Singularity formation in geometric flows
蘇瑋栢博士國家理論科學研究中心 15:30 – 17:00 鴻經館 M107
Abstract：
A defining feature of nonlinear PDEs is the formation of singularities, where certain quantities diverge to infinity, causing the PDE to break down in the classical sense. These singularities often indicate extreme physical phenomena, such as shock waves or the formation of black holes. Understanding how and when singularities form is therefore essential.
Since singularities typically occur on very small scales, one can "zoom in" around the singular region to study their structure more closely. The resulting limiting solutions are known as singularity models. Classifying these models reveals potential singular structures, while conversely, one can investigate whether a given model can arise as the blow-up limit of a solution.
In this talk, I will explore both perspectives, focusing on Lagrangian mean curvature flow (LMCF) and curve shortening flow (CSF). I will present our construction of solutions to LMCF that develop finite-time / infinite-time singularities, with prescribed singularity models and precise blow-up rates for the curvature. Additionally, I will discuss the construction of new singularity models in LMCF and partial classifications in CSF.