Special Colloquium
Eric Larson
Stanford University
The Maximal Rank Conjecture
Abstract: Curves in projective space can be described by either parametric or
Cartesian equations. A natural question is how the parametric and
Cartesian descriptions of a curve relate to each other. We describe
the Maximal Rank Conjecture, formulated originally by Severi in 1915,
which prescribes a relationship between the "shape" of the parametric
and Cartesian equations --- i.e. which gives the Hilbert function of a
general curve of genus $g$, embedded in $\mathbb{P}^r$ via a general linear series
of degree $d$.
We then discuss the "interpolation problem" which asks how many
general points a curve of given type can pass through (for example a
line can pass through two general points but not three). We conclude
by sketching how recent results on the interpolation problem can be
used to prove the maximal rank conjecture.
Wednesday December 5, 2018 at 3:00 PM in 636 SEO