Victoria Hoskins: On the motive of the stack of vector bundles on a curve

Following Grothendieck's vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I will explain how to define the motive of certain algebraic stacks. Then I will report on joint work in progress with Simon Pepin Lehalleur, in which we study the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers.