Fall, 2009 Teaching
MWF T/Th
9 MATH 673 Margetis
9:30 MATH 608 (Modular forms) Washington
MATH 648R* (Attractors) Jakobson
10 MATH 600 Haines
MATH 748* (Index theory) Rosenberg
AMSC (Finance) von Petersdorff
STAT 740 Smith
11 MATH 634 Warner 11 MATH 632 Tzavaras
MATH 712 Kueker MATH 718B* (Independence proofs) Laskowski
AMSC 614 Wolfe AMSC 663 Liu/Ziman
STAT 705 Slud STAT 750 Kagan
12 MATH 730 Cohen
12:30 MATH 660 Jakobson
MATH 740 Melnik
1 MATH 606 Ramachandran
MATH 670 Dolgopyat
STAT 600 Koralov
2 MATH 642 Forni 2 MATH 630 Fitzpatrick
AMSC 666 Tadmor
STAT 698 Freidlin
5:00-6:15 STAT 700 Yang
Tues 6-8:30 MATH/MAIT 648* Benedetto
* = Description follows
MATH 748 Rosenberg: The Atiyah-Singer Index Theorem is one of the great accomplishments
of 20th century mathematics. It relates PDE theory, geometry, and topology
in a very deep way. Today, many proofs of this theorem are known,
and there are also literally dozens of variants and generalizations,
as well as a huge stock of interesting applications. The purpose
of this course will be to explore the Atiyah-Singer Theorem and its
variants. We will develop a lot of the background material along the
way, though any previous exposure to elliptic PDE, functional analysis,
Riemannian geometry, and characteristic classes, such as developed in
MATH 631, 632, 673, 674, or 740, will be useful. The minimal prerequisites
are MATH 630 (real analysis) and MATH 734 (algebraic topology).
MATH 648R Jakobson: "Attractors and Sinai-Ruelle-Bowen measures in
small dimensions"
We study attractors for families of dynamical systems such as
quadratic family, Lorenz family, Henon family and others.
Sinai-Ruelle-Bowen measures also called "physical measures"
are important because they describe asymptotic distribution of trajectories
corresponding to almost all initial conditions.
Prerequisite : basic analysis courses (630,660 and equivalent and introductory
courses in dynamics 642/643 or 670/671).
MATH 718B Laskowski: "Independence proofs"
We study what it means for a statement of mathematics to be independent of a set
of axioms, learn how to properly STATE the "Independence of the continuum hypothesis"
and then introduce both Godel's constructible universe and Cohen's method of forcing.
Prerequisite: Formally nothing. Math 712-713 may be helpful, but the necessary notions
will be presented in the class.
MATH 648F / MAIT 679F Benedetto: "Topics in harmonic analysis and applications"
Fourier series, Discrete Fourier series (DFT) and the Fast Fourier
Transform (FFT); The theory of frames, both finite and infinite;
Wavelet and Gabor frames; Sampling theory; Frame potential and the
characterization of finite unit norm tight frames; Frame potential and
the characterization of finite unit norm tight frames; Quantum
detection and finite frames; Grassmannian frames; Compressive sensing;
Current research and applications in sampling, frames, and fusion
frames including classification.