Mathematics Graduate Students Organization

Seminar:

Date: September 19

F. Sottile: "Numerical analysis is the future of computation in algebraic geometry"

Abstract: The ability to represent and manipulate objects in algebraic geometry on a computer has had a great effect on the subject.The current dominant paradigm is symbolic computation using exact arithmetic. Current and likely future trends in computer technology will lead to a diminished role for symbolic computation, which is not parallelizable, and an increased role for parallelizable numerical computation.

My talk will discuss computation in algebraic geometry,both symbolic and numeric. After an overview which includes the role of parallelism in symbolic and numeric computation for algebraic geometry, I will discuss some of the basics of numerical computation in algebraic geometry, and explain how working towards this numerical future fits into the research of those with whom I work.

A. Bonito: "The Critical Role Played by the Geometry in Numerical Simulations"

Abstract: We are interested in deformable domains where the geometry is one of the driving force leading to shape deformations. Several applications are presented with a special focus on "bending actuators". The latter process relies on the large deformation produced when a plate made of two thin layers with different material properties is heated. It turns out that the effect of the heat translates into a plate with an interesting geometric property, namely a spontaneous curvature. Shape differential calculus and gradient flows are introduced to these studies and are briefly discussed.