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 $\Gamma$-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.

报告人简介： 

Liangbing Luo works in the intersection of probability, analysis and geometry. Her research focus on functional inequalities on both finite-dimensional and infinite-dimensional geometric spaces. She published papers in Trans. Amer. Math. Soc., J. Funct. Anal., IMRN, etc. She obtained her PhD from University of Connecticut under the supervision of Prof. Maria Gordina in 2022 and had postdoctoral position at Lehigh University (2022-2024). She is currently a postdoc at Queen’s University from 2024.