Geometry and Physics--Higher structures: derived geometry and quantization

This award provides partial support for U.S.-based participants in two summer schools in Geometry and Physics (GAP): GAP XIII (2015) to be held at the IBS Center for Geometry and Physics at POSTECH, Republic of Korea, July 6--10, 2015, and GAP XIV (2016) to be held at Penn State University in summer 2016. The main purposes of the proposed activities are: (1) gathering leading experts and young researchers working in rapidly developing subjects and (2) fostering interaction between groups of mathematicians and physicists working on different aspects of related problems to facilitate cross-fertilization between different fields and dissemination of the most recent results of current research. There are many talented young people working in this area. GAP XIII and GAP XIV will provide them with excellent opportunities to disseminate their ideas and to broaden their perspective. The organizers anticipate inviting many mathematicians at the postdoctoral and graduate student level (from Asia, Europe, and the United States) to these summer schools. Both summer schools will include a poster session so as to give young researchers a chance to present their recent work. Each summer school will also constitute an excellent opportunity for young American scientists to exchange ideas with their foreign peers and launch collaborations. The website for GAP XIII is http://cgp.ibs.re.kr/conferences/gapxiii/

The theme of the schools is 'Higher Structures: Derived Geometry and Quantization.' GAP XIII (2015) will be devoted to derived geometry and GAP XIV (2016) to quantization. Higher structures has emerged as a new field in mathematics, as well as in mathematical and theoretical physics. The subject has undergone tremendous exploration recently due to its close connection to a number of areas of mathematics and mathematical physics, including algebraic topology, Lie theory, homotopy algebras, mirror symmetry, string theory, quantum field theory and noncommutative geometry. The project will be devoted to bringing together different aspects of higher structures, in particular derived geometry and quantization, as well as identifying new emerging directions of investigation, which is becoming more and more urgent as the field progresses. Derived geometry develops a powerful machinery for studying the residual geometry of badly behaved intersections and quotient spaces of high current interest in different areas of mathematics and mathematical physics while quantization establishes bridges between classical and quantum physics. Roughly speaking, quantization is the study and prediction of quantum phenomena, which are normally described by noncommutative associative algebras, based on the geometry of the underlying classical objects.