University of Bath: Thursday 18th September, 2025

Directions: From Bath Spa station, you can either take the U1 bus at the front (~20 minutes from the station to campus, buses come every ~15 minutes), or you can walk (45-50 minutes, steep uphill). See the University's "how to get here" page for more details

Lecture room: We will be in 4 West, Lecture Room 1.2 on the ground floor. See the campus map for directions. Note that you can enter 4 West from the parade, and then you go down the stairs


Registration is now closed: if you have missed the deadline, please email jp907@bath.ac.uk, and we'll see if we can squeeze you in.

 

Schedule



Speakers


Andrew Pearce-Crump (Bristol)

Title: Characteristic polynomials, the Hybrid model, and the Ratios Conjecture.

Abstract: In the 1960s, Shanks conjectured that $\zeta'(\rho)$ (where $\rho$ is a non-trivial zero of of the Riemann zeta function), is, on average, both real and positive. Conjecturing and proving this result has a rich history, but efforts to generalise it to higher moments have so far failed. Building on several distinct approaches used to form conjectures in related problems, we derive conjectures for the full asymptotics of higher moments of the derivatives of the zeta function. This is joint work with Chris Hughes.

Sudip Pandit (King's College London)

Title: Explicit Mordell–Lang bound for curves in low rank

Abstract: In this talk, we will discuss the Buium–Coleman method to study the Mordell–Lang conjecture for curves, i.e., studying the points on a curve that lie in a finite rank subgroup inside the Jacobian. With rank less than the genus assumption, we can prove the conjecture, obtaining an explicit bound. As a corollary, we can also derive a p-adic proof of Mordell implies Mordell–Lang. This is a joint work with Netan Dogra. 

Elvira Lupoian (University College London)

Title: Ceresa Cycles of Modular Curves 

Abstract: The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is always homologically trivial. Ceresa proved that for a very general complex curve of genus at least 3, this cycle is not trivial as an element of the Chow group.  Notably, hyperelliptic curves with a Weierstrass point have trivial Ceresa cycle. Beyond this, there are few explicit examples where triviality/non-triviality is known. In this talk I will discuss the non-vanishing of the Ceresa cycle attached to the modular curve X_0(N). This is joint work with James Rawson. 

Joni Teräväinen (Cambridge)

Title: Linnik's problem and variants

Abstract: In 1944, Linnik showed that the least prime in an arithmetic progression is bounded polynomially in terms of the modulus of the progression. There has since then been a lot of work on improving the exponent in the polynomial dependence. In this talk we present a new approach to Linnik's problem using additive combinatorics. We also consider an analogue of Linnik's problem for the Möbius function and prove that for that variant the exponent can be taken to be 2. This is based on joint works with Kaisa Matomäki and Jori Merikoski.