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,