Special Lagrangian equations
Speaker: Professor Yu Yuan (MSRVP), University of Washington
We survey some new (since our last visit at ANU in 2004) and old, positive and negative results on a priori estimates, regularity, and rigidity for special Lagrangian equations with or without certain convexity.
The "gradient" graphs of solutions are minimal or maximal Lagrangian submanifolds, respectively in Euclidean or pseudo-Euclidean spaces. In the latter pseudo-Euclidean setting, these equations are just Monge-Ampere equations. Development on the parabolic side (Lagrangian mean curvature flows) will also be mentioned.
Optimal transport for dendritic structures
Speaker: Professor Young-Heon Kim, University of British Columbia
Optimal transport gives an effective way to make geometric averages of different shapes, by giving a metric barycentre of a distribution over the space of probability measures. This metric barycentre is called the Wasserstein barycentre. We will discuss how this notion can be applied to studying dendritic structures, such as plant roots. Based on joint work with Brendan Pass (U. Alberta) and David Schneider (U. Saskatchewan and Global Institute for Food Security (GIFS).