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Nóra Frankl - MPhil/PhD Mathematics 2016-2020
Nóra currently holds an MSc in Mathematics from Loránd Eötvös University, Budapest; she graduated with a PhD in Mathematics in 2020.
What are you currently researching?
I am mostly interested in discrete geometry, which includes combinatorial questions about geometric objects. Sometimes I also think about purely combinatorial questions, for example I am currently working on a question about partitioning edge coloured hypergraphs into monochromatic cycles.
Why did you choose this area of study?
I like combinatorics and geometry, and this area is a mixture of these two.
What do you hope to do career-wise, long term?
I would like to stay in academia and do research.
Can you provide any advice to prospective students about the most effective way to approach research and keep stress levels down?
Of course, this varies from individual to individual and from area to area, but there are some things that can be useful in general. Set realistic expectations: you should not anticipate finding results quickly. It is a slow procedure. For me the recipe is to try to be happy even with small results: don’t let failure disappoint you too greatly. I think it is also good to not separate weekdays and weekends too much; when you have ideas and feel motivated, don't stop for the weekend, but treat yourself to much-needed rest days later.
What resources are available at LSE to help young researchers?
There are several funds at both School and Departmental level. Mathematicians need whiteboards – we’re lucky to have many in our PhD office, plus all the basic provisions we could ever need (stationery, printing, equipment, etc.). Our PhD Office itself is a really good, productive environment to work in, where we can focus solidly on our research but also collaborate and share thoughts. The Department as a whole, alongside the PhD Academy and our Research Manager, assist with the essential practicalities of PhD study. The Department invites key visitors to present at our seminar series. Crucially, we have a fantastic coffee machine in the Department :-)
In a few words, what is the best thing about studying at LSE?
Everyone is very nice; I am a valued member of the Department.
Ewan Davies - MPhil/PhD Mathematics 2013-2017
Ewan Davies was a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Jozef Skokan and Peter Allen. He successfully completed his studies in October 2017. His research interests lie in combinatorics, particularly extremal graph theory and probabilistic combinatorics, as well as the intersection of these areas with other fields such as statistical physics and number theory. During his time at LSE, amongst many other activities, Ewan contributed extensively to the department, through committees and teaching, was awarded grants to facilitate his research visits and gave many talks around the world.
I started my PhD at LSE after spending four years in Cambridge for a combined undergraduate and masters in mathematics. I wanted to retain the freedom and intellectual rigour of university life, but also move to a different city and discover new and exciting aspects of life outside work. A mathematics PhD in London was ideal for this; pure mathematics is a rigorous and highly distilled form of problem solving that I find exceptionally rewarding, and London is a near-limitless trove of opportunities to explore.
My work isn’t tied to a specific title or single unifying idea, I have enjoyed working on a variety of projects which are broadly from the same branch of mathematics, but use different techniques and ideas. This is great for motivation, there’s often something appealing to work on and I’m not pressured to make everything fit some central theme. Recently I’ve been focusing on a new method for optimising the observable properties of certain probability distributions that link combinatorics and statistical physics. With a few simple mathematical tricks I have been answering a variety of questions in combinatorics using ideas from statistical mechanics. I’m essentially analysing the average behaviour of a physical system with the property that any possible state of the system occurs with a probability proportional to its energy. Selecting an interesting system and the right definition of energy yields a variety of mathematical applications and I hope to spend the final year of my PhD trying to develop a general theory based on the early successful examples of the technique.
The atmosphere in the department at LSE is excellent; people are friendly, supportive and approachable. When I joined I was jokingly told, “we might not be the best maths department in the world, but we probably are the friendliest”. This succinctly captures the slightly British sense of humour and light-hearted environment that I’ve enjoyed being a part of. It’s also rather too modest, I frequently work with world-leading academics and feel very positive about the quality of the research I’m able to do here. After my PhD I hope to continue in academia with postdoctoral research, and I feel the high quality of the mathematics department at LSE is extremely beneficial for my goals.
Barnaby Roberts - MPhil/PhD Mathematics 2013-2017
Barnaby Roberts was a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Peter Allen and Jozef Skokan. He successfully completed his studies in September 2017. His research interests lie in discrete mathematics, particularly Graph Theory. In his fourth, final year, Barnaby wrote this commentary about his time at LSE.
Written in March 2017
Whilst I enjoyed undergraduate maths I didn’t want to dedicate so much time to maths without doing some of my own research. Once I decided to pursue a PhD in Graph Theory I decided I wanted to go to a university where there were more than one academic in that area. LSE was one of just a few such institutions in the UK. In fact, LSE has a large and very active group of researchers in Graph Theory, Combinatorics and Discrete Mathematics.
I have loved research which, as well as being a good intellectual challenge, is also a surprisingly sociable activity. Discussing ideas with fellow PhD students and other academics is a really invigorating experience and the atmosphere at LSE makes collaborations really easy to get involved in. At LSE, my supervisors have been very flexible in allowing me to choose my own projects whilst also offering guidance and suggesting fruitful directions of study. I have not only worked with other members of LSE but also with various people I have met at conferences and with invited guests who have visited LSE to give a seminars (we have a very active, engaging seminar series in Combinatorics, Games and Optimisation).
There are many aspects to a PhD beyond research. Presenting work, attending conferences and teaching are all part of it too. All three of those seemed a little daunting at first but quickly became really enjoyable. Learning to present work well and similarly to teach maths clearly are both good challenges. They are also very transferrable skills. From being at LSE I have attended conferences across the world. A particular highlight was spending 6 weeks in Brazil working with mathematicians in Rio and Sao Paulo. This was made possible by funding accessible through LSE.