How might you prepare talks for different audiences (specialised seminar, colloquium-style talk, talk to a non-mathematical audience, job interview)? Join us for advice on this, and on how to connect with your audience and get them to feel involved.
There are many opportunities within Oxford to communicate your excitement about mathematics and your own research to a wider audience, whether adults or school students. In this session we'll hear about some of those opportunities, and have some training on how to write a press release, so that you are well placed to share your next research paper with the public.
Featuring
Rebecca Cotton-Barratt, Schools Liaison Officer and Admissions Coordinator in the Mathematical Institute
Mareli Grady, Schools Liaison Officer in the Statistics Department and Mathemagicians Coordinator in the Mathematical Institute
Stuart Gillespie, Media Relations Officer for the University of Oxford
Across the physical and biological sciences, mathematical models are formulated to capture experimental observations. Often, multiple models are developed to explore alternate hypotheses. It then becomes necessary to choose between different models.
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.
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
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.
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.
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.
