# Matthias Paulsen: The degree of algebraic cycles on hypersurfaces

**Time: **
Thu 2021-09-16 14.00 - 15.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Lecturer: **
Matthias Paulsen (Mittag-Leffler)

**Abstract:** Let *X* be a very general hypersurface of dimension 3 and degree *d* at least 6. Griffiths and Harris conjectured in 1985 that the degree of every curve on *X* is divisible by *d*. Substantial progress on this conjecture was made by Kollár in 1991 via degeneration arguments. However, the conjecture of Griffiths and Harris remained open in any degree *d*. In this talk, I will explain how to prove this conjecture (and its higher-dimensional analogues) for infinitely many degrees *d*.