This (rescheduled) half-day workshop will look at recent research at the interface between number theory and algebraic geometry, focussing on unlikely intersections and rational points on algebraic varieties. It is funded by an LMS Celebrating New Appointments grant.
The workshop will take place on the afternoon of Thursday 21 September 2023 in the University of Manchester. Talks will take place from 13.00 to 16.30, followed by a reception and dinner. All are welcome to attend.
Registration: If you are planning to attend, please complete the short registration form to help us estimate the number of participants. There is no registration fee.
Contact: For queries and further details, please contact martin.orr@manchester.ac.uk
Schedule
Talks are in Frank Adams 1, on the first floor of the Alan Turing Building.
| 13.00-14.00 | Rosa Winter (King's College London)
Weak weak approximation for del Pezzo surfaces of degree 2 |
| 14.15-15.15 | Rodolphe Richard (University College London)
On generalised André-Pink-Zannier conjecture |
| 15.30-16.30 | Martin Orr (University of Manchester)
Large Galois orbits for abelian varieties with endomorphisms |
| 16.30 | Reception in Alan Turing building |
| 18.30 | Dinner in Zouk (Indian restaurant, Chester Street) |
Abstracts
Rosa Winter: Weak weak approximation for del Pezzo surfaces of degree 2
Del Pezzo surfaces are classified by their degree d, an integer between 1 and 9. The lower the degree, the more arithmetically complex these surfaces are. It is generally believed that, if a del Pezzo surface has one rational point, then it has many, and that they are well-distributed. After giving an overview of different notions of ‘many’ rational points and what is known so far for del Pezzo surfaces, I will focus on joint work with Julian Demeio and Sam Streeter where we prove weak weak approximation for del Pezzo surfaces of degree 2 with a general point.
Rodolphe Richard: On generalised André-Pink-Zannier conjecture
I will present some recent results obtained with Pr. Andrei Yafaev on André-Pink-Zannier and generalised Hecke orbits in Shimura varieties, such as moduli spaces of abelian varieties.
Martin Orr: Large Galois orbits for abelian varieties with endomorphisms
The Zilber-Pink conjecture predicts that, in a generic one-parameter family of abelian varieties of dimension at least 3, there are only finitely many members of the family with non-trivial endomorphisms, generalising the André-Oort conjecture. The hardest step in proving conjectures of this type is proving that the members of the family with non-trivial endomorphisms have large Galois orbits. I will talk about joint work with Christopher Daw in which we prove this large Galois orbits conjecture for families with multiplicative degeneration, using André's idea of studying relations between period G-functions.