The Goldbach conjecture is a famous unsolved problem in mathematics. It asks whether every even number greater than or equal to 4 is the sum of two primes. I will discuss some of the history of the problem, explaining among other things why the answer is surely yes, and also why this appears to be very hard to prove.

New undergraduates often find that they have a lot more time to spend on independent work than they did at school or college.  But how can you use that time well?  When your lecturers say that they expect you to study your notes between lectures, what do they really mean?  There is research on how mathematicians go about reading maths effectively.  We'll look at a technique that has been shown to improve students' comprehension of proofs, and in this interactive workshop we'll practise together on some examples.  Please bring a pen/pencil and paper! 

This session is likely to be most relevant for first-year undergraduates, but all are welcome, especially those who would like to improve how they read and understand proofs.

In this interactive workshop, we'll discuss what mathematicians are looking for in written solutions.  How can you set out your ideas clearly, and what are the standard mathematical conventions?  Please bring a pen or pencil! 

This session is likely to be most relevant for first-year undergraduates, but all are welcome.

What should you expect in intercollegiate classes?  What can you do to get the most out of them?  In this session, experienced class tutors will share their thoughts, and a current student will offer tips and advice based on their experience.  

All undergraduate and masters students welcome, especially Part B and MSc students attending intercollegiate classes. (Students who attended the Part C/OMMS induction event will find significant overlap between the advice offered there and this session!)
 

We consider vector-valued maps which minimize an energy with two terms: an elastic term penalizing high gradients, and a potential term penalizing values far away from a fixed submanifold N. In the scaling limit where the second term is dominant, minimizers converge to maps with values into the manifold N. If the elastic term is the classical Dirichlet energy (i.e. the squared L^2-norm of the gradient), classical tools show that this convergence is uniform away from a singular set where the energy concentrates. Some physical models (as e.g. liquid crystal models) include however more general elastic energies (still coercive and quadratic in the gradient, but less symmetric), for which these classical tools do not apply. We will present a new strategy to obtain nevertheless this uniform convergence. This is a joint work with Andres Contreras.

Lagrangian Floer homology has been used by Ozsvath and Szabo to define a package of three-manifold invariants known as Heegaard Floer homology. I will give an introduction to the topic.

I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality.  New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including  Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems.