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.