(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
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Descriptions of some topics courses:
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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).
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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.
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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
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