Math 70330
Intermediate Geometry/Topology
Fall Semester, 2008
Schedule
Date Talk by Topic References
8-27 Stephan introduction
9-1 Stephan introduction
9-3 Katie Chern- and Stiefel-Whitney classes
9-8 Katie Chern- and Stiefel-Whitney classes
9-15 Ryan complex cobordism Quillen: Complex Cobordism
9-24 Ryan complex cobordism
9-29 Bernadette Sheaves Hartshorne p. 60-65
10-1 Megan cohomology of sheaves Hartshorne p. 201-208 & p. 72 & p. 109
10-6 Megan A Vanishing Theorem of Grothendieck Hartshorne p. 208-211
10-8 Bernadette Cech Cohomology Hartshorne p. 218-220
10-13 Brandon K-Theory Hatcher's book on K-theory, section 2.1
10-15 Brandon K-Theory Hatcher's book on K-theory, section 2.1
10-27 Brandon K-Theory as cohomology theory Hatcher's book, section 2.2
10-29 Katie Index Theory Atiyah-Singer survey paper
11-3 Andy Index Theory
11-5 Katie Index Theory
11-10 Andy Index Theory
11-12 Andy Index Theory
11-14 Jian Morse Theory a la Witten Excerpts from the books by
11-17 Jian Morse Theory a la Witten Weiping Zhang and John Roe
11-19 Jian Morse Theory a la Witten
11-21 Ryan Classifying spaces Cohen Lecture Notes
11-24 Ryan Classifying spaces
12-1 Megan Ideal and Varieties in Affine and Projective Space (Schenck, Ch 1 - 2.1, except 1.3; book is available in library)
Graded Rings/Modules and Hilbert Functions (Schenck, 2.2-2.3)
12-3 Bernadette Geometry of Hilbert functions; Hilbert functions of points and Artinian Reduction (Schenck Ch 7)
Theorem of Macaulay and Gotzmann (Bigatti-Geramita-Migliore paper section 0)
12-8 Bernadette Various theorems in the paper by Bigatti-Geramita-Migliore
12-10 Megan Inverse Systems (Geramita, Lecture 2)
(another) Macaulay's Theorem (Geramita, Lecture 8)