All lectures to be held in Frances Searle Building Room 1-441. Click here for a campus map.
Please be aware that because of construction on campus some paths to the Frances Searle Building may be closed. Please give yourself an extra time to find the building on Monday morning.Registration and coffee starts at 8.30am on Monday, July 31, in Frances Searle Building Room 1-441.
|Monday, July 31||Tuesday, August 1||Wednesday, August 2||Thursday, August 3||Friday, August 4|
|8.45am - 10.15am||Roy-Fortin||Roy-Fortin||9.00am - 10.30am||Visan||9.00am - 10.30am||Visan||Roy-Fortin|
|10.45am - 12.15pm||Auffinger||Auffinger||11.00am - 12.30pm||Roy-Fortin||11.00am - 12.00pm||Problem Session Auffinger||Problem Session Roy-Fortin|
|2.00pm - 3.30pm||Visan||Visan||Free afternoon||2.00pm - 3.30pm||Auffinger||Auffinger|
|4.00pm - 5.00pm||Problem Session Roy-Fortin||Problem Session Visan||Free afternoon||4.00pm - 5.00pm||Problem Session Visan||Problem Session Auffinger|
Monday July 31, 5.15pm there will be Pizza in the Mathematics Department Common Room, 2nd floor Lunt Hall
Antonio Auffinger   (Northwestern). Title: Probabilistic methods in PDE
Abstract: This mini-course is devoted to basic connections between partial differential equations and probability theory. First, we will introduce Brownian motion (BM) and derive some of its main properties. We will study hitting and exit times of subsets of Rd. Then, we will learn how solutions of classic parabolic and elliptic PDEs can be expressed using expectations of functionals of BM. In the last lecture, we will go over some interacting particle systems where PDEs appear naturally as hydrodynamic limits.
Guillaume Roy-Fortin   (Northwestern). Title: Eigenfunctions and eigenvalues
Abstract: It is the middle of the summer, the temperature is very warm and you hear a nice drum beat as you quietly sit on the beach by the lake shore. Your mind starts to wander: I can hear that drum, but can't quite see it. How big is it? Does it have to be circular? Can there be more than one drum producing such a soothing sound? Haunted by these fascinating questions, you eagerly leave the beach (don't forget your flip-flops) and attend this mini-course about eigenvalues and eigenfunctions of the Laplace operator.
Monica Visan   (UCLA). Title: Introduction to the nonlinear Schrödinger equation
Abstract: We introduce the Schrödinger equation as an example of a dispersive equation. Focusing on one concrete model, we illustrate some of the tools and techniques used to prove the existence of solutions and describe their asymptotic behavior.