Drinfeld associators; Lie theory; Topological Quantum Field Theory
Monnier Samuel, Moore Gregory W., Park Daniel S. (2018), Quantization of anomaly coefficients in 6D N=(1,0) supergravity, in J. High Energy Phys.
, February 2018(2018:20), 1-40.
Alekseev Anton, Naef Florian, Xu Xiaomeng, Zhu Chenchang (2018), Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators, in Lett. Math. Phys.
, 108(3), 757-778.
Alekseev Anton, Kawazumi Nariya, Kuno Yusuke, Naef Florian (2018), The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem, in Adv. Math.
, 326, 1-53.
Alekseev Anton, Naef Florian (2017), Goldman-Turaev formality from the Knizhnik-Zamolodchikov connection, in C. R. Math. Acad. Sci. Paris
, 355(11), 1138-1147.
Alekseev Anton, Kawazumi Nariya, Kuno Yusuke, Naef Florian (2017), Higher genus Kashiwara-Vergne problems and the Goldman-Turaev Lie bialgebra, in C. R. Math. Acad. Sci. Paris
, 355(2), 123-127.
This project is at the interface between Mathematics and Theoretical Physics. The motivations often come from the Physics side while the methods and the framework are in most cases placed within Mathematics. The project covers several themes which are unified by the use of Drinfeld associators and by the notions of Topological Quantum Field Theory (TQFT).The project addresses various questions which range from relatively easy (and more realistic) ones to more difficult and more ambitious ones. The following problems/themes are of importance within the project:1) To use the language of derived geometry for better understanding of Lagrangian TQFTs.2) To develop the theory of higher associators and Grothendieck-Teichmüller groups, and to relate it to the LMO functor.3) To study uniqueness of Rouvière's e-function in the theory of symmetric spaces, and to obtain explicit formulas for the e-function in terms of Drinfeld associators.4) To construct quantum Poisson sigma models as fully extended TQFTs.5) To develop the theory of Wilson surfaces in 3D Chern-Simons theory and in the 4D topological Yang-Mills theory.These topics are rooted in my previous research on group valued moment maps and on the Kashiwara-Vergne Conjecture, and they develop it in various directions. The project is built around the activity of my research group at the University of Geneva. It includes funding for 3 graduate students: Olga Chekeres and Elise Raphael are working within the previous project, and their Ph.D. studies will enter the decisive phase under this project. Donald Youmans is currently a Ph.D. student at MPI Bonn, and he is scheduled to move to Geneva in September 2016. The project also includes funding for a postdoctoral fellow. Dr. Philippe Humbert is currently a fellow with the previous project and he will be completing his work during the first 6 months of the current project. He will then be replaced by Dr. Pavel Safronov. Safronov is a rising star in his field. A possibility to attract him to Geneva is a great opportunity for our research group. This hiring has a very high priority within the project.The project relies on a close collaboration with the groups of Dr. Pavel Mnev (MPI Bonn) and Prof. B. Enriquez (Strasbourg). It includes funding for travel of collaborators to conferences and summer/winter schools and for running a research seminar.