Counting differentials with fixed residues
SEMINARS: HARVARD-MIT ALGEBRAIC GEOMETRY
When: April 25, 2023
3:00 pm - 4:00 pm
Where: Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Dawei Chen - Boston College
In this talk, we investigate meromorphic differentials on the Riemann sphere with a single zero and several poles of predetermined orders. Our aim is to determine the number of such differentials that satisfy the condition where the residue at each pole is fixed. This question was previously explored by Gendron and Tahar, who employed graph counting techniques derived from the flat geometry of differentials. We introduce a new approach using intersection theory on moduli spaces of differentials. This is joint work with Miguel Prado Godoy.