“The bread and butter of first semester calculus are optimization problems. In this talk we will start with a classic example: given a rectangular sheet of metal/paper/cardboard, cut equal size squares from each corner so that the sides can be folded up to make an open top box. Given the dimensions of the original rectangle,

MINIMIZATION METHODS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR DIFFERENTIAL EQUATIONS The purpose of this lecture is to demonstrate the power of variational methods in the study of nonlinear partial differential equations to people working in other field of mathematics. The equations considered here are variational, namely there is an energy functional ˆ defined on certain Sobolev spaces, whose

Spintronics is a rapidly growing research field with many emerging technologies that aim to exploit the “spin” of the electron in addition to its electric charge. The design of new materials with specific properties optimized for a particular application is of paramount importance for widespread adoption of spintronic technologies. This requires an understanding of the fundamental mechanisms responsible for the magnetization

Dr. Tim Ferguson - Basic Extremal Problems I will talk about extremal problems, which are one of my favorite things to research. These problems involve maximizing or minimizing certain quantities (sort of like optimization in Calculus I). Even though these problems can be difficult to solve and understand, they are often simple to state. I