Modern Harmonic Analysis encompasses areas as diverse as group representation theory, functional
analysis and applications in signal processing, machine learning and data analysis. These techniques
deliver the answers desired by engineers and scientists working with big data sets or searching for novel
methods to connect experiments with theory. With the new form of the Moore’s Law, where CPU clock
frequency doubling is replaced by parallel processing, the applied mathematics community is now faced
with a new paradigm. The IMA 2011‐2012 Annual Program on “Mathematics of Information” and the
upcoming 2014 PI Summer Graduate Program “Modern Applications of Representation Theory” reflect
this trend.
However, what makes 2015 a special year is the fact that in 2016 there is going to be a summer school at Park City/Institute for Advanced Study devoted to “Mathematics of Data,” and the lecturers of our
PI Summer Graduate Program will be deeply involved in those activities. (In particular, Anna Gilbert is a co‐organizer of the 2016 Park City Summer School). Additionally, in May 2015, the American
University (DC) will host the 2015 SampTA International Conference (Sampling Theory and Applications)
with support from the Department of Mathematics at UMD. Together, with the annual February Fourier
Talks (FFT) Conference organized by the Norbert Wiener Center of UMD, we envision the 2015 PI
Graduate Student Summer Program at UMD as an educational platform reaching out to the next
generation of STEM graduates and complementing existing research activities.
Program Outline
The three weeks of this summer school are divided equally among seven speakers grouped thematically into three sections, each including at least one organizer and one invited speaker:
1. Theoretical harmonic analysis:
a. John Benedetto (UMD): Fourier analysis
b. Chris Heil (GaTech): Frames and time‐frequency analysis
2. Applied harmonic analysis (1):
a. Kasso Okoudjou (UMD): Preconditioning of finite frames
b. Radu Balan (UMD): Nonlinear analysis with frames
c. Anna Gilbert (UM): Sparse Fourier transform
3. Applied harmonic analysis (2):
a. Gilad Lerman (UMN): Geometric and analytic methods for modeling data and applications
b. Wojtek Czaja (UMD: Harmonic analysis and big data
In addition to lectures, we shall have:
-Problem sessions for assistance with assigned theoretical exercises;
-Computer lab sessions for work on problems and projects requiring computation
