Monday October 09, 2017 4:00 PM  5:00 PM Physics P128
 Michael Albanese, Stony Brook University
The Dirac OperatorAfter constructing the spin/spin^c bundles, we will define the Dirac operator and work through some low dimensional examples explicitly. If there is time, we will derive a formula for the Dirac operator on a Kahler manifold.

Monday October 16, 2017 4:00 PM  5:00 PM Physics P128
 Michael Albanese, Stony Brook University
The Dirac operator on a Kahler manifoldContinuing on from last week's discussion, we will prove that the Dirac operator on a Kahler manifold is, up to a multiplicative constant, just the sum of the Dolbeault operator and its adjoint.

Monday October 30, 2017 4:00 PM  5:00 PM Physics P128
 Charlie Cifarelli, Stony Brook University
The Dirac Operator on a Kahler Manifold (continued)We will continue our proof that the Dirac Operator on Kahler Manifolds is simply the sum of the Dolbeault operator and its adjoint, up to multiplicative constant. If time permits, we will begin to introduce the SeibergWitten equations.

Monday November 06, 2017 4:00 PM  5:00 PM Physics P128
 David Hu, Stony Brook University
The Seiberg Witten EquationsIn this talk, we will begin our investigation of the SeibergWitten equations. After introducing and understanding the various terms of the equations, we will spend some time setting up the framework from which we can best study them. This includes defining the configuration space (a Sobolev completion of the naive choice), the gauge group, and the action of the gauge group on the configuration space. Our goal is to show that the quotient space of the configuration space by the action of the gauge group is "reasonable" in a way that we will make precise.

Monday November 13, 2017 4:00 PM  5:00 PM Physics P128
 David Hu, Stony Brook University
The SeibergWitten Moduli SpaceWe will continue our study of the configuration space for the SeibergWitten equations from last week. Wrapping up loose ends from last time, we will compute the differential of the SeibergWitten map, and introduce the gauge group and its action on the configuration space. We will then show that the quotient space of the configuration space by this action is a Hausdorff space and prove local slice theorems and corollaries.

