Mathematics

 I will start by introducing the basics of intersection theory on moduli spaces as presented in  "Towards an enumerative geometry of the moduli spaces of curves" (Mumford '85). The second section of this talk will cover Mumford's method to compute Chow ring of the moduli space of stable curves of genus 2. In conclusion, I will state Faber's conjecture regarding the tautological ring of M_g, following his approach in "A conjectural description of the tautological ring of the moduli space of curves" ('99).