# Decomposition along a non-linear flag – Gabriele Vezzosi (Università di Firenze)

#### Venue

Dipartimento di Matematica, Aula Magna.

#### Abstract

We define a non-commutative version of the punctured formal neighborhood in algebraic geometry, and apply this construction to give decompositions of the (derived) stacks $\mathbf{Coh}^-(X)$, $\mathbf{Perf}(X)$, and $\mathbf{Bun}_G(X)$ along a non-linear flag of sub-stacks of X. This is joint work with B. Hennion and M. Porta. Time permitting, I will also sketch an application to the construction of Hecke operators associated to a non-linear flag on a surface.

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