The Great Western Number Theory Seminar

The GWNT Seminar is a regional number theory seminar for the Southwest of England, bringing together departments from the following institutions: University of Bath, University of Bristol, University of Exeter, University of Oxford and University of Reading. We are funded by a London Mathematical Society Scheme 3 grant, together with contributions from each university.

The next GWNT meeting:

16th September 2026

University of Reading

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.

Registration is now closed

Schedule

• 10:30-11:00am: Arrival

• 11:00am-12:00pm: Julian Lyczak

• 12:00-12:30pm: Break

• 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 (venue TBC)

Titles & Abstracts

Julian Lyczak (Antwerpen)

Title: TBC

Abstract: TBC

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)  

Organisers:

Daniel Loughran (Bath), Julie Tavernier (Bath), Jesse Pajwani (Bristol), Sam Streeter (Bristol), Happy Uppal (Bristol), Henri Johnston (Exeter), James Newton (Oxford), Hanneke Wiersema (Oxford) and Christopher Daw (Reading).