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Hamiltonian and Lagrangian perspectives on elliptic cohomology

The physics proof of the Atiyah-Singer index theorem relates the Hamiltonian and Lagrangian approaches to quantization of N=1 supersymmetric mechanics. Similar ideas applied to the N=(0,1) supersymmetric sigma model construct two versions of elliptic cohomology: elliptic cohomology at the Tate curve over the integers and the universal elliptic cohomology theory over the complex numbers. Quantization procedures give analytic constructions of wrong-way maps in these cohomology theories. Relating these to the Ando-Hopkins-Strickland-Rezk string orientation of topological modular points to intricate torsion invariants associated with these sigma models. 

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Event Date: 
Monday, April 10, 2017 - 14:00 to 15:30
Location: 
Sky Room
Room #: 
394