# Past Junior Geometry and Topology Seminar

The first half of this talk will be an introduction to the wonderful world of Higgs bundles. The last half concerns Fourier--Mukai transforms, and we will discuss how to merge the two concepts by constructing a Fourier--Mukai transform for Higgs bundles. Finally we will discuss some properties of this transform. We will along the way discuss why you would want to transform Higgs bundles.

In the sixties Griffiths constructed a holomorphic map, known as the local period map, which relates the classification of smooth projective varieties to the associated Hodge structures. Fiorenza and Manetti have recently described it in terms of Schlessinger's deformation functors and, together with Martinengo, have started to look at it in the context of Derived Deformation Theory. In this talk we propose a rigorous way to lift such an extended version of Griffiths period map to a morphism of derived deformation functors and use this to construct a period morphism for global derived stacks.