Spring 2008 graduate courses
Courses with an asterisk are special topics courses.
Title and sometimes a description are below.
MWF T TH
8 MATH 631 (Fitzpatrick)
9:30 MATH 648M* (Margetis)
10 MATH 601 (Haines) AMSC 614 (Nochetto)
MATH 748D* (Schafer)
STAT 798L* (Slud)
11 MATH 734 (Rosenberg) 11 MATH 648I* (Okoudjou)
STAT 741 (Kedem) AMSC 661 (Elman)
AMSC 667 (Levy) MATH 648J* (Tamvakis)
MATH 643 (Forni)
12 MATH 636 (Adams)
MATH 671 (Kaloshin)
meets WF for 1h 15min.
12:30 MATH 661 (Jakobson)
STAT 601 (Koralov)
MATH 674 (Machedon)
1 STAT 601 (Koralov)
2 MATH 742 (Novikov) 2 AMSC 698T* (Tadmor)
STAT 705 (Slud) MATH 608E* (Prasanna)
MATH 713 (Laskowski)
3 Faculty meeting hour
3:30
5 STAT 650 (Dolgopyat) 5 STAT 701 (Kagan)
AMSC 664 (Balan)
MAIT
MAIT 623
MAIT 633
MAIT 679E (Benedetto) Wed. 6 - 8:45 pm
MAIT 679M/AMSC698M (Balan) Wed. 6 - 8:45 pm
MAIT 679T
Special Topics Courses
MATH 608E (Prasanna) Topics in Iwasawa theory
About the subject: Iwasawa theory is a central area of research in
algebraic number theory that has played a very important role in some
of the most spectacular results of the past two decades, most notably
the proof of Fermat's last theorem. The main objects of study in
Iwasawa theory are certain arithmetic analogues of the Tate module in
algebraic geometry. The "Iwasawa main conjecture" seeks to provide a
description of these modules in terms of analytic objects called
p-adic L-functions. It may thus be considered part of a long
tradition in number theory that seeks to relate arithmetic (or
algebraic) objects with analytic ones.
Outline of the class: After reviewing the necessary background from
class field theory, we will discuss p-adic L-functions and the
Iwasawa main conjecture in various contexts. Finally, we will discuss
the method of "Euler systems" and its application to proving some
cases of the main conjecture.
Prerequisites: Basic algebraic number theory, some familiarity with
class field theory, elliptic curves and Galois cohomology.
MATH 648M (Margetis) Advanced analytic methods with applications
(back by popular demand)
The course will include material on asymptotics for integrals, ODEs
PDEs and integral equations; perturbation theory; some introduction to
probability and stochastic processes; applied stochastic ODEs and PDEs;
renormalization group and other methods of statistical mechanics;
and introduction to multiscale analysis. Applications
would include current problems in physical science and engineering.
MATH 648I (Okoujdou) Analysis on Fractals
description: The goal of this course is to introduce the students to some
analytical tools on a class of fractals that includes the Sierpinski
gasket. Topics include: Measure, Energy, and Metric on the Sierpinski
gasket; Weak and Pointwise formulations of the Laplacian on the Sierpinski
gasket; Spectrum of the Laplacian; Postcritically Finite Fractals.
Moreover, selected topics such as Polynomial, and Power series; heat
kernel estimates; and convergence of Fourier Series will be explored based
on the interest of the audience.
(I'll be using the following book: Differential Equations on Fractals. A
Tutorial, by Robert S.~Strichartz, Princeton University Press, Princeton,
NJ, 2006).
MATH 648J (Tamvakis) Riemann surfaces
This is a course on Riemann surface theory from the point of view of
complex geometry, and can be taken as a second course after complex
variables. We will only assume a rigorous background in real and
one variable complex analysis, and cover any additional prerequisites
during the lectures. The topics to be covered are a classic meeting
ground of complex analysis and algebraic geometry, but the algebraic
aspect of the theory will lie mostly in the background.
After discussing the basic facts and examples of Riemann surfaces,
we will proceed to more advanced topics: the Riemann surface of an
algebraic function, cohomology of line bundles, divisors and the
Riemann-Roch theorem, the canonical bundle and Serre duality. Our
proofs will be analytic, for example Serre duality will be proved
using a regularity theorem for the d-bar operator. We will then
discuss Abel's theorem and the Jacobian, and continue with a
treatment of theta functions, the theta divisor, and Riemann's
beautiful theorem about meromorphic functions and theta. If
time permits we will prove Torelli's theorem and talk about
the Dirichlet problem on Riemann surfaces and the uniformization
theorem.
MATH 748D (Schafer) Homotopy Theory
AMSC 698T (Tadmor) Time dependent nonlinear PDE's