Motives of the Hitchin system
Motives of the Hitchin system

Junliang Shen, Yale University
IAS  Simonyi Hall Seminar Room SH101
Topology of the Hitchin system has been studied for decades, and interesting connections were found to orbital integrals, nonabelian Hodge theory, mirror symmetry etc. I will explain that a large part of the symmetries in these geometries above are “motivated” by algebraic cycles; in particular, I will discuss a proof of the motivic decomposition conjecture for the Hitchin system, and a proof of the motivic “\chi”independence phenomenon. In the proofs, the desired algebraic cycles are constructed by a combination of the the FourierMukai duality for the derived category of coherent sheaves and Springer theory. Based on joint work with Davesh Maulik and Qizheng Yin.