Returning Students 2019

Returning students

Students returning to PROMYS Europe are encouraged to revisit those parts of the number theory course that they didn't have time to explore fully as a first-year student.  There is always more to investigate, and returning students often welcome this opportunity to deepen their understanding.  Students will be able to talk to their counsellor and to the faculty to design the most suitable individual programme for them.

In addition, returning students can pursue lectures and problems specifically aimed at returning students, and can work in a small group on a research project.

In 2019, Vicky Neale will give a course on Combinatorics aimed at returning students. It is hard to define combinatorics in an abstract sense, but not so hard to recognise when you spot it in the wild. Combinatorics is sometimes described as being about counting, and certainly it includes some of that, but it is much broader than that might suggest, including the study of a wide variety of finite systems and discrete collections.  In this course, we'll explore a variety of topics from combinatorics, some rather old and some relating to very recent research.  The precise plan is, at the time of writing, still to be decided, but might well include some graph theory, some extremal combinatorics, some probabilistic combinatorics, and some Ramsey theory.  The area of combinatorics includes numerous problems that are easy to state and yet very difficult to solve, and often the key to progress is hard work and ingenuity in problem solving rather than the application of sophisticated theory.  The course will give lots of opportunity for working on problems and for playing around with ideas.

Returning students also have the option of working in a small group on a research project.  Projects are designed by leading mathematicians, and give returning students an opportunity to explore an area of mathematics in great detail and potentially to work on open research questions. In recent years projects have included:

"Class Groups of Function Fields" (proposed by Erick Knight and Ananth Shankar)
"Permutation Weights" (proposed by Paul Gunnells)
"2-Torsion in class groups" (proposed by Erick Knight)
"Unimodular lattices and modular forms" (proposed by Victor Rotger)
"Extremal problems in ordered graphs" (proposed by David Conlon),
"Project 691" (proposed by Kevin Buzzard),
"Modular representations of GL2(Fp)" (proposed by Laurent Berger and Sandra Rozensztajn), and
"Graph colouring problems" (proposed by David Conlon).

Returning students working on research projects have been mentored by PhD students from the Oxford Mathematical Institute.