We introduce the concept of m-shifted symplectic Lie n-groupoids and symplectic Morita
equivalences between them. We then build various models for the 2-shifted symplectic …

We explain how to translate several recent results in derived algebraic geometry to derived
differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie …

Classical limits of quantum groups give rise to multiplicative Poisson structures such as
Poisson-Lie and quasi-Poisson structures. We relate them to the notion of a shifted Poisson …

This note is an expanded and updated version of our entry with the same title for the 2006
Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson …

A Lie groupoid can be thought of as a generalization of a Lie group in which the
multiplication is only defined for certain pairs of elements. From another perspective, Lie …

We present a construction of weak graded Lie 2-algebras associated with quasi-Poisson
groupoids. We also establish a morphism between this weak graded Lie 2-algebra of …

First, we prove a decomposition formula for any multiplicative differential form on a Lie
groupoid G. Next, we prove that if G is a Poisson Lie groupoid, then the space Ω mult∙(G) of …

Berwick-Evens and Lerman recently showed that the category of vector fields on a geometric
stack has the structure of a Lie $2 $-algebra. Motivated by this work, we present a …

Generalized Kähler (GK) geometry was discovered in the study of N=(2, 2) supersymmetric σ-
models. In this thesis we develop a new approach to GK geometry by addressing the …

We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (ie quasi-
symplectic groupoids) using twisted Dirac structures and show that it satisfies properties …