Geometry seminars

Michael Borinsky introduces tropical quantum field theory as a simpler deformation limit that preserves useful information about an interacting theory. Its numerical algorithm computes massive-scalar perturbation theory with runtime polynomial in loop order and external-leg count, avoiding the factorial growth of a Feynman-diagram expansion and making very high loop orders feasible. Geometrically, amplitudes become volumes of graph-moduli spaces, whose recursions resemble those for Weil–Petersson volumes. The talk connects the limiting construction, geometry and algorithm.

Resolving 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.

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.

This talk introduces non-negative Ollivier–Ricci curvature on graphs and examines what it implies for the large-scale geometry of bounded-degree networks. It presents recent results developed jointly with Camillo Brena and Florentin Munch without assuming prior familiarity with this curvature notion.

Continuum Glauber dynamics samples Gibbs point processes with repulsive interactions, including hard spheres. This talk develops continuous spectral-independence and localization tools to establish spectral gaps and efficient sampling for arbitrary-range repulsive potentials. The approach improves fixed-density packing thresholds and works directly in the continuum rather than discretizing the model.

Classical isoperimetric inequalities on the Boolean hypercube can extend beyond independent product measures. The talk proves KKL, Talagrand and Eldan–Gross inequalities under a Dobrushin-type weak-dependence condition, including a class of Ising models. The method combines semigroup arguments, discrete Bakry–Émery theory and gradient estimates.