Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - MST (Moonshine and String Theory)

Teaser

- What is the nature of the mysterious relation between modular objects and final groups? Why are these two fundamentally different mathematical structures related to each other? - This is curiosity driven research. Just as any research in pure mathematics, as a civilisation...

Summary

- What is the nature of the mysterious relation between modular objects and final groups? Why are these two fundamentally different mathematical structures related to each other?
- This is curiosity driven research. Just as any research in pure mathematics, as a civilisation we explore new possibilities by continuously pushing the boundary between known and unknown.
- We would like to understand the nature, in particular in relation to string theory that stems from physics, of the novel type of moonshine recently discovered by the PI.

Work performed

With the ERC team we have performed a lot of thinking and computations, which has led to 8 manuscripts (5 published, 3 submitted). They constitute a deeper understanding of the new moonshine from a number theory, algebraic, and string theoretic point of view.

Final results

\"There are 23 cases of umbral moonshine. One particularly simple case was \"\"solved\"\", in the sense that a module has been constructed for it, in 2014. In 2017 we have solved 7 more cases. We expect all the cases to be solved by the end of the project. Moreover, we expect to have arrived at a understanding why these modules are natural mathematical objects.\"