Mehdi Tavakol: Tautological classes on curves with special linear systems

Let \(M_g\) be the moduli space of smooth curves of genus \(g \geq 2\). In a recent joint work with Petersen and Yin we studied the tautological part of Chow groups of \(M_g\) with coefficients in a representation of the symplectic group \(\mathrm{Sp}(2g)\). In an ongoing project we study such groups for curves with special linear systems. I will present a summary of results and conjectures arising from this study.