# PROMYS Europe Connect 2021

PROMYS Europe Connect 2021 saw a group of enthusiastic and high-achieving young mathematicians gather (online) in July and August for a four-week intensive summer programme designed to give them the experience of thinking deeply about mathematics in a community of similarly mathematically excited students and staff. In other circumstances, PROMYS Europe is a six-week residential programme in Oxford, organised by a partnership of PROMYS (Boston), Wadham College and the Mathematical Institute at the University of Oxford, and the Clay Mathematics Institute. Circumstances being what they were, the 2021 programme, PROMYS Europe Connect, was tailored for an online format, in which we sought to capture as much as possible of the essence of the traditional event.

PROMYS Europe Connect 2021 was attended by 28 students, 2 of whom were returning students who first took part in PROMYS Europe in 2019, and 9 undergraduate counsellors. Participants represented Austria, Bulgaria, Czech Republic, Germany, Hungary, Norway, Romania, Serbia, Spain, Sweden, Switzerland, the UK and Ukraine. Places are offered to students on the basis of their academic potential as demonstrated in their application; we waive some or all of the fee (which is already heavily subsidised) for students who would otherwise be unable to participate. The programme is funded and resourced by the PROMYS Europe partnership, and by further financial support from alumni of the University of Oxford and Wadham College, and from the Heilbronn Institute for Mathematical Research.

This year, as usual, the core of the programme was a Number Theory course, taught by Glenn Stevens (Boston University, founding Director of PROMYS) and Henry Cohn (Microsoft Research, MIT). Students are encouraged to discover as much as possible for themselves, through their work on daily problem sets and through careful individual mentoring by their counsellor.

Alongside this was a Group Theory course with a similar philosophy, taught by Vicky Neale (Oxford), primarily aimed at the returning students, but also well attended by the first years. The returning students also worked on a research project on elliptic curves. Alongside their own mathematical seminars on category theory and analytic number theory, the counsellors organised social activities to help the students get to know each other and to build the sense of the community that is so important to the programme. These were complemented by guest lectures, exposing students to a range of current mathematical research. Plans are already under way for summer 2022, when we expect to return to the in-person format.

Here’s what participants said after PROMYS Europe Connect 2021:

*Thank you for organizing all this, I feel like I almost cannot grasp the impact that this programme has had on my life in these three years of p*articipation. [Returning student]

*The online experience was actually much more engaging than I had expected. *[Student]

*PROMYS Europe Connect has left me with so many fantastic memories. I have truly felt like I am part of an amazing community of mathematicians who are all so passionate about what they do*. [Counsellor]