9 papers · 1 filter
Infinitesimally Equivariant Bundles on Complex Manifolds
Emile Bouaziz
We show that any continuous -linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential…
Non-Archimedean Fréchet Algebras and the Loop Space of a Hypersurface Complement
Emile Bouaziz
We study the space of loops into a hypersurface complement, and show that the corresponding topological algebra of Laurent series with coefficients in $\mathcal{O}(L\mathbf{A}^{d}_…
Derived Geometry and Non-Linear Differential Equations on the Punctured Disc
Emile Bouaziz
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to…
Topology of Singularities on Algebraic Loop Spaces
Emile Bouaziz
We study the topology of some simple infinite dimensional singularities arising from spaces of \emph{algebraic formal loops}. We prove that in some simple cases the natural analogu…
Tamarkin-Tsygan Calculus and Chiral Poisson Cohomology
E. Bouaziz
We construct and study some vertex theoretic invariants associated to Poisson varieties, specialising in the conformal weight case to the familiar package of Poisson homology a…
Poisson Vertex Cohomology and Tate Lie Algebroids
Emile Bouaziz
We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} str…