Award: DMS 1242046, Principal Investigator: John W. Morgan
This award provides partial support for graduate student workshops on "String Phenomenology" (July 2012) and "Symplectic Topology" (October 2012) at Stony Brook University. The Simons Center has programs at the cutting edge of research in geometry, in theoretical physics, and in areas of overlap between the two fields. These programs bring together senior researchers, mid-career experts, and postdocs with a common interest around a topic in geometry or physics. The purpose of this project is to expose these fields to graduate students and give them access to the expertise of the assembled workers in the field. The project calls for workshops aimed specifically at graduate students with approximately 40 students being invited to each workshop. The graduate students are invited to the Center and supported during their stay, which will be either one week or two weeks. They will listen to introductory talks in the chosen area by experts in the field, and then later in the workshop by more specialized talks by other graduate students.
The programs at the Simons Center for Geometry and Physics bring together experts on various topics in geometry and physics to exchange ideas and to learn of the results of other workers in the field. This is one of the best ways for various workers in the field to become aware on all the latest trends and ideas in their subject. The project extends the scope of these programs by providing activities within the overall scientific framework aimed specifically at graduate students, who are not otherwise usually included in the activities. A week or two is dedicated to a workshop aimed at graduate students and approximately 40 students are invited to the Center and supported during their stay. During the workshop experts in the field give talks suitable for graduate students; also there are more specialized talks by the graduate students. This exposes the students to the field, to many of the leading researchers in the field, and to other graduate students with similar interests. This will ease their integration into the field and assist them as they launch their own research careers.
The URL for the first of these workshops is: http://scgp.stonybrook.edu/archives/3978
The project served as a pilot program for graduate student centered activities at the Simons Center for Geometry and Physics. The funds were used to support three weeks of graduate student centered activities described below. Workshop on Symplectic and Contact Topology – Fall 2012 This graduate student workshop was associated with the program in Symplectic Topology at the Center during the Fall of 2012, organized by Yakov Eliashberg and Mohammed Abouzaid. There have been tremendous advances in Symplectic Topology and Contact Topology over the last 10 years with the introduction symplectic field theory and new algebraic methods in Floer theory. The goal of the workshop was to introduce graduate students to developments in the study of the symplectic topology of Stein manifolds via pseudo-holomorphic curves, with a focus on symplectic cohomology. The first part of the workshop consisted of student lectures about the basics of holomorphic curves and Floer homology, culminating in the construction of symplectic cohomology, and its computation in the simplest examples. Following those were lectures by the organizers and other senior mathematicians in residence who provided perspective on the applications of the theory, and its interaction with related mathematical fields. Assessment of Outcomes According to exit interviews of the 40 students, the participants felt that the workshop was very well organized, which allowed them to open their minds to new, intriguing subjects while also networking with their peers. As two students stated, "I got excited about a topic that I didn’t know that much about before" and "I learned a lot of new things, and made a lot of new friends in this field." The students were also pleased with the facilities at the Center, reporting that the "support staff were very helpful" and that there was a "very good AV setup." One student expressed his opinion that graduate workshops should become a staple for the Simons Center, "I hope student workshops with a similar format become a feature at SCGP – felt I learned a lot more than at a "regular" research conference, or even that at other workshops directed at graduate students. Having graduate students present really forces us to engage with the material – stereotypes about "active learning" being realized." Graduate Workshop on Kahler Geometry – Summer 2013 Recently there have been spectacular developments in Kahler geometry which cut across a wide variety of mathematical fields ranging from the analysis of PDE’s to Algebraic Geometry. The workshop was organized by Xiuxiong Chen, Sir Simon Donaldson, Paul Gauduchon, and Sean Timothy Paul. The goal of the program was to lay the groundwork for further advances in the following subjects: the existence of Canonical metrics on Kahler Manifolds; the alpha invariant, log canonical threshold, and stability conditions from algebraic geometry; Geometric Flows (Kahler Ricci and Calabi flows); and the theory of the Complex Monge Ampere equation. The first part of the workshop consisted of short courses delivered by the organizers and other senior mathematicians in residence followed by student seminars which expanded on the topics covered in the minicourses. Assessment of Outcomes According to the exit interviews with the 31 students whp participated, this workshop had "nice introductory to advanced talks," and the lecturers had "ways of understanding math [being] very impressive." The students, ranging in all years of graduate study, felt they benefitted from workshop due to working closely with their peers, while also having the opportunity to give their own lecture during the student seminars. One student stated, "Since most conference talk are not as detailed and most university classes are not as specialized, this lecture series format is a rare opportunity to get a proper introduction to an active area of research." Another student felt that this workshop has allowed his "horizon [to be] largely broadened."The students, lecturers, and organizers, were all pleased with the facilities and the staff of the Simons Center, saying it was "excellent all around." The activities funded by NSF under this award served to increase the pipeline of future researcher collaborators and impart at the pre-professoriate level the need for cross-disciplinary research to answer the most complex and vexing questions in geometry and theoretical physics today. In addition to formal training, the mission of these activities was also to give networking opportunities to students who may not otherwise meet the number of renown national and international faculty that the Center draws as its members and visitors All talks and lectures at the workshop were recorded and are available on the Center’s website. Our recordings are both widely available and searchable by topic and/or speaker and are intended to facilitate the training of young professionals and graduate students who were not able to participate directly in the workshops.
