Bott Periodicity and the "Periodic Table" of Topological Insulators and Superconductors

Explore the fascinating intersection of topology and condensed matter physics in this 1-hour 5-minute lecture by Martin Zirnbauer at the Hausdorff Center for Mathematics. Delve into the concept of Bott periodicity and its surprising application to topological insulators and superconductors. Discover how symmetry-protected ground states of gapped free-fermion systems form a periodic table-like structure, as explained through twisted equivariant K-theory. Follow the journey from physical context to new mathematical physics results, covering topics such as family constraints, time reversal, charge conservation, particle-hole conjugation, pseudosymmetries, and momentum conservation. Gain insights into the historical context and important papers in the field, while exploring pictorial representations and physical language interpretations of these complex concepts.

Intro
The Periodic Table
The Mathematical Model
Challenge to the Brain
Step 1 Family constraint
Step 2 Time reversal
Step 3 Charge conservation
Step 3 Particle whole conjugation
Step 3 Particle whole
Step 4 Particle whole
Step 5 Subspace
Pseudosymmetries
Historical credit
A very important paper
Momentum is conserved
Example
Message
So here pictorially
Diagonal map
S pseudosymmetries
One parameter group
Verification
Physical language
Result
Time is up