Maths students from the University of Sheffield took part in a summer school aimed at the best undergraduate mathematicians in the UK.
This year's London Mathematical Society Undergraduate Summer School was postponed from 2020 and took place online in July, hosted by Swansea University.
The aim is to introduce exciting mathematics to UK undergraduates who will enter their final year the following autumn, particularly those who may be considering an academic career in maths.
Topics are chosen to complement standard undergraduate modules and there are a range of activities, including short lecture courses, Q&A sessions and colloquium-style talks.
One of the courses at this year’s summer school was ‘Combinatorics of Young tableaux and symmetric groups’, led by the University of Sheffield’s Professor Sarah Whitehouse.
She said: “A Young tableau is a certain type of array containing natural numbers. They appear in lots of places, particularly in the systematic study of the actions of the symmetric groups. I focused on some explicit counting problems related to these and then went on to sketch the importance of the formulas obtained in the representation theory of symmetric groups.
“The online setting had its limitations but also some advantages, notably in allowing many more students to participate – more than 100. I particularly enjoyed the Q&A session for my course – the students had a wide range of excellent questions.”
Below, you can read comments some of the University of Sheffield students who took part in this year's LMS summer school. The other University of Sheffield participants were Muhammad Majul (Mathematics BSc) and Lola Cabrillana Craig (Mathematics MMath).
Namitha Philip, Mathematics BSc
“Over the two weeks, there were several different lectures on a wide range of topics, most starting at an undergraduate level, but then went far beyond any undergraduate syllabus. This was initially quite a shock at first but as the school progressed all the topics stepped it up a level, to make it more interesting as well as more challenging.
“It was encouraging that all of the lecturers spoke very well, with a clear passion for their subject – topics were as diverse as conics, analytic inequalities, and combinatorics of Conway–Coxeter frieze patterns! But it was the colloquium-style talks given by the guest lecturers that I found fascinating, as they offered a glimpse at the modern horizon of mathematics.
“Among the talks, a memorable one was Ian Leary's talk on a finite description of an infinite group. I found it fascinating how the finiteness properties of the group are equivalent to the algorithmic properties of the group.”
Calum Hughes, Mathematics MMath
“The LMS summer school gave me a chance to learn some current research mathematics that is accessible to an undergraduate. It's really good to know some of the things that people are studying at the moment, and with the mini-courses given, it was more than just an overview that you'd get from watching a Numberphile video or something like that.
“Also, it was lovely to be able to just chat with other enthusiastic young maths nerds and PhD students in the coffee breaks!”
Cameron Heather, Mathematics MMath
“I had a wonderful experience participating in the LMS summer school! It was a great opportunity to meet students across the country and also have the opportunity to talk to PhD students too. It was interesting and engaging and allowed us to learn content that we wouldn’t have seen during university.”