# Research Seminar Series

### Applied Mathematics Seminars

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is far from settled. I will report on work in progress with Kris Klosin on the modularity of Galois representations $G_{\mathbf{Q}} \to {\rm GSp}_4(\mathbf{Q}_p)$ that are residually reducible. I will explain, in particular, how this can be used in certain cases to verify Brumer and Kramer's paramodular conjecture for abelian surfaces over Q with a rational torsion point of order p.

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Arithmetic Study Group

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is far from settled. I will report on work in progress with Kris Klosin on the modularity of Galois representations $G_{\mathbf{Q}} \to {\rm GSp}_4(\mathbf{Q}_p)$ that are residually reducible. I will explain, in particular, how this can be used in certain cases to verify Brumer and Kramer's paramodular conjecture for abelian surfaces over Q with a rational torsion point of order p.

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Centre for Particle Theory Colloquia

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is far from settled. I will report on work in progress with Kris Klosin on the modularity of Galois representations $G_{\mathbf{Q}} \to {\rm GSp}_4(\mathbf{Q}_p)$ that are residually reducible. I will explain, in particular, how this can be used in certain cases to verify Brumer and Kramer's paramodular conjecture for abelian surfaces over Q with a rational torsion point of order p.

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Computing Seminars/Talks

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### CPT Student Seminar

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Departmental Research Colloquium

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Distinguished Lectures and Public Lectures

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Geometry and Topology Seminar

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Informal HEP Journal club

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Maths HEP Lunchtime Seminars

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Pure Maths Colloquium

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Statistics Seminars

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information

### Stats4Grads

## Arithmetic Study Group: Paramodularity of abelian surfaces

12 December 2017 14:00 in *CM 219*

Contact athanasios.bouganis@durham.ac.uk or pankaj.vishe@durham.ac.uk for more information