Department of

October 2020November 2020December 2020 Su Mo Tu We Th Fr Sa Su Mo TuWeTh Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12 11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19 18 19 20 21 22 23 24 22 23 242526 27 28 20 21 22 23 24 25 26 25 26 27 28 29 30 31 29 30 27 28 29 30 31

Tuesday, November 17, 2020

**Abstract:** Given the ubiquity of vector bundles, it is perhaps surprising that there are so many open questions about them -- even on projective spaces. In this talk, I will outline some results about vector bundles on projective spaces, including my ongoing work on complex rank 3 topological vector bundles on CP^5. In particular, I will describe a classification of such bundles which involves a surprising connection to topological modular forms; a concrete, rank-preserving additive structure which allows for the construction of new rank 3 bundles on CP^5 from simple ones; and future directions related to this project.

Please email vesna@illinois.edu for Zoom info.