Welcome to the home page of the Graduate Analysis Seminar. This page will list the past and upcoming talks for the seminar. For the Spring 2015 Semester, the seminar will run at 9:00 am on Thursdays in the Graduate Student Lounge (Hill 701).
In Fall 2014, the seminar was led by Matt Charnley. Please click here for the information from that semester.
Click here to return to my personal homepage, or here to return to the Rutgers Math Department Home Page.
Speaker: Manuel Larenas
Date: April 2, 2015
Abstract: I will show an abstract method (integration by parts-free!) to derive decay estimates for dispersive equations based on commutator identities.
Speaker: Gyu Eun Lee
Date: March 26, 2015
Abstract: Brouwer degree is a classical tool that is often used to deduce existence results for ODEs. In this talk, we investigate a class of quasilinear equations with omega-periodic data and a small omega-periodic perturbation, and the question of the existence of omega-periodic solutions for a sufficiently small perturbation. We will see how to recast this problem into a degree-theoretic formulation, and then apply this procedure to a problem of physical significance.
Speaker: Érik de Amorim
Date: February 26,2015
Abstract: We will discuss and prove the 1950's theorem by Bernard Malgrange and Leon Ehrenpreis that states that a linear partial differential equation with constant coefficients can always be locally solved, both in the classical and the weak sense. The proof we will present is an early and very simple nonconstructive proof, relying on norm estimates of polynomial expressions involving L2 operators and their adjoints, so no prerequisite is needed beyond an introductory course on PDE.
Speaker: Matt Charnley
Date: February 19, 2015
Abstract: This talk will discuss a method for solving first order PDEs (in two dimensions) using Integral Surfaces and Characteristic Strips. The general method will be presented in both the non-linear and quasi-linear case, and several examples will be shown. This talk mostly follows chapter 1 of Fritz John.