The colloquium typically meets Mondays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall.
The colloquium is preceded by tea starting at 3:30 in the Faculty Lounge, adjacent to Room 617. Click on title for abstract.
Mete Soner, Princeton University
Stochastic optimal control has been an effective tool for many problems in a wide range of fields including social sciences. Although it provides the much needed quantitative modeling for such problems, until recently it has been intractable in high-dimensional settings. However, several recent studies report impressive numerical results. All these papers use a Monte-Carlo type algorithm combined with deep neural networks proposed by Han, E and Jentzen. In this talk I will outline this approach. Numerical results, while validating the power of the method in high dimensions, show the dependence on the dimension and the size of the training data. Also, studies for the optimal stopping problem illustrate the potential difficulties. This is joint work with Max Reppen of Boston University and Valentin Tissot-Daguette from Princeton.
Emmy Murphy, Princeton University
Abstract: We survey a number of recent results in symplectic geometry, related to h-principle type techniques. For one example, a Lagrangian submanifold of \(C^n\) is by definition a smooth real n-manifold embedded in \(C^n\) so that \(iTL\) is the orthogonal complement of \(TL\) at every point. Which diffeomorphism types admit Lagrangian embeddings into \(C^n\)? The answer is surprisingly nuanced, and gives a sort of "rigid-flexible dichotomy". We'll discuss related phenomena for Stein manifolds and some other geometric situations. No background in geometry will be assumed for the talk.