2026 Analysis on Metric Space Seminar: "Discrete Approximation on Metric Measure Spaces of Controlled Geometry via Graphs: Dirichlet Forms and Harmonic Functions" by Dr.Liangbing Luo, Queen's University

Speaker: Dr.Liangbing Luo,Queen’s University

Title: Discrete Approximation on Metric Measure
Spaces of Controlled Geometry via Graphs:
Dirichlet Forms and Harmonic Functions

Abstract:

Based on the approximation of a metric measure space via discrete graphs, we construct
a Dirichlet form. This Dirichlet form is comparable to the upper gradient energy and can
be realized as a -limit of a sequence of induced bilinear forms projected from the discrete
energy form on the approximating graphs. Moreover, we approximate harmonic functions
on a bounded domain with a prescribed Newton-Sobolev boundary data. Based on joint
work with A. Butaev and N. Shanmugalingam.

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