PIRSA:17040005 Scientific Series Mathematical physics

DOI10.48660/17040005

Series: Mathematical Physics

Berwick-Evans, D. (2017). Hamiltonian and Lagrangian perspectives on elliptic cohomology. Perimeter Institute. https://pirsa.org/17040005

Berwick-Evans, Daniel. Hamiltonian and Lagrangian perspectives on elliptic cohomology. Perimeter Institute, Apr. 10, 2017, https://pirsa.org/17040005 

@misc{ pirsa_PIRSA:17040005,
  doi = {10.48660/17040005},
  url = {https://pirsa.org/17040005},
  author = {Berwick-Evans, Daniel},
  keywords = {Mathematical physics},
  language = {en},
  title = {Hamiltonian and Lagrangian perspectives on elliptic cohomology},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {apr},
  note = {PIRSA:17040005 see, \url{https://pirsa.org}}
}

Abstract

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. 

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