# Samuele Anni

## Samuele AnniResearch Fellow |

**Teaching Responsibilities 2015/16:**

Term 2: MA426 Elliptic Curves

Post-Doc fellowship at the University of Warwick for the research project LMF: L-functions and Modular Forms from October 2013.

I was an ALGANT Ph.D. student at Universiteit Leiden and at Université Bordeaux 1, supervisors Professor Bas Edixhoven and Professor Pierre Parent.

I have defended my Ph.D. thesis on October 24th 2013.

## Publications and preprints

A note on the minimal level of realization for a mod $\ell$ eigenvalue system, preprint (arXiv link)

with Pedro Lemos and Samir Siksek, *Residual Representations of Semistable Principally Polarized Abelian Varieties, *Research in Number Theory 2016, doi:10.1007/s40993-015-0032-4 (arXiv link)

with Samir Siksek,* Modular elliptic curves over real abelian fields and the generalized Fermat equation* *$x^{2\ell}+y^{2m}=z^p$,* preprint (arXiv link)

with Vladimir Dokchitser, *l-Adic Representations and their Associated Invariants*, lecture notes (arxiv link)

with Samir Siksek, *On Serre's uniformity conjecture for semistable elliptic curves over totally real fields*, Mathematische Zeitschrift 2015; doi:10.1007/s00209-015-1478-8 (arxiv link)

*A local-global principle for isogenies of prime degree over number fields,* Journal of the London Mathematical Society 2014; doi: 10.1112/jlms/jdu002 (arXiv link)

*Images of Galois representations*, Ph.D. thesis, avaliable at the following link or click here to download .

PhD thesis (October 2013) supervisors Professor Bas Edixhoven, Universiteit Leiden, and Professor Pierre Parent, Université Bordeaux 1;

Master Thesis (July 2010) supervisors Professor Luis V. Dieulefait, Universitat de Barcelona, and Professor Alberto Canonaco, Università di Pavia;

Bachelor Thesis (December 2007) supervisor Professor Paola Frediani, Università di Pavia.

## Teaching

Lecturer for MA426 Elliptic Curves, University of Warwick, Spring 2016. For lecture notes and assignments go to the following link.

Lecturer for MA426 Elliptic Curves, University of Warwick, Fall 2014. For lecture notes and assignments go to the following link.

Lecturer for MA246 Number Theory, University of Warwick, Spring 2014. For notes, tests and exams solutions go to the following link (you need to be logged in).

Teaching assistant for the Mastermath course taught by Professor Bas Edixhoven, Algebraic Geometry - Spring 2011.

## Data

Data collected by Ciaran Schembri on degrees of isogenies of elliptic curves over number fields.

## Talks

Maeda's conjecture |
Number theory study group, "Our favourite conjectures" |
6/5/16, University of Warwick |

Diophantine equations and semistable elliptic curves over totally real number fields |
Algebra, Geometry and Number Theory Seminar | 18/4/16, Universiteit Leiden |

Congruence Graphs |
Speed talk at BMC | 30/3/16, University of Bristol |

The inverse Galois problem and uniform realizations |
Séminaire et Groupe de travail Théorie des Nombres |
15/3/16, Université Blaise Pascal, Clermont-Ferrand |

Congruences | Number Theory Seminar | 1/2/16, University of Warwick |

Inverse Galois problem and uniform realizations | STNB 2016 (30th edition) | 26/1/16, Universitat de Barcelona |

The inverse Galois problem, abelian varieties and uniform realizations | Number theory seminar | 1/12/15, University of Copenhagen |

On the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$ | STNB, Barcelona Fall Workshop on NUMBER THEORY | 26/11/15, Universitat de Barcelona |

Abelian varieties and the inverse Galois problem | Number Theory Seminar | 17/11/15, Johns Hopkins University, Baltimore |

The generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$ |
Peer to Peer Seminar | 5/10/15, ICERM, Brown University, Providence |

Genus 3 curves and the inverse Galois problem (link to the video) |
Modular Forms and Curves of Low Genus: Computational Aspects |
29/09/15, ICERM, Brown University, Providence |

Higher genus curves and the inverse Galois problem |
Congreso de Jóvenes Investigadores de la RSME |
11/09/15, Universidad de Murcia |

Serre's uniformity conjecture for elliptic curves over totally real number fields | Computational Representation Theory in Number Theory | 31/07/15, Oregon State University, Corvallis |

On the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$ | 29th Journées Arithmétiques | 06/07/15, Debrecen |

Residual modular Galois representations: images and applications | London Number Theory Seminar | 20/05/15, King's College London |

On Serre's uniformity conjecture for elliptic curves | Number Theory Seminar | 12/05/15, The university of York |

Twists and local data of residual modular Galois representations | 16/12/14, Universidad de Buenos Aires | |

Residual Galois representations: a database | Sheffield Number Theory Seminar | 18/11/14, The university of Sheffield |

On Serre's uniformity conjecture for elliptic curves | Heilbronn Seminar | 15/10/14, University of Bristol |

Residual modular Galois representations: an algorithmic approach | Algebra and Number Theory Seminar | 22/09/14, University College Dublin |

Twists and residual modular Galois representations | BUILDING BRIDGES | 10/07/14, Bristol |

Minimal Models and Integral Models | Algebraic Geometry for Number Theory (TCC) | 05/12/13, University of Warwick |

Residual modular Galois representations and their images | Number Theory Seminar |
02/12/13, University of Warwick |

Image of residual modular Galois representations: an algorithm | Sage Days: Algorithms in Arithmetic Geometry | 24/07/13, Lorentz Center |

A local-global principle for isogenies between elliptic curves over number fields | 28th Journées Arithmétiques | 04/07/13, Grenoble |

Modular forms as sections of line bundles | Seminar on Modular Forms | 23/05/13, Leiden University |

k-fold differentials | Seminar on Modular Forms | 05/05/13, Leiden University |

Images of modular Galois representations mod l | Algant meeting | 23/02/13, Leiden University |

Un principe local-global pour isogénies de degrée premier sur les corps de nombres |
Colloque Jeunes Chercheurs en Théorie des Nombres |
14/06/12, Lyon ENS |

Image of mod l modular Galois representations | Algant meeting | 18/02/12, Bordeaux IMB |

Frobenii and Cohomology with compact support | Algebraic Geometry Seminar: étale cohomology | 14/06/11, Leiden University |

Images of residual modular Galois representations | DIAMANT symposium | 27/05/11, Heeze |

Constructible sheaves and torsion sheaves | Algebraic Geometry Seminar: étale cohomology | 24/05/11, Leiden University |

Complex multiplication of elliptic curves II | Seminar on Class Field Theory | 11/11/10, Leiden University |

Complex multiplication of elliptic curves I | Seminar on Class Field Theory | 4/11/10, Leiden University |

Modular modular Galois representations | Algebra Geometry and Number Theory seminar | 10/10/10, Leiden University |

## Links