Homotopy theory for filtered L-infinity algebras, the de Rham theorem for twisted cohomology and descent for L-infinity algebras

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1) Homotopy theory for filtered L-infinity algebras

In this talk, we explain how to use Brown's axioms for a category of fibrant objects to the homotopy theory of L-infinity algebras.

2) The de Rham theorem for twisted cohomology

In this talk, we explain how to use homological perturbation theory to prove a de Rham theorem for twisted cohomology of a manifold.

3) Descent for L-infinity algebras

In this talk, we explain how to prove that the descent infinity-groupoid of the stack of infinity-groupoids attached to a sheaf of filtered L-infinity algebras is the infinity-groupoid associated to its Tot L-infinity algebra.

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