Introduction to a motivic point of view on the cohomology of moduli spaces of bundles on curves
Seminar Room 1, Newton Institute
For moduli spaces of vector bundles on curves and some moduli spaces of Higgs bundles, it is possible to compute their cohomology groups in a geometric way, i.e., one can describe the space by a cut-and-paste procedure in terms of cells and symmetric products of the base curve.
This gives a rather explicit description of the "motive" of the space.
For moduli space of vector bundles this is due to Behrend and Dhillon, relying on an argument of Bifet, Ghione, and Letizia.
We will try to give an introduction to this point of view on cohomology calcuations for moduli spaces.