This award will support an NSF/CMBS regional conference to be held at Clemson University in the summer of 2013 on uncertainty principals in harmonic analysis. The principal speaker will be Professor Alexei Poltoratski from Texas A&M University. The lectures will cover such areas as gap and type problems, Beurling-Malliavin theory for Teoplitz kernels, and Bernstein's Problem on weighted polynomial approximation. In addition to the 10 main lectures by Dr. Poltoratski, lectures will be presented by other experts in the field.
Hallmarks of the NSF/CBMS regional conference series are focus on a single important and timely area of research by a leading practitioner, a published monograph for a wider audience, and continued effect and local stimulation through regional recruitment emphasis. The conference will provide a venue for advanced graduate students and recent Ph.D. recipients to interact with leading researchers in this field. This award will support approximately 30 participants in the conference, mostly at early stages of their careers.
A version of the Heisenberg Uncertainty Principle formulated in terms of Harmonic Analysis claims that a non-zero measure (distribution) and its Fourier transform cannot be simultaneously small. This broad statement raises a multitude of deep mathematical questions. It includes problems on completeness of exponentials and polynomials, formulated by Wiener and Kolmogorov over 70 years ago, inverse spectral problems for differential operators and Krein's canonical systems, classical problems in the theory of stationary Gaussian Processes, signal processing, etc. The scientific theme of the CBMS conference ``Uncertainty Principles in Harmonic Analysis'' centered around many of the above problems and their connection to various areas of mathematical analysis. In recent years, several of these long-standing open problems were finally solved, and this conference provided a first oportunity for many junior mathematicians to become familiar with the powerful new techniques that were used in their solution. The conference took place on August 14-18 at Clemson University in Clemson, South Carolina. Funds from the National Science Foundation were primarily used to enable participation of the early career mathematicians and those from under-represented groups. The organizers of the conference were committed to supporting the participation of women, minorities, and young researchers. This project provided participant support and funded advanced graduate students and recent Ph.D.s, allowing them to attend this major conferenceon analysis, discuss new ideas, and interact and learn from the many other mathematicians in attendance. Apart from the organizers, there were 37 registered participants. Thirty two of them received at least partial support, with preference for graduate students, postdocs, junior colleagues and minorities. Amongst the participants there were 14 graduate students, 3 postdocs and 5 women mathematicians. As usual for a CBMS conference, there were 10 lectures delivered by the principal lecturer A. Poltoratski. In addition, there were 6 invited lectures delivered by some of the most prominent expert in this field. The goal of these additional lectures was to supplement and expand the topics presented by the principal lecturer. Moreover, there was also a session on Open Problems during which several potential research questions and directions were presented that were of interest to the majority of the participants. Below is the schedule of the lectures that were presented at the conference. Monday: 9:00-10:00 Lecture 1: A. Poltoratski 10:00-10:30 Coffeee Break 10:30-11:30 Lecture 2: A. Poltoratski 11:30-2:00 Lunch Break 2:00-3:00 Invited Lecture: W. Ross 3:00-3:30 Coffee Break 3:30-4:30 Invited Lecture: M. Lacey Tuesday: 9:00-10:00 Lecture 3: A. Poltoratski 10:00-10:30 Coffeee Break 10:30-11:30 Lecture 4: A. Poltoratski 11:30-2:00 Lunch Break 2:00-3:00 Invited Lecture: D. Lubinsky 3:00-3:30 Coffee Break 3:30-4:30 Discussion and Open Problems Wednesday: 9:00-10:00 Lecture 5: A. Poltoratski 10:00-10:30 Coffeee Break 10:30-11:30 Lecture 6: A. Poltoratski 11:30-2:00 Lunch Break 2:00-3:00 Invited Lecture: S. Treil 3:00-3:30 Coffee Break 3:30-4:30 Invited Lecture: S. Nitzan Thursday: 9:00-10:00 Lecture 7: A. Poltoratski 10:00-10:30 Coffeee Break 10:30-11:30 Lecture 8: A. Poltoratski 11:30-2:00 Lunch Break 2:00-3:00 Invited Lecture: C. Sundberg 3:00-3:30 Coffee Break 3:30-4:30 Discussion and Open Problems Friday: 9:00-10:00 Lecture 9: A. Poltoratski 10:00-10:30 Coffeee Break 10:30-11:30 Lecture 10: A. Poltoratski
