Fall 08 Special topics courses marked with * have additional information listed below. MWF TTH 9 9:30 602 (Schafer) AMSC 660 (O'Leary) STAT 698F* (Freidlin) 10 600 (Prasanna) STAT 740 (Smith) 11 660 (Forni) 11 673 (Tzavaras) 718L (Laskowski) 748E* (Goldman) AMSC 607 (O'Leary) 632 (Fitzpatrick) 12 642 (Brin) 608V* (Ramachandran) 630 (Warner) 12:30 606 (Tamvakis) AMSC 666 (Elman) 648K* (Kaloshin) STAT 710 (Kagan) 1 712 (Goodrick) 744 (Adams) STAT 600 (Koralov) 2 730 (Novikov) 2 670 (Dolgopyat) AMSC 612 (Nochetto) 3 Faculty meeting hour 5 STAT 700 (Slud) 5 AMSC 663 (Balan/Zimin)) 6-8:30 MATH 648W/MAIT 679 (Benedetto) MAIT courses ~~ MAIT 623 "Modern Mathematical Methods of Signal and Image Processing I", I. Konstantinidis M......... 6:00pm- 8:45pm MAIT 633 "Applied Fourier Analysis", Dennis Healy Th........ 6:00pm- 8:45pm MAIT 679E "Computational Time-Frequency Analysis", G. Easley Th........ 6:00pm- 8:45pm MAIT 679G/MATH 648B "Harmonic Analysis and Waveform Design", J. Benedetto Tu..... 6-8:30 pm MAIT 679T "Target Tracking and Filtering", T. Haug Tu........ 6:00pm- 8:45pm Additional information for special topics courses MATH 608V Abelian Varieties This course will provide an introduction to abelian varieties. The lectures will focus on complex abelian varieties. Student presentations (one per student) will deal with topics from abelian varieties over finite fields and number fields. We will assume some familiarity with basic topology, some algebraic geometry and arithmetic. Since there are several online resources available, there is no required textbook for the course. Excellent references are the course notes of Milne, the expository articles of Milne and Mike Rosen in Arithmetic Geometry (Proc. Conference on Arithmetic Geometry, Storrs, August 1984) Springer, 1986 edited by Cornell-Silverman. The books of George Kempf, H.P. Swinnerton-Dyer, Birkenhake-Lange, David Mumford provide more information about abelian varieties. MATH 648W Topics in Harmonic Analysis: Wavelet theory and waveform design Course Material Introduction 1. Real analysis and Hilbert spaces 2. History and background of wavelet theory 3. The role of the classical sampling theorem 4. Poisson summation formulas Wavelet theory 1. The Haar system 2. Quadrature mirror filters 3. Multiresolution analysis (MRA) 4. MRA wavelet orthonormal bases 5. Fast wavelet transform Waveletpackets 1. The Walsh system 2. Waveletpacket theorems and best bases algorithms 3. Fast waveletpacket transform Waveform Design 1. Periodic and aperiodic waveform constructions 2. Ambiguity function analysis 3. Vector-valued waveform design Multidimensional wavelet theory 1.MRA wavelet orthonormal bases 2. Non-MRA wavelet orthonormal bases The uncertainty principle 1. The classical setting 2. The ambiguity function 3. Gabor and wavelet systems Frames 1. Theory 2. Sigma-Delta modulation and finite frames 3. Sampling theory and frames 4. Frame potential energy 5. Quantum detection and finite frames MATH 648K Instabilities for the 3 body problem. This course will be complementary to the class I taught in the fall of 2007. We shall discuss topics around the restricted planar circular 3 body problem. It includes discussion of Hill regions of this problem, regions of stability and unstability. Stability regions include Lagrange equilibria and nearly circular motions. Instability regions include nearly parabolic motions. One of the most fascinating motions there are called oscillatory. We shall prove its existence following the book of Moser ``Stable and Random motions''. Time permitting we shall discuss the restricted planar elliptic 3 body problem, where there are many open equations. MATH 698F Stochastic Differential Equations and PDEs. This will be an introductory course in stochastic differential equations and their relations with PDE's. I will introduce Wiener process and stochastic integral and consider their properties. Then stochastic differential equations will be considered. These equations describe a wide class of stochastic processes-deffusion processes. Each such process is closely related to a second order elliptic, maybe degenerate, differential operator, so that many interesting characteristics of the process can be found as solutions of appropriate initial boundary problems for corresponding differential equations. This allows also to use probabilistic methods to study PDE's. I will consider shortly some limit theorems for stochastic processes and their applications to asymptotic problems for PDE's. I plan to teach a special topic course on asymptotic problems for PDE's in the Spring of 2009. MATH 748E Differential Geometry This course will cover basic graduate-level differential geometry with an emphasis on connections and curvature. The rough list of topics include: 1. Review of smooth manifolds, vector bundles and tensors 2. Riemannian metrics and their generalizations 3. Examples: Lie groups and homogeneous spaces 4. Connections on vector bundles, principal bundles, and curvature 5. Geodesics, projective differential geometry, invariants of submanifolds This course will substitute for Math 740 (Riemannian geometry) but will be somewhat broader in scope. It is being listed as a topics to accommodate students who had taken earlier versions of Math 740, which emphasized more traditional Riemannian geometry,