The project of this awarded proposal is a conference, entitled "Ergodic Theory and Related Fields Workshop". It will be held at the University of North Carolina at Chapel Hill from March 17 to March 21, 2011. The workshop will focus on a fundamental theme in ergodic theory: connections between ergodic theory and number theory. Several of the topics covered are central and extremely active areas of current research in ergodic theory; limit theorems for the Gauss map, rigidity of group actions, the pointwise convergence of nonconventional ergodic averages and the pointwise convergence of ergodic averages along subsequences of integers).
The funds provided will support participants, especially women, graduate students, postdocs and young faculty. Young researchers will be given ample opportunities to speak and to participate in the conference activities and will be exposed to the latest developments in the connections between number theory and ergodic theory.
We organized an ergodic theory workshop on March 17-21, 2011 in the Department of Mathematics at the University of North Carolina at Chapel Hill. This workshop received the financial support of the National Science Foundation, the Department of Mathematics, the College of Arts and Sciences and the Vice Chancellor for research office at UNC-Chapel Hill. In terms of Intellectual merit the workshop had two main aspects 1) Young (graduate students, Post Doc, Assistant Professors) and senior researchers were brought together during the four days of the workshop. Senior researchers gave semi expository talks which allowed junior researchers to be introduced to some active research areas. The workshop started with a Departmental Colloquium talk given by Prof. Y. Sinai from Princeton University. "Mobius function and statistical mechanics". A list of talks with their abstracts can be found at http://ergwork.web.unc.edu/past-workshops/2011-ergodic-theory-workshop/ 2) The main talks were given on recent breakthroughs on connections between ergodic theory and number theory. This led to discussions between mathematicians from interconnected research areas, such as Harmonic Analysis, Ergodic Theory, Probability Theory and Number theory. A list of questions was gathered during the problem session. This list will appear in the proceedings of this workshop. Several participants submitted papers for these proceedings. In terms of broader impact the workshop had several components. 1) Particular attention was paid to women participation. Eleven women participated in the workshop; four of them gave 45 minutes talks. All talks were 45 minutes long. 2) The workshop was advertised on a website where interested researchers registered and applied for financial support. 3) Graduate students (2) originally from KNUST in Kumasi (Ghana) and Cameroon (1) participated in the workshop. 4) The geographical location of the participants covered a broad spectrum (USA, France, Russia, Israel, England, Ghana, Cameroon, Poland,). It helped disseminate the results presented and added visibility to the University of North Carolina at Chapel Hill.