Description
CACAAG seminar.
Speaker: Dhruv Ranganathan
Time & Date: 5pm Tuesday, September 18.
Venue: Room 215
Title and abstract:
Curves, maps, and singularities in genus one
I will outline a new framework based on tropical geometry to study genus
one curve singularities and discuss its relationship with the geometry of
moduli spaces. I will focus on the application of this framework to
construct new nonsingular compact moduli spaces parameterizing elliptic
curves in projective space. This also reveals a modular interpretation for
Vakil and Zinger’s famous desingularization of the space of elliptic curves
in projective space, as well as a short and conceptual proof of that
result. If time permits, I will discuss applications to some questions in
the classical enumerative geometry of surfaces. This is based on joint work
with Keli Santos-Parker and Jonathan Wise, building on prior work of
Speyer, Smyth, Viscardi, Vakil, and Zinger.