Workshop on Geometric Quantisation

Geometric quantisation has been an increasingly active area since before the 1980s, with links to physics, symplectic geometry, representation theory, index theory, and differential geometry and geometric analysis in general. In addition to its relevance as a field on its own, it acts as a focal point for the interaction between all of these areas, which has yielded far-reaching and powerful results. At this workshop, a large number of world-leading international speakers will come together. This exceptional concentration of expertise in geometry and analysis is a great opportunity for anyone working in these areas to exchange ideas with some of the top mathematicians in the world.

Invited Speakers

Prof. Jean-Michel Bismut (Université Paris-Sud) 
Prof. Bismut is an absolute world-leader in index theory, and geometry and analysis in general. He has written 176 research articles, most of which appeared in high-level journals. These include 4 articles in the Journal of the AMS, 1 in Acta Mathematica, 2 in Inventiones Mathematicae, and 2 in the Annals of Mathematics. He is a member of the French Academy of Sciences, was a plenary speaker at the International Congress of Mathematicians in 1998, was editor in chief of Inventiones Mathematicae, and has received many other awards. The analytic proof by Tian and Zhang that quantisation commutes with reduction was based on methods developed by Bismut and Lebeau. Although this conference is focused on geometric quantisation, this is only a very small part of Prof. Bismut’s vast expertise. He will be a great inspiration to any conference attendees working in geometry and analysis. 

Prof. Maxim Braverman (Northeastern University, to be confirmed) 
Prof. Braverman is an expert on index theory and geometric anaylsis. He has done hard analytic work on index theory, also related to geometric quantisation. He developed index theory on noncompact manifolds that has been used in the quantisation commutes with reduction problem. He will be able to provide invaluable input on difficult analytical questions during the conference. 

Prof. Nigel Higson (Pennsylvania State University) 
Prof. Higson was well established as a leader in noncommutative geometry and index theory before he turned his attention to geometric quantisation and representation theory several years ago. His fresh input has given the field new momentum and has been a great inspiration to many. He is one of the driving forces behind the successful program since the early 2000s to integrate noncommutative geometry (in particular K-homology) and geometric quantisation. He has supervised 25 Ph.D. students, many of which have gone on to become successful academics. He is widely known for his excellent presentation skills. 

Prof. Yael Karshon (University of Toronto, to be confirmed) 
Since obtaining her Ph.D. at Harvard in 1993, Prof. Karshon has played an increasingly important role in symplectic geometry. She co-authored a book on geometric quantisation that has become a standard reference. Very few can match her expertise on Hamiltonian group actions, the principal objects of study in geometric quantisation. She has published in high-level journals such as the Journal of Differential Geometry, and her contributions will undoubtedly help make this workshop a great success. 

Prof. Eckhard Meinrenken (University of Toronto) 
Prof. Meinrenken was the first to prove Guillemin and Sternberg’s conjecture that quantisation commutes with reduction, which made him instantly famous. Rather than resting on his laurels, he proceeded to (co-)develop group valued moment maps, which have proven highly effective in the study of actions by loop groups. He is an outstanding (symplectic) geometer, and a great speaker. 

Prof. Xiaonan Ma (Université Paris 7) 
Prof. Ma has worked on various aspects of index theory and geometric analysis, including analytic torsion, elliptic genera and geometric quantisation. Together with Zhang, he proved that quantisation commutes with reduction for compact groups acting on noncompact manifolds. He gave an invited talk at the International Congress of Mathematicians in 2010, and is among the most well-known names in geometric quantisation. 

Prof. Paul-Émile Paradan (Université Montpellier 2) 
Prof. Paradan has worked on the quantisation commutes with reduction problem for many years, and understands it like few others. Using a topological approach, he gave one of the proofs in the compact case, and proved an extension to noncompact manifolds. His deep understanding of the links between geometric quantisation and representation theory have allowed him to obtain various important applications. Together with Vergne, he recently generalised the quantisation commutes with reduction principle from symplectic to Spinc-manifolds, which opens up the possibility of far-reaching applications. 

Prof. Michèle Vergne (Institut de Mathématiques de Jussieu) 
Prof. Vergne was one of the pioneers on Guillemin and Sternberg’s quantisation commutes with reduction conjecture, and gave a proof for torus actions. She has done highly influential work in many related areas, including representation theory, index theory and equivariant cohomology. She has published 96 articles, 2 of which appeared in the Journal of the AMS, 3 in Inventiones Mathematicae, and 1 in the Annals of Mathematics. She is a member of the French Academy of Sciences, and was a plenary speaker at the International Congress of Mathematicians in 2006. Her recent work with Paradan on quantisation of Spinc-manifolds is an exciting development. 

Prof. Jonathan Weitsman (Northeastern University, to be confirmed) 
Prof. Weitsman is a well-known expert on symplectic geometry, mathematical physics, and the interplay between these fields through geometric quantisation. He has published his work in high-level journals, such as the Journal of Differential Geometry and Inventiones Mathematicae. Prof. Weitsman’s understanding of geometric quantisation from many angles often allows him to ask the right question at the right time. 

Prof. Siye Wu (University of Hong Kong) 
Prof. Wu has been active in geometric quantisation, symplectic geometry and mathematical physics since the 1980s. He has obtained results on many aspects of the quantisation commutes with reduction problem and related (and unrelated) topics in mathematical physics. At this workshop, he will be able to help participants understand the links with physics, as well as the deep mathematical principles involved in geometric quantisation. 

Prof. Weiping Zhang (Chern Institute of Mathematics) 
A former director of the Chern Institute of Mathematics, Prof. Zhang is a highly prominent, if not the most prominent, Chinese mathematician. He has received numerous awards and prizes. He has published 92 articles, and two of these on geometric quantisation appeared in Acta Mathematica and Inventiones Mathematicae. In his Inventiones paper with Tian, he gave an analytic proof that quantisation commutes with reduction, which shed completely new light on this problem and has inspired many others. In his Acta paper with Ma, he generalised this result to noncompact symplectic manifolds.