##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Morgan Opie

#### Harvard University

## Vector bundles on projective spaces

##### 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 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.

Host: Zhouli Xu

### December 8, 2020

### 10:30 AM

### Zoom information: Meeting ID: 933 6734 4286 Password: topology

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