Mirror symmetry for 3d N=4 supersymmetric gauge theories has recently received plenty of attention in both representation theory and mathematical physics. It predicts that Higgs and Coulomb branches of a pair of dual theories are interchanged, and hence that both pairs of homologous branches (Higgs-Higgs and Coulomb-Coulomb) share exceptional topological and geometric properties. One of the...
In this talk I will describe a local Poisson structure (up to homotopy) associated to corners in four-dimensional gravity in the coframe (Palatini--Cartan) formalism. This is achieved through the use of the BFV formalism. This is a joint work with A. S. Cattaneo
Applying the BFV-BRST techniques from field theory to the hamiltonian reduction of degree one graded symplectic manifolds, we obtain a homotopy version of the classical Konstant-Sternberg BRST algebra in a generalized hamiltonian context. This is based on the correspondence between hamiltonian symplectic degree one manifolds and Poisson manifolds, due to Roytenberg, and the relation between...
We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a neighborhood of the unit manifold, that, in turn give Poisson integrators. We also insist on the role of the Magnus formula, in the context of Poisson geometry, for...
The celestial holography program centres around a conjectural holographic duality between a QFT in an asymptotically flat 4d bulk and a 2d CFT on the celestial sphere, the "CCFT". There is no dynamical evidence for this conjecture to date but symmetries of the bulk theories restrict the CCFT. For (selfdual) gravity in the bulk, Strominger et al found a symmetry algebra closely related to...
Symplectic duality is an observation that symplectic resolutions tend to come in pairs with matching geometric properties. Equivariant Hikita-Nakajima conjecture is one such statement, which connects the geometric and algebraic properties of symplectically dual pairs. In this talk I try to explain, what is usually meant by symplectic duality, provide some examples and state the conjecture I am...
I will present the operad $O(Lie_d)$ obtained by applying a functor constructed by S. Merkulov and T. Willwacher to the operad $Lie_d$ of (degree shifted) Lie algebras. Then I will show some applications and properties of said operad.
