Principal Investigator: Markus J. Pflaum
The award serves to support participants from the U.S. at the conference and school "Quantization of Singular Spaces" in December 2010 at the Center for Quantum Geometry of Moduli Spaces in Aarhus, Denmark.
The supported conference will be aimed at recent approaches to quantization of singular spaces. The goal of the conference is to encourage cross-fertilization among various approaches, to bring seemingly independent lines of research together, and to consider where the field can go in the future. It is expected to give a strong impetus to innovative work in the field. In addition, the workshop is aimed at training young researchers in the field by internationally renowned experts. A mathematically rigorous theory of singular quantization would have considerable repercussions. For example, in mathematical physics a better understanding of the nonperturbative structure of gauge theories would come within reach, which would be essential preparation for the construction of quantized Yang--Mills theories and grand unified theories. In mathematics, new index theorems for singular spaces would emerge, among other.
Support for the conference will ensure that experts from the U.S. working in the field of quantization theory will be able to significantly contribute to the conference and will profit from the exchange of cutting-edge research. Moreover, support for the school and conference will enable U.S.-based young researchers to participate in the special training which will be offered through three minicourses on foundational material and recent achievements in the field during a school preceeding the conference. The conference and school in Denmark will also strengthen US-Scandinavian research connections and will lead to new scientific collaborations.
Conference webpage:
http://qgm.au.dk/events/dec-2010-conference-quantization-of-singular-spaces/
A main motivation to study the commutative and noncommutative geometry of singular phase spaces comes from the attempt to gain a full mathematical understanding of gauge theory. This is a central theme in modern physics, since gauge theory provides the common language for the description of all fundamental interactions except gravity. For the description of singular phase spaces there are various approaches, which are of course interrelated. The idea of the conference "Quantization of Singular Spaces" has been to take an unbiased point of view, and bring together researchers working on the mathematical theory of quantization of singular phase spaces in any of its incarnations. Since the last meetings addressing the singular case took place a couple of years ago, the new results in the field appeared to be scattered and had to be made accessable for non-experts. A main purpose of the conference was to facilitate communication between the competing philosophies, with the idea that this will lead to new substantial insights and future results. It was intended that the event helps to establish and maintain a community of scientists interested in the problem of quantization of singular phase spaces, and to draw the attention of young researchers to this interesting field of research. The school and conference "Quantization of Singular Spaces" was held December 8–10 and 13–17 2010, respectively, at the Centre for Quantization of Moduli Spaces, which is part of the Department of Mathematical Sciences of Aarhus University, Denmark. The Organizing Committee consisted of Jørgen Ellegaard Andersen (QGM, Aarhus University), Hans-Christian Herbig (QGM, Aarhus University), and Markus J. Pflaum (University of Colorado at Boulder). The school was adressed to junior researchers (i.e. postdocs and PhD students) coming mostly from Europe and the United States. It comprised of 3 courses, 3 times 2 academic hours each, which were meant to serve as a introduction to the themes of the conference to follow. During the conference 19 one-hour-talks were given. The participants of the conference were mainly European and US based researches working in quantization theory, non-commutative geometry, gauge theory, representation theory, complex and microlocal analysis and mathematical physics. The funding was provided by the Centre for Quantization of Moduli Spaces (QGM), by the National Science Foundation (NSF) and by the ESF Research Network ITGP. In total, there were 25 participants in the school and 49 participants in the conference. The organizers believe that the school and conference Quantization of Singular Spaces has been a substantial step towards establishing a research commutity for the subject. The lively discussions in between the talks indicate that the idea of bringing researches together, which otherwise rarely have the chance to interact, has been a success. It is expected, that the new perspectives on the field will lead to new collaborations and publications in the near future. Moreover, a number of talented young researchers has been exposed and introduced to the material, and had the chance to get acquainted with senior experts in the field and with their recent results. As the video recordings and slides of lectures and talks are permanently available at the conference homepage http://qgm.au.dk/video/conf/quantization/ the material is accessable for a wider audience.
