Topological phases can be divided into two classes corresponding to whether the microscopic degrees of freedom supporting the phase are purely bosonic (e.g., spins or qubits) or whether they include fermions (e.g., electrons). Imposing a symmetry on a topological phase enriches the classification by restricting and possibly fracturing the phase space. Fermionic topological phases additionally include an underlying fermionic particle of the system, the physical fermion. This talk will present recent results on the algebraic structure and classification of fermionic topological phases with on-site unitary symmetry using G-crossed braided tensor categories. I will emphasize the new obstructions which appear, contrast them with their bosonic counterparts, and provide a complete characterization of all symmetric unobstructed invertible fermionic phases.
The seminar will be held in hybrid mode. Join Zoom Meeting https://cuboulder.zoom.us/j/94002553301 Passcode 790356
Thinking mathematically, something so powerful a book was written about it. We will explore three questions: (1) How do we learn? (2) What is mathematics? (3) What is mathematical thinking? We will then use our answers to these questions to investigate how we learn to think mathematically.