Towards a compactification of the moduli space of K3 surfaces of degree 2
Abstract
Ever since moduli spaces of polarised K3 surfaces were constructed in the 1980's, people have wondered about the question of compactification: can one make the moduli space of K3 surfaces compact by adding in some boundary components in a "nice" way? Ideally, one hopes to find a compactification that is both explicit and geometric (in the sense that the boundary components provide moduli for degenerate K3's). I will present on joint work in progress with V. Alexeev, which aims to solve the compactification problem for the moduli space of K3 surfaces of degree 2.
The Clinical Sciences Centre based at Imperial College in London has launched a new initiative to celebrate women in maths and computing. As a new branch of the existing Suffrage Science scheme, it will encourage women into science, and to reach senior leadership roles.
14:15
Ricci Solitons
Abstract
We review the concept of solitons in the Ricci flow, and describe various methods for generating examples, including some where the equations
may be solved in closed form
17:30
Pfaffian functions and elliptic functions
Abstract
After giving some motivation, I will discuss work in progress with Harry Schmidt in which we give a pfaffian definition of Weierstrass elliptic functions, refining a result due to Macintyre. The complexity of our definition is bounded by an effective absolute constant. As an application we give an effective version of a result of Corvaja, Masser and Zannier on a sharpening of Manin-Mumford for non-split extensions of elliptic curves by the additive group. We also give a higher dimensional version of their result.
17:30
Profinite groups with NIP theory and p-adic analytic groups
Abstract
I will describe joint work with Katrin Tent, in which we consider a profinite group equipped with a uniformly definable family of open subgroups. We show that if the family is `full’ (i.e. includes all open subgroups) then the group has NIP theory if and only if it has NTP_2 theory, if and only if it has an (open) normal subgroup of finite index which is a direct product of finitely many compact p-adic analytic groups (for distinct primes p). Without the `fullness’ assumption, if the group has NIP theory then it has a prosoluble open normal subgroup of finite index.
16:00
Joint Logic/Number Theory Seminar: Arithmetic applications of $\omega$-integral curves in varieties
Abstract
In 2000, Vojta solved the n-squares problem under the Bombieri-Lang conjecture, by explicitly finding all the curves of genus 0 or 1 on the surfaces related to this problem. The fundamental notion used by him is $\omega$-integrality of curves.
In this talk, I will show a generalization of Vojta's method to find all curves of low genus in some surfaces, with arithmetic applications.
I will also explain how to use $\omega$-integrality to obtain a bound of the height of a non-constant morphism from a curve to $\mathbb{P}^2$ in terms of the number of intersections (without multiplicities) of its image with a divisor of a particular kind. This proves some new special cases of Vojta's conjecture for function fields.
17:30
The theory of the entire algebraic functions
Abstract
Van den Dries has proved the decidability of the ring of algebraic integers, the integral closure of the ring of integers in
the algebraic closure of the rationals. A well-established analogy leads to ask the same question for the ring of complex polynomials.
This turns out to go the other way, interpreting the rational field. An interesting structure on the
limit of Jacobians of all complex curves is encountered along the way.
Towards a drive-through wheel alignment system
Abstract
As part of a suite of products that provide a drive thorough vehicle tyre inspection system the assessment of wheel alignment would be useful to drivers in maintaining their vehicles and reducing tyre wear. The current method of assessing wheel alignment involves fitting equipment to the tyre and assessment within a garage environment.
The challenge is to develop a technique that can be used in the roadway with no equipment fitted to the vehicle. The WheelRight equipment is already capturing images of tyres from both front and side views. Pressure sensors in the roadway also allow a tyre pressure footprint to be created. Using the existing data to interpret the alignment of the wheels on each axle is a preferred way forward.