Cattaneo

Fakultäten » Mathematisch-naturwissenschaftliche Fakultät » Mathematik, Institut für » Reine Mathematik » Prof. Dr. Alberto Cattaneo » Cattaneo

Current research project

Title / Titel	Homotopy quantum symmetries, monoidal categories and formality
PDF	Abstract (PDF, 14 KB)
Summary / Zusammenfassung	The main objectives are: (I) to develop a theory of homotopy quantum groups. This can be understood as the natural theory that should sit at the intersection of four important disciplines of mathematics and physics: monoidal categories, homotopy theory, quantum groups and higher categories. This fact gives a clear multidisciplinary aspect to the project. (II) to prove the formality of \({\mathcal{L}_\infty^{cois}}\), the \(\mathcal{L}_\infty\) algebra governing simultaneous deformations of a Poisson manifold and its coisotropic submanifolds}. This is the key step in solving the problem of quantization of symmetries from the point of view of deformation quantization, giving interdisciplinary applications. This project will be hosted at the MIT (outgoing host) and at the University of Zurich (return host).
Project leadership and contacts / Projektleitung und Kontakte	Prof. Alberto Cattaneo (Project Leader) alberto.cattaneo@math.uzh.ch
Funding source(s) / Unterstützt durch	EU
In collaboration with / In Zusammenarbeit mit	Yael Fregier Massachusetts Institute of Technology Department of Mathematics Building 2, 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA United States
Duration of Project / Projektdauer	Jan 2012 to Dec 2014