Simons Courses: Special Seminar by Ryosuke Takahashi, Harvard

Title: The moduli space of S1-type zero loci for Z/2-harmonic spinors in
dimension 3 and the guideline to define a new invariant
Speaker: Ryosuke Takahashi, Harvard
Date: Thursday, May 14, 2015
Time: 10:00am – 11:30am
Place: Seminar Room 313, Simons Center

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Abstract: Let M be a compact oriented 3-dimensional smooth manifold. In this talk, we will construct a moduli space consisting of the following date {(S, P)} where S is a C1-embedding S1 curve in M, P is a Z/2-harmonic spinor vanishing only on S and |P|=1. We will prove that this moduli space can be parametrized by the space X = { all Riemannian metrics on M } locally as the kernel of a Fredholm operator. In addition, I will show you the possibility to define a new invariant on 3 or 4 dimensional manifolds.