Week 28.09.2026 – 04.10.2026

Studying the Ising model using its graphical representations has been tremendously successful.These representations are coupled to each other using the uniform even subgraph, which is invariant under XOR. This trick enables simple proofs of equality of critical points between loop O(1) and Ising and exponential decay for the two-dimensional near-critical Ising model. The scaling limit of the latter is famously conjectured to be related to the exceptional Lie Algebra E_8. Joint work with Ulrik Hansen, Jiangping Jiang and Peter Wildemann.

I'll discuss a connection between topological field theories and topological phases of lattice models, which shows how partition functions of field theories can inspire order parameters for lattice models. After some generalities, I'll use this connection to develop, out of lens space partition functions, a novel order parameter for distinguishing two-dimensional symmetry protected topological (SPT) phases. The resulting procedure takes a wavefunction, such as a ground state of a lattice model, and detects its SPT invariants as expectation values of finitely supported operators, similar to how string order parameters work for 1D SPT phases.