Summer Northwestern Analysis Program

SNAP 2017

Northwestern University

Week 2 - Topics in PDE

July 31-August 4, 2017

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.

Group Photo

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.

TA: Xavier Garcia (Northwestern)

Problem Set 1
Problem Set 2

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.

TA: Nick McCleerey (Northwestern)

Problem Set 1
Solution of Problem Set 1

Some extra references

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.

TA: Casey Jao (Berkeley)

Problem Set 1