A Conference on Infinitary Ramsey Theory will be held at the University of Denver May 24 - 28, 2014. In the past thirty years, Ramsey theory has risen to a prominent place in mathematics, providing the key to solutions of long-standing problems, in particular, Gowers' solution to the distortion problem. Recently, the paper of Kechris, Pestov, and Todorcevic connecting Ramsey theory with topological dynamics led to the recent boom in research regarding applications of Ramsey theory applied to finding minimal flows; and the recent book of Todorcevic on Ramsey Spaces has prepared a path for a surge in progress on Ramsey theory. This conference will focus on Ramsey theory of an infinite flavor and its applications in the fields of Banach spaces, homogeneous structures, set theory, and topological dynamics.
This conference will promote cross-pollination of ideas and results among Ramsey theorists from different four or more continents, many of whom have never met each other. It will serve as a unifying point for the subject of infinitary Ramsey theory and increase future collaborations. It will also provide entry to the field for young researchers with diverse backgrounds. As such, the field of infinitary Ramsey theory will be strengthened, very likely speeding up the rate of progress in this area and areas in which it is applied. The conference website is at https://portfolio.du.edu/ramsey
The Conference on Infinitary Ramsey Theory was held at the University of Denver May 24-28, 2014. This was the first conference on Ramsey theory to be focused solely on infinitary and structural Ramsey theory. The talks showcased recent major breakthroughs in partition theorems for trees, general frameworks for Galvin-Glazer type theorems and the Van der Corput Lemma, developments in topological Ramsey space theory, and better quasi-orderings, as well as applications to Banach spaces, ordinal partition relations, dynamics, graph theory, measure theory, metric spaces, model theory, non-standard analysis and arithmetic, and ultrafilters. The list of speakers, abstracts, and slides can be obtained from the conference website at https://portfolio.du.edu/ramsey/ The conference brought together a large portion of leading experts in structural and infinitary Ramsey theory and younger researchers including 6 postdocs and 7 graduate students. There were 19 invited talks and 8 contributed talks. Four of the ninteen invited talks were given by graduate students obtaining their PhD's in 2014 to showcase their thesis work. In all, there were 36 particpants from Brazil, Canada, Colombia, France, Israel, Italy, Mexico, Spain, Switzerland, United Kingdom, United States, and Venezuela. The conference had a good mix of demographic, ethnic and gender diversity, including 7 women (6 of them invited speakers), 7 researchers who either grew up in or are currently working in Central or South American countries (6 of them invited speakers), and other ethnic backgrounds which are traditionally under-represented in mathematics the United States. The conference provided a meeting point for the many different research groups around the world working on infinitary and structural Ramsey theory and its diverse applications. Many of the participants had not met before, and the conference served to make bridges for future collaborations between the different groups. The longer breaks (intended for research) built into the schedule and the congenial atmosphere provided time for participants to develop deeper understanding of each others' research and discuss future directions. This was especially seen in more established researchers mentoring, encouraging, and sharing ideas and research directions with younger researchers. The National Science Foundation grant provided support for the travel and lodging for 11 participants. This included 3 PhD students, 5 Postdocs, 6 women, 2 working in Brazil, 2 from South American countries, and 1 from Africa.
