Sponsored by ICTP and EPSRC

Workshop photo (click to enlarge)

Giambiagi Lecture Room, Adriatico Guest House

Lecture courses (4 lectures each)
| |

Galois representations | by Tim and Vladimir Dokchitser TD/VD |

Lecture 1+2, Exc 1, Exc 2, Lecture 3, Exc 3, Lecture 4, Exc 4. | |

L-functions and BSD | by Adam Morgan AM |

Selmer groups and descent | by Michael Stoll MS |

Modularity | by Jack Thorne JT |

Monday Aug 28 | |
---|---|

09:00-11:10 | registration |

11:10-11:20 | official welcome (Fernando Rodriguez Villegas) |

11:20-12:20 | AM 1 Review of arithmetic of elliptic curves |

lunch break | |

14:00-15:00 | VD 1 Local l-adic representations and elliptic curves |

15:00-18:00 | work on exercises and projects, coffee break 16:15-16:45 |

18:00-19:00 | exercise presentations |

19:30 | welcome reception |

Tuesday Aug 29 | |

09:00-10:00 | AM 2 Zeta functions, L-functions and BSD |

10:10-11:10 | VD 2 l-adic and Weil/Weil-Deligne representations |

11:20-12:20 | MS 1 Selmer sets |

lunch break | |

14:00-15:00 | JT 1 Modular parametrisation of elliptic curves |

15:00-18:00 | work on exercises and projects, coffee break 16:15-16:45 |

18:00-19:00 | exercise presentations |

Wednesday Aug 30 | |

09:00-10:00 | JT 2 Modularity over number fields |

10:05-11:05 | MS 2 Selmer groups |

11:25-12:25 | AM 3 BSD over functions fields |

lunch break | |

14:00-15:00 | TD 3 Compatible systems of l-adic representations |

15:00-18:00 | work on exercises and projects, coffee break 16:15-16:45 |

18:00-19:00 | exercise presentations |

ThursdayAug 31 | |

09:00-10:00 | MS 3 Selmer groups of elliptic curves |

10:10-11:10 | JT 3 Potential modularity |

lunch break | |

free afternoon | |

Friday Sep 1 | |

09:00-10:00 | TD 4 H^{1} of curves |

10:05-11:05 | AM 4 The BSD story in higher dimensions |

11:25-12:25 | MS 4 Selmer sets of hyperelliptic curves |

lunch break | |

14:00-15:00 | JT 4 Automorphic representations and abelian varieties |

15:00-18:00 | work on exercises and projects, coffee break 16:15-16:45 |

18:00-19:00 | exercise presentations |

Kastler Lecture Room, Adriatico Guest House

Monday Sep 4 | |
---|---|

09:00-09:50 | Jennifer Balakrishnan - Explicit Coleman integration for curves |

10:00- | registration |

+ project presentations from the summer school | |

(workshop participants are welcome if they are there) | |

10:00-10:20 | project presentation: Elliptic curves with rational Z_{2}xZ_{8}-torsion |

10:40-11:00 | project presentation: Generic rank of a family of elliptic curves |

11:10-11:30 | project presentation: Szpiro's constants, the hyperelliptic case |

11:40-12:00 | project presentation: Detecting good and bad reduction of curves |

lunch break | |

14:50 | official welcome (Fernando Rodriguez Villegas) |

15:00-15:50 | Qing Liu - New points on algebraic curves |

coffee break | |

16:30-17:20 | Jennifer Park - A heuristic for boundedness of ranks of elliptic curves |

Tuesday Sep 5 | |

09:00-09:20 | Vladimir Dokchitser - Arithmetic of hyperelliptic curves over local fields |

09:30-09:50 | Celine Maistret - Parity of ranks of abelian surfaces |

10:00-10:20 | Alex Betts - Computing Tamagawa numbers of hyperelliptic curves |

coffee break | |

11:00-11:50 | David Holmes - Arakelov geometry of hyperelliptic curves |

lunch break | |

14:30-15:20 | Wei Ho - Odd degree number fields with odd class number |

15:30-15:50 | Matthew Bisatt - Root Numbers of Abelian Varieties |

coffee break | |

16:30-16:50 | Samuele Anni - The inverse Galois problem for symplectic groups |

17:00-17:20 | Tim Dokchitser - Models of curves |

19:00 | reception |

Wednesday Sep 6 | |

09:00-09:20 | Julie Desjardins - Density of rational points on rational elliptic surfaces |

09:30-09:50 | Emmanuel Lecouturier - Higher Eisenstein elements in weight 2and prime level |

10:00-10:20 | Gonzalo Tornaria - Explicit modularity for typical genus 2 curves |

coffee break | |

11:00-11:50 | John Voight - Explicit modularity for atypical genus 2 curves |

lunch break | |

free afternoon | |

Thursday Sep 7 | |

09:00-09:20 | Adam Morgan - Parity of Selmer ranks in quadratic twist families |

09:30-09:50 | Tom Fisher - Visualizing elements of order 7 inthe Tate-Shafarevich group of an elliptic curve |

10:00-10:20 | Raymond van Bommel - Numerical verification ofthe Birch and Swinnerton-Dyer conjecture |

coffee break | |

11:00-11:50 | Steffen Muller - Canonical heights on Jacobians of curves of genus two |

lunch break | |

14:30-15:20 | David Roberts - An inverse Hodge problem and some solutionsfrom hypergeometric motives |

15:30-15:50 | Bartosz Naskrecki - Hypergeometric motives of low degreesand their connection to elliptic and hyperelliptic curves |

coffee break | |

16:30-16:50 | Davide Lombardo - Computing twists of hyperelliptic curves |

17:00-17:20 | Fernando Rodriguez Villegas - Hypergeometric hyperelliptic curves |

Friday Sep 8 | |

09:00-09:20 | Netan Dogra - Rational points on hyperelliptic curvesvia the Chabauty-Kim method |

09:30-09:50 | Michael Stoll - Arithmetic of hyperelliptic curves in Magma |

10:00-10:20 | Jeroen Sijsling - Databases of curves |

coffee break | |

11:00-11:50 | Kiran Kedlaya - L-functions via deformations: from hyperellipticcurves to hypergeometric motives + Jupyter notebook |

lunch break | |

14:00-14:50 | Andrew Sutherland - Computing L-series of hyperelliptic curves |

If you have questions on the scientific side, please contact one of the organisers

Tim Dokchitser, Vladimir Dokchitser, Fernando Rodriguez Villegas.

For organisational questions, please contact smr3175@ictp.it (School+Workshop) or smr3144@ictp.it (Workshop only).