Room 509, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館509研討室+ Zoom)
Singularities of Symmetric Lagrangian Mean Curvature Flow
Albert Wood (The Chinese University of Hong Kong)
Abstract: Special Lagrangians are calibrated, volume-minimising submanifolds in Calabi–Yau manifolds. It is expected that special Lagrangians exist in any Calabi-Yau manifold, yet most have no known examples. To prove existence, one might hope that the mean curvature flow (as the gradient descent for volume) deforms Lagrangian submanifolds toward special Lagrangian representatives; the main obstruction to this programme is the formation of singularities, which are often modelled on self-similar solutions known as solitons.
In this talk, I will introduce Calabi-Yau manifolds and Lagrangian mean curvature flow, and explain how symmetry makes singularity analysis and constructing self-similar solitons more tractable. In particular, I will discuss my results on singularities of cohomogeneity-one LMCF, including joint work with Jesse Madnick and upcoming joint work with Ben Lambert.
Organizer: Daniel Spector (NTNU)
