# Index Formulae for Line Bundle Cohomology on Complex Surfaces

- Institution: CERN
- Department: Conferences & Workshops
- Speaker: Callum Brodie
- Year: 2019
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3016413)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

In many string theory applications, line bundle cohomologies are required input, for example in model-building with heterotic string theory, Type II string theories, or F-theory. There exist various case-by-case methods to compute individual cohomologies, but it would be beneficial to have further understanding of and formulae for cohomologies. Recently there have been signs that closed-form expressions may exist. I will report recent progress on this: we have found general formulae that describe all line bundle cohomologies on a large class of surfaces. In particular, any cohomology on these spaces can be computed as a topological index..

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## Lectures

1. [Index Formulae for Line Bundle Cohomology on Complex Surfaces](https://invisiblenetwork.ai/learn/cern/3016413/ec02d2931cf0), 17 min (CERN's player)