(For descriptions of some topics courses, see below) Spring, 2012 Teaching MWF T/Th 9 MATH 748 Rosenberg 9:30 MATH 601 Schafer (Homotopy theory) AMSC 667 Nochetto MATH/AMSC 674 Machedon 10 MATH 660 Wolpert 11 MATH 713 Kueker 11 MATH 607 Gholampour MATH 631 Fitzpatrick MATH 643 Dolgopyat 12 MATH 636 J. Adams 12:30 MATH/AMSC 671 Jakobson MATH 648? Czaja MATH 742 Novikov STAT 601 Cerrai 1 MATH 648M Grillakis 2 STAT 741 Smith 2:00 MATH 734 Cohen MATH 608? Brosnan (Quadratic Forms) (Quadratic forms) AMSC 661 Levy AMSC 612 Tadmor 5:00 STAT 701 Kagan 5:15-6:30 AMSC 664 Balan/Ide _________________________________________________________________________________________________________________ Descriptions of some topics courses: _________________________ Math 607 (A. Gholampour): Algebraic Geometry II This will be a continuation of Math 606 and mainly follow Algebraic Geometry by Hartshorne. The topics that will be covered are Projective morphisms, Differentials, Divisors and Linear systems, Sheaf cohomology, Serre duality, Flat and Smooth morphisms, Semi continuity theorems (if time allows). ------------------------ MATH 643 (D. Dolgopyat): Hyperbolic Dynamics Some of the following topics will be covered. (1) Expanding maps of the circle (a) Existance of absolutely continuous invariant measures; Dependence on parameters. (b) Decay of correlations; (c) Limit Theorems. (2) Attractors of iterated systems of contractions (a) Hausdorff Dimension; (b) Multifractal analysis. (3) Multidimensional piecewise expanding maps (4) Anosov diffeomorphisms (a) Classifications on a torus (b) Construction of physical measures and dependence on parameeters (5) Quadratic family. (6) Systems with non-zero exponets (a) Overview of the main results; (b) Methods of estimating exponents (c) Introduction to dispersing billiards. ---------------------------- MATH748R (J. Rosenberg): Homotopy Theory This course will cover the basic aspects of algebraic topology that one needs for research in almost any aspect of geometry and topology and that aren't covered in MATH 730-734. Topics will include the following: fibrations and cofibrations basic properties of higher homotopy groups the long exact homotopy sequence of a fibration and applications the Hurewicz theorem and related results relating homotopy and homology spectral sequences, the Serre spectral sequence of a fibration and applications vector bundles and characteristic classes If time permits we may also begin to discuss the foundations of "modern" (post-Quillen) homotopy theory. References (all available free online): Hatcher, Algebraic Topology, Ch. 4 Hatcher, Vector Bundles & K-Theory May, A Concise Course in Algebraic Topology _________________________________