### Arithmetic Manifolds, Hecke operators and Diophantine Equations

Heilbronn Number Theory Seminar

14th February 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

Arithmetic manifolds form an important class of Riemannian manifolds. A

special feature of these manifolds is that they are rich in symmetries.

These symmetries give rise to the so-called 'Hecke operators' acting on

various structures associated to the manifold. We will discuss some of

these Hecke modules. In the second part, we will discuss the connections

to number theory and finish with a sketchy discussion of how one may

apply these number theoretic connections to Diophantine equations. The

first part of the talk will be based on work with Bram Mesland (Bonn)

and the second part with Samir Siksek (Warwick).

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