Dates: June 28 - July 16, 2010

Application and recommendation deadline: April 1, 2010. Apply via our online application. Recommenders may submit their letters here.

Overview

A three-week summer school giving advanced undergraduates and beginning graduate students the opportunity to study with the University of Washington's integrated Inverse Problems/PDE group. Students will attend lectures in the morning and problem sessions in small groups with mentors in the afternoon. Advance your career by learning from experts in these fields while visiting Seattle during summer 2010, when the Pacific Northwest is at its best.

The Radon transform and the X-Ray Transform (Gunther Uhlmann, Peter Kuchment). This course will describe in detail the essential properties of these transforms including inversion formulas. The X-ray transform is one of the basic inverse problems, which consists of determining the density of tissue by measuring the attenuation of X-rays passing through the body. The inverse problem for the Radon transform consists of determining a function from integrals along planes. Students will also work on Matlab programs implementing the filtered backprojection algorithm which is commonly used in CT scans. Problem sessions and computer labs will be scheduled during the afternoon.

Orthogonal Bases and Multiscale Analysis (Hart Smith) This course will discuss the use of different orthogonal bases used in the representation of functions in 1 and 2 dimensions, and the role they play in signal and image compression. Emphasis will be placed on the discrete case to keep the presentation elementary. Lectures will be accompanied by assignments using Matlab. Topics will include: the Euclidean and discrete Fourier transform bases, the Fast Fourier Transform algorithm, the Haar basis, the local cosine transform and the JPEG algorithm, and an overview of wavelet theory.

Program details

• Open to advanced undergraduates and beginning graduate students.
• A few undergraduates may be offered the opportunity to come to the UW campus a week early (June 21-27) to prepare for the IPDE Summer School. Click here for more information.
• On-campus accommodation and meals will be provided, plus a travel allowance of up to $500.
• Must be a U.S. citizen or permanent resident.

  Note: Applications from international students may be considered, but international students must provide their own support for travel, accommodation, and meals. In particular Canadian students should contact Ken Leung at PIMS for possible support.

To Apply:

Submit via the online application:

• Personal statement about why you would like to attend the IPDE Summer School at the University of Washington.
• Names of two people whom you will ask to submit letters of recommendation.

and submit by post:

• Unofficial transcript

Please direct questions or comments about the IPDE Summer School to ipdemail@math.washington.edu.