Directions: please see www.reading.ac.uk/about/visit-us
Lecture room: Slingo Lecture Theatre, JJ Thomson Building — west end of building 3 on this map — right next to the lecture theatre used for the last GWNT at Reading.
Schedule
10:30-11:00am: Arrival — tea/coffee will be available in Mathematics (not JJT) Room 212
11:00am-12:00pm: Julian Lyczak
12:00-12:30pm: Break — tea/coffee will be available in Mathematics (not JJT) Room 212
12:30-1:30pm: Vandita Patel
1:30-3:00pm: Lunch
3:00-4:00pm: Vahagn Aslanyan
4:00-4:30pm: Break
4:30-5:30pm: Tomos Parry
6:30pm onwards: Dinner at Zerodegrees in Reading
Titles & Abstracts
Julian Lyczak (Antwerpen)
Title: Counting quadratic points on Fano varieties
Abstract: I will present a general framework for counting quadratic points of bounded height on a Fano variety X. If X is a surface, the outcome of this counting problem is predicted by the Manin-Peyre conjecture for the symmetric square of X. I will explain how the framework can be used to verify this conjecture for the infinite family of symmetric squares of non-split quadric surfaces.
This talk is based on joint work with Francesca Balestrieri, Kevin Destagnol, Jennifer Park and Nick Rome.
Vandita Patel (Manchester)
Title: Power values of power sums
Abstract: we discuss key results and milestones achieved while studying certain families of Diophantine equations as well as touching on open problems. We note that this is an overview of a large body of work involving multiple collaborators, including; A. Argáez-García (UADY), M. Bennett (UBC), N. Coppola (Padova), M. Curcó-Iranzo (Utrecht), S. Siksek (Warwick), M. Khawaja (Warwick) and Ö. Ülkem (Academia Sinica).
Vahagn Aslanyan (Manchester)
Title: Modular Zilber-Pink for geometrically generic varieties
Abstract: I'll report on recent join work with S. Eterovic and G. Fowler where we prove the Zilber-Pink conjecture for varieties in Y(1)^n assuming certain projections are not defined over the algebraic numbers.
Tomos Parry (formerly Alfréd Rényi Institute, Budapest)
Title: L^1 means of exponential sums and the binary additive divisor problem.
Abstract: Let S(alpha) be the exponential sum of a sequence of interest. The L^1 mean may give us some insight on the sequence itself, the most famous result probably being that of Vaughan [2] that for the primes the L^1 mean is >>root(x) but it's not known if this is sharp. The same argument shows the mean to be >>root(x) for k-fold divisor functions d_k too but again it wasn't known if this was sharp. We showed [1] that for the divisor function itself (k=2) this is indeed sharp and float the idea that a similar result for d_3 might be of use in the binary additive divisor problem.
[1] - Parry. The L^1 mean of the exponential sum of d(n). Mathematika 72 (2026)
[2] - Vaughan. The L^1 mean of exponential sums over primes. BLMS 20 (1988)