Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University)
X
Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter.
With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions Sponsored by the Meyer Fund
Tue, Oct. 13 1:30pm (Math350)
Math Phys
Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University)
X
Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter.
With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions
With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions