This award is for support of graduate students from US institutions to participate in GAP 2013, a summer school in Pittsburgh, PA, in August 2013. The "Geometry and Physics" (GAP) summer school series has been running successfully for over ten years in various locations around the world. The organizers are planning to host this school in the USA for the first time. The theme of this school will be higher geometry involving some notion of higher categories. Such structures have started to become central in the description of various objects in quantum field theory, string theory and M-theory. For example, stacks and higher gerbes, higher differential characters, and n-bundles, all require categorical notions. The goal of the summer school is to expose students to new and hot ideas of research and provide them the tools needed to attack problems in this area. The main lecturers are leading experts in this area and are excellent expositors. The broader impacts of the activity include training a new generation of students in this interesting and fast-growing area of research. The school has been running outside the US for ten years and the organizers would like to bring it back to the US, thus making it easier for US-based students to benefit from such a useful meeting. The interactions among participants often lead to new collaborations as well as continuation of existing ones. The meeting will be interdisciplinary and the list of speakers will include researchers in various areas such as algebraic topology, differential geometry, algebraic geometry, mathematical physics, and theoretical physics. This will help make more connections among such areas.
The NSF support for the Project was to allow graduate students from US institutions to participate in GAP 2013, a summer school at the University of Pittsburgh, PA, in August 2013. The summer school, coming for the first time to the US since its inception ten years ago, was a big success. This was evident from the ability of the organizers to provide support to all that they were hoping to support, from the excellent feedback they got, and from the smooth flow of the meeting. The theme was ``Higher Geometry and Quantum Field Theory". This is currently a very active area of interaction between higher geometry and physics, and involves algebraic topology, algebraic geometry, and differential geometry on the mathematic sides, and quantum field theory, string theory, and M-theory on the physics side. There were three mini-courses, given by distinguished speakers: Ulrich Bunke (Regensburg) Kevin Costello (Northwestern) Stephan Stolz (Notre Dame) In addition, there were twelve plenary speakers: Kai Behrend (UBC) Jonathan Block (UPenn) Peter Bouwknegt (ANU) Ralph Cohen (Stanford) Vasily Dolgushev (Temple) Domenico Fiorenza (Rome) Kenji Fukaya (Simons Center) Gregory Ginot (Paris 6) Owen Gwilliam (Berkeley) Tony Pantev (UPenn) Urs Schreiber (Nijmegen) Jean-Louis Tu (Metz) The main objectives of the Project have been delightfully met, thanks to the support from the NSF. These objectives are: (i) Train US graduate students in this active area of higher geometry and physics. The school provided an excellent setting for doing so. (ii) Provide opportunities for students to hear lectures from leading experts in this area. (iii) Make it easier for more US graduate students to participate in the summer school by bringing the activity to the US. This also saves on funding. (iv) Encourage interaction among young researchers, especially graduate students, and learn about each other's research. There was ample time for informal discussions. (v) Bring direct benefit to local students, as the topic of the school was closely related to the research of several local PhD students. This also benefited the Department of Mathematics and added to the University of Pittsburgh's reputation in this area of research. The funds were fully used to provide support in the form of travel and/or local expenses to twenty graduate students from US insitutions. The website for the meeting is: www.geometryandphysics.org
