3:45PM: The maximal rank conjecture (Part I)Eric LarsonIn the first hour, we discuss the problem of interpolation for curves in projective space: When does there exist a curve of degree d and genus g passing through n general points in P^r?

5:00PM: The maximal rank conjecture (Part II)Eric LarsonIn the second hour, we discuss the Maximal Rank Conjecture, a conjecture formulated originally by Severi in 1915 which prescribes a relationship between the "shape" of the parametric and Cartesian equations of curves in projective space  that is, which gives the Hilbert function of a general curve of genus g, embedded in P^r via a general linear series of degree d. We then explain how results on the interpolation problem can be leveraged to prove this conjecture.
