Seiberg-Witten invariants
A learning seminar on Seiberg-Witten gauge theory will meet this semester on Wednesdays at 1 in the QM Seminar Room. We will mainly follow The Seiberg-Witten equations and applications to the topology of smooth four-manifolds by John Morgan.
Talk 1: February 7 Morgan 2-3.1 Spin bundles and Clifford bundles (Joel)
Talk 2: February 14 Morgan 3.2, 3.3, 4.1 Dirac operator and the Seiberg-Witten equations (Siva)
Talk 3: February 21 Morgan 4-5 Physical motivation and compactness of the moduli space (Devon)
Talk 4: February 28 Morgan 6 Seiberg-Witten invariants (Adrian)
Talk 5: March 6 Morgan 7 Properties and applications of SW invariants (Ikshu)
Other references:
An introduction to the Seiberg-Witten equations on symplectic manifolds, Michael Hutchings and Cliff Taubes
Lectures on Seiberg-Witten invariants, John Moore
Methods of classical homotopy theory
A learning seminar on homotopy theory will meet this semester on Fridays at 3 in the QM Seminar Room. We will mainly follow Hatcher's Algebraic Topology and Spectral Sequences.
This seminar deals with the results and techniques of classical homotopy theory, such as the Freudenthal suspension theorem, Serre's theorem on the finiteness of homotopy groups of spheres, and the Adams spectral sequence. We will focus on these concrete results and avoid a lengthy discussion of the modern categorical language. Also, this seminar should serve as a good introduction to spectral sequences for graduate students who want practice with computations.
Anyone is welcome to attend or give a talk. A rough outline of the schedule of the talks is given below. This schedule may be subject to change.
Talk 1: February 9 Hatcher 4.1-4.3 Long exact sequence of a pair, exicision, Freudenthal suspension, stable homotopy groups (Yuki)
Talk 2: February 16 Hatcher 4.1, 4.2. 4.B Hurewicz homomorphism, long exact sequence of a fibration, Hopf Bundles, Hopf invariant (Zhongyu)
Talk 3: February 23 Hatcher 5.1 Serre Spectral sequence, Serre's theorem (Alyosha)
Talk 4: March 1 Introduction to spectral sequences (Gard)
Talk 5: March 8 Hatcher 4.L, 5.2 Steenrod squares (Gard)
Talk 6: March 15 Adams spectral sequence, spectra (Gard)