Algebra and Topology in Interaction; Davis, CA; September 2009

University Of California-Davis, Davis CA

Investigators

Abstract

Under the guidance of the Scientific Advisory Board consisting of Yakov Eliashberg (Stanford University), Nicolai Reshetikhin (UC Berkeley), and Serge Tabachnikov (Pennsylvania State University) serving as Chair of the Board, the PI and Co-PIs propose to organize a conference, Algebra and Topology in Interaction, celebrating the 40 years of spectacular developments in the interplay of these two fields since the birth of the Gelfand-Fuchs cohomology. The conference will be held on the UC Davis campus in September 2009. The main theme of the conference is to illuminate the particular type of interaction which characterizes the past 40 years of developments in algebra and topology, including the most recent results in contemporary mathematics. The topics to be discussed in the conference will include the current exciting developments in symplectic field theory, representations of infinite- dimensional Lie algebras, and topological quantum field theory, as well as the recent achievements in the topological applications of cohomology of infinite-dimensional Lie algebras, characteristic classes of foliations, contact homology, Chekanov- Eliashberg differential graded algebra, and Legendrian knot theory. The most important goal of the conference is to provide an opportunity for a diverse group of mathematicians including postdoctoral researchers, those with traditionally underrepresented background, graduate students, and faculty from primary undergraduate institutions, to meet and discuss mathematics with the invited leading experts of the field. To facilitate the discussions, the organizers will make every effort to bring the diverse audience to the conference, and request the speakers to prepare their talks aimed at the level at which a second-year graduate student can understand. The conference will bring three generations of researchers together, and foster scientific interactions across the generation, providing an opportunity to exchange ideas and to initiate new collaborations among participants. The younger generation can learn the newly established results, new perspectives, and possible future directions of research specifically addressed to them from the leading experts. The founders of the theories will inject how their discoveries were made and what was their vision back then. Expository talks can connect this vision with the current developments, and provide to the audience a sense of strong current and flow of mathematics. The participants will devote one session to compiling a list of open problems in the area that are most likely to shape the research in the near future. The conference will also include components for dissemination of results as well as outreach to local high school students and the general public. The Scientific Advisory Board will form an editorial board for the conference proceedings volume to be published. Reflecting the tone of the conference, the authors will be encouraged to provide expository articles, survey papers, and research papers readable to graduate students. The talks presented at the conference will be placed on the Conference Website by the local organizers. The outreach activity will comprise an expository talk by a distinguished speaker in an evening session during the conference. This talk will be an integrated component of the year-long outreach activity of the Department of Mathematics, UC Davis, which brings as many as 400 local high school students and general public to the event.