Topology seminars
1 result
December 2026
The string group through shifted geometric quantization
Aditya Dwarkesh· University of Regina, Canada
Aditya Dwarkesh explains how geometric quantization extends from ordinary symplectic geometry to higher stacks represented by simplicial manifolds. Whereas ordinary prequantization produces line bundles, the shifted setting leads to bundle gerbes, higher-categorical analogues of principal bundles. For a compact simple Lie group G, the string group provides an example of a multiplicative bundle gerbe over G and can be understood through prequantization of BG with a 2-shifted symplectic structure. The talk develops this relationship and may include a sketch of a new model for String(G).
Thu, Dec 10 · 10:00 UTC · Online
Recent recordings
22 recorded talksResolving singular Spin(7) spaces links exceptional geometry with gauge-theory vacuum structure. This talk builds torsion-free structures on compact orbifold resolutions from local ALE data encoded by harmonic self-dual forms. It explains the relation to supersymmetric gauge equations and asks when local solutions extend globally. Gluing methods and Dirac operators identify analytic obstructions, with explicit examples attaining full Spin(7) holonomy.
Recorded
Video · 1 h 4 minDifferential GeometryDifferential EquationsSeries: Perimeter Institute Recorded Seminar Archive
Quantum algebras from generalized Poisson sigma models
Keyou Zeng· Harvard University
Poisson sigma models connect geometric deformation with quantum field theory. This talk extends them into higher-dimensional theories with holomorphic and topological directions and relates the construction to quantization of factorization algebras. It develops interfaces, boundaries and defects, then uses Koszul duality to connect the models with quantum-group structures, including examples involving Lie bialgebras, W-algebras and Yangians.
Recorded
Trickle-down Theorems for High-dimensional Expanders via Log-concave Polynomials
Jonathan Leake· University of Waterloo
Expansion properties of low-dimensional links can propagate through a simplicial complex. This talk presents recent results for partite high-dimensional expanders and their consequences for approximate sampling. It explains how Lorentzian and log-concave polynomials provide the mathematical basis for these local-to-global arguments.
Recorded
Tensor networks, topological physics and operator algebras
Yasuyuki Kawahigashi· University of Tokyo
Tensor networks help describe the structures underlying two-dimensional topological phases and topological quantum computation. This talk develops an operator-algebra perspective on those connections and presents recent mathematical understanding of topological order. The introduction is designed to be accessible without prior training in operator algebras.
Recorded
Video · 1 h 3 minCondensed Matter PhysicsAlgebraSeries: Perimeter Institute Recorded Seminar Archive
From the theory of gapless boundaries of 2+1D topological orders to topological Wick rotation
Liang Kong· Southern University of Science and Technology (SUSTech)
Liang Kong reviews a unified mathematical treatment of gapped and gapless boundaries in topological orders in two spatial dimensions. It leads to topological Wick rotation, proposed as a broader organising principle for suitable quantum field theories. The talk examines generalisations and applications, including how familiar topological holography and sandwich constructions emerge as special cases.
Recorded
This survey presents the construction and classification of extended geometric functorial field theories. After reviewing classical definitions, it builds the relevant geometric bordism category, states two principal results and sketches the locality theorem and possible applications, drawing on joint work with Dmitri Pavlov.
Recorded