The Geometry and Geometric Analysis Seminar at Purdue in Fall 2026 is usually on Mondays 11:30am-12:20pm Eastern Time in MATH 731 if we meet in person. Some talks will be on zoom and the link will be included in the email announcement.
Lvzhou Chen, Mathew George, and Nicholas McCleerey are organizing this seminar in Fall 2026. If you have any questions or would like to suggest speakers, please contact one of us. If you would like to be on the mailing list, please email Lvzhou.
Title: On a construction of Hermitian metrics on holomorphic vector bundles
Abstract: A fundamental construction in geometry associates with any holomorphic vector bundle E over a compact base a line bundle L (sometimes denoted O_{PE} (1)). According to a conjecture of Griffiths from the 1960s, if L admits a positively curved hermitian metric k, then E also admits a positively curved hermitian metric h. While the conjecture may be correct, we will show that it is not possible to obtain h out of k by a fiberwise construction that is functorial.