Number Theory Seminar
The Number Theory Seminar is a 55-minute in-person research seminar, including questions. Talks are suitable for PhD students (including new PhD students) from all fields of number theory.
The seminar is at 15:00 on Mondays (except bank holidays). On seminar days we meet for lunch at 12:30 and coffee at 16:00 in the common room. Seminars are held in B3.02 of the Zeeman building. Sometimes a different room is used, see the entry below.
Colleagues and especially number theory group members are warmly encouraged to suggest speakers by emailing the organisers: Adam Harper , Harry Schmidt , Akshat Mudgal.
We kindly remind members that it is polite to the speaker, to come to talks we might not personally expect to be interested in, and in compensation there will be a good audience for the speakers each of us is interested in!
A list of members of the group and research interests is available.
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03 November 2025 at 15:00 in B3.02
Speaker: Ross Paterson (University of Bristol)
Title: TBA
Abstract: TBA
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10 November 2025 at 15:00 in B3.02
Speaker: Cathy Swaenepoel (Paris Cite)
Title: Prime numbers with an almost prime reverse
Abstract: Let b ≥ 2 be an integer. For any integer n ≥ 0, we call `reverse' of n in base b the integer obtained by reversing the digits of n. The existence of infinitely many prime numbers whose reverse is also prime is an open problem. In this talk, we will present a joint work with Cécile Dartyge and Joël Rivat, in which we show that there are infinitely many primes with an almost prime reverse. More precisely, we show that there exist an explicit integer \Omega_b > 0 and c_b > 0 such that, for at least c_b b^ℓ / ℓ^2 primes p ∈ [b^{ℓ-1},b^ℓ[, the reverse of p has at most \Omega_b prime factors. Our proof is based on sieve methods and on obtaining a result in the spirit of the Bombieri-Vinogradov theorem concerning the distribution in arithmetic progressions of the reverse of prime numbers.
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17 November 2025 at 15:00 in B3.02
Speaker: David Hokken (Universiteit Utrecht)
Title: TBA
Abstract: TBA
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24 November 2025 at 15:00 in B3.02
Speaker: Adam Morgan (University of Cambridge)
Title: TBA
Abstract: TBA
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27 October 2025 at 15:00 in B3.02
Speaker: Hung Bui (University of Manchester)
Title: Weighted central limit theorem for central values of L-functions.
Abstract: A classical result of Selberg says that \log|\zeta(1/2 + it)| has a Gaussian limit distribution. We expect the same thing holds for \log|L(1/2, \chi)| for \chi being over the primitive Dirichlet characters modulo q, as q tends to infinity. Proving such a result remains completely out of reach, as it would imply 100% of these central L-values are non-zero, which is a well-known open conjecture. In this talk, I will describe how one can establish a weighted central limit theorem for the central values of Dirichlet L-functions. Under the Generalized Riemann Hypothesis, one can also obtain a weighted central limit theorem for the joint distribution of the central L-values corresponding to twists of two distinct primitive Hecke eigenforms. This is joint work with Natalie Evans, Stephen Lester and Kyle Pratt.
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20 October 2025 at 15:00 in B3.02
Speaker: Holly Krieger (University of Cambridge)
Title: Uniformity in arithmetic dynamics
Abstract: The periodic points of a discrete algebraic dynamical system control its local and global dynamical behaviour. When we impose an arithmetic structure on such a system, we do not generally expect periodic points to be rational. The central open conjecture in arithmetic dynamics asks whether this arithmetic structure imposes uniform constraints on the possible periods of points for families of algebraic dynamical systems. In this talk, we will discuss this conjecture, how it generalizes the torsion conjecture—in particular, the celebrated theorems of Mazur and Merel on rational torsion of elliptic curves—and survey some recent progress on and strategies for attacking this problem.
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13 October 2025 at 15:00 in B3.02
Speaker: Thomas Bloom (University of Manchester)
Title: TBA
Abstract: TBA
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06 October 2025 at 15:00 in B3.02
Speaker: Chris Hughes (University of York)
Title: Discrete moments of the Riemann zeta function
Abstract: I will discuss some new results on moments of zeta'(rho), the derivative of the Riemann zeta function evaluated at the zeta zeros. Despite being a complex function evaluated at complex points, it turns out to be real and positive on average. We will discuss this from both theoretical and heuristic viewpoints.
Click on a title to view the abstract!