# 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 FregierMassachusetts Institute of TechnologyDepartment of MathematicsBuilding 2,77 Massachusetts AvenueCambridge, MA 02139-4307USA United States
Duration of Project / Projektdauer Jan 2012 to Dec 2014