In Spring 2026, the Math Department Colloquium Series will be held on Wednesdays 3:30 pm at CU 218. Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).
If you have any questions, please reach out to the organizers Taeho Kim (tak422 AT lehigh DOT edu) and Ao Sun (aos223 AT lehigh DOT edu).
Date: 2/4/2026
Speaker: Lingfu Zhang (Caltech)
Title: 2D random geometry from an i.i.d. field
Abstract: On Z^2, assign an i.i.d. nonnegative random weight to each edge. The distance between two points is defined as the minimum total weight over all paths connecting them, which induces a random metric on Z^2. A central problem in this area is the Strong KPZ Universality Conjecture, which predicts that this random metric converges to a universal random directed metric on R^2. I will discuss recent developments that reveal rich and surprising geometric properties of such random metrics (on Z^2 or R^2). These 2D geometries are also closely connected to a broad class of probabilistic models, from random growth to interacting particles. I will explain how geometric viewpoints can provide new insights into resolving open problems in these related models. No prior knowledge in this topic is assumed.