Two 30 minute talks will be given by the Department's Mellon Fellowship winners.
(i) Victor DeCaria
Title : Variable stepsize, variable order methods for partial differential equations
Abstract: Variable stepsize, variable order (VSVO) timestepping methods are commonly used to solve difficult ODEs. Existing VSVO methods are computationally complex, and do not scale well for PDE applications with many unknowns. Furthermore, their implementation often requires developing a monolithic code from scratch. I will discuss new methods we've developed that bridge the gap between what is computable for ODEs and PDEs. These methods are computationally inexpensive, can adapt well to parallel architectures, and are easy to implement on top of an existing codebase. These methods are general, but I will specifically discuss their application to the incompressible Navier-Stokes equations and show some numerical results.
(ii) Priyadip Mondal
Title: Hidden Symmetries of Hyperbolic Knot Complements
Abstract: A manifold equipped with a hyperbolic metric is referred as a hyperbolic manifold. In the talk, I will try to give an account of some aspects of three dimensional hyperbolic geometry. My exposition will be centered around hyperbolic knot complements, complements of embedded circle in S^3 with a hyperbolic metric. Finally, I will mention some results from my joint work with Eric Chesebro and Jason DeBlois.