# Topic: Statistical Applied Mathematics

## Sequential Logarithmic Spoons (SLS)

(Blog jointly written by Elizabeth Gray and Cameron Smith)

It has come to our attention that nearly a year has passed since the mighty managerial mission to mastermind SLS was comprehensively conferred to our eagerly awaiting shoulders; bright eyed and uninitiated in the ways of SAMBa as they were.

It is thus with a modicum of nostalgia that we reminiscently relish the (w)riting of this review.

It all began one whimsical Wednesday when we decided to take one for the team and volunteer to organise SLS for the term (sorry, *Semester, what is this place?). What could possibly go wrong?

Well, for starters, THIS:

Have we lost you yet? Perhaps we should explain.

In truth, SLS stands for neither sequential logarithmic spoons nor spicy lentil soup, sautéed lobster salad or slightly lacklustre sultanas but does in fact stand for Student Led Symposium. "What is that?", we hear you cry in eager anticipation. Believe us, it's a common question, one which we often ask ourselves.

SLS is a tri-weekly forum in which speakers invited by yours truly, industrial partners, and students give talks, workshops and lead mathematically informative sessions in the lead up to SAMBa's flagship activity, the ITT.

In order to prepare ourselves for such a task and to morph ourselves into the highly developed and effective interdisciplinary statisico-mathematicians which now appeareth before thine eyes, we organised many engaging activities. We present... our greatest hits:

1. Straight in at number five are the industrial partner visits and their fascinating and mathematically unformulated problems. Problems included personalised medicine, absorption of pesticides through the skin and shaking seeds, or bees, or some undetermined small objects. Who knew seeds in a box could be so much fun?
2. A non-mover at number four with our invited speakers. Topics included clinical trials, statistics for Syngenta problems, inverse problems and Susie's "how grown up mathematicians get money" talk about EPSRC project proposals.
3. Clinging onto the charts for yet another year at number three are the student talks, where SAMBa students presented any previous research they had done. We learnt about general relativity, symplectic geometry, a history of probability in Mongolia and torturing rats. An overall enlightening experience.
4. At number two, an entry so controversial, that not even the website saw it. That's right, its the ethical discussion session! We talked about the ethical questions surrounding research and industrial collaboration.
5. And finally, a brand new entry at number one, FUN FRIDAYS!!!! This was a (semi) successful attempt at harnessing the fundamental ability ingrained in all SAMBa students, to talk about and apply maths off the cuff in fun situations such as: Rugby, dinosaurs, optimal time to buy your lunch, buses and flies in Elizabeth's flat. A series of highly competitive and mathematically charged sessions pushed the boundaries of mathematical creativity, weirdness and team collaboration which seemed an ideal environment to dip our toes into the murky world of problem formulation in preparation for the ITT. Below, we see team Finite Dinosaur Method defining and presenting on the Flinstone probability:

What more can be said for such a wonderful year. Not much as we would like to go home at some point today, before sense of humour levels dip below critical. Thus we will leave you with our most ambitious SLS session to Las Vegas¹ with a picture:

SLS love
Camzabeth x

¹ If anyone from EPSRC is reading, this never happened.

In June 2017, a group of Prof Chris Budd's PhD students (Me (Hayley Wragg), Matthew Griffith, and Susan Kgmotso Morupisi) ventured across the sea, to the west of Bath, all the way to Limerick! Travelling for the 128th European study group with industry. Greeted by stunning Irish countryside (and weather) we arrived at the University of Limerick ready for a week of maths.

For those wondering what an Industry study group actually is, here is a brief overview. Several Industrial Partners present mathematical problems to a group of mathematicians. The mathematicians come from all over the world to spend a week working on the problems together.

How is that different to SAMBa's ITT's? Well, the study groups take place in the university but aren't connected to a CDT like the ITT is. The problems are already formulated at the start of the week and the aim is to get some results by the end. There are more preparation days for the ITT, whereas the study group starts the week it's on.

On our first Monday morning (after some surprisingly good coffee!) the industry partners introduced the problems. There were 5 problems in total. Monday afternoon participants chose their groups and got started on the problems. Work continued until Friday broken up by a guest lecture and study group dinner. Matthew and Susan were both working on a problem modelling vehicle collisions and I was looking at wave propagation through materials.

The guest lecture featured Jacqueline Christmas, who gifted us with an insight into her work modelling ocean waves.

The week finished with a presentation from each group on the work they had completed on the problem (Matthew, Susan and I all presented).
The work didn’t stop after the event though since reports were submitted to the partners within 3 weeks of the event finishing.

But one Industry study group wasn’t enough for the Budd Brigade and in August 2017 a new group of Buddlings formed ( me and Kate Powers). We travelled further west to Montreal in order to test our French (and maths).

Along with Chris we attended the Eighth Montreal Industrial Problem Solving Workshop at the University of Montreal.

With a similar structure to the ESGI, the week begin with problem introductions from the industrial partners on Monday morning. This time there were 9 problems in total. Monday afternoon work began. Kate was looking at friction stir welding; I was looking at registration of hyperspectral images of the retina ; and Chris was looking at data assimilation on hydroelectric power.
Wednesday evening gave visiting participants the chance to visit Old Montreal where we were blessed with views of some of the amazing architecture as well as a walk along the waterfront. Work on the problems kept going until Friday.
All 9 problems were presented to the rest of the participants on the Friday (Chris and I presented), before the Budd Brigade returned to the UK.

The working structure of both study groups was intense but exciting. Discussions with professors, academics and students all working together to, categorise the problem,
work out the maths, and get results at the end of the week. The problems covered many areas of maths, including (but not limited to): fluid dynamics, statistics, probability, computational modelling, and numerical analysis.

I would thoroughly recommend the weeks to all applied mathematicians. Prepare to have a great time whilst getting lots of maths done. It is also essential to carry a SAMBa CDT keep cup at all times.
Anyone feeling inspired to attend a study group in the future can check Maths in Industry for future events.

## Yeah! It's a conference in the USA!

(Title: with apologies to Miley Cyrus and inspired by "Wierd Al" Yankovic)

In May this year I travelled to the University of Minnesota, Minneapolis for WAVES 2017 (or to give it its full title, the "International Conference on Mathematical and Numerical Aspects of Wave Propagation"). I was accompanied to the wild (mid) west by Elizabeth Arter, Ivan Graham and Euan Spence from the Department of Mathematical Sciences, here in Bath.

So with heady hopes for my first major conference (and my first trip to the USA) I made my way (changing planes in Iceland!) to Minneapolis.

I should explain why I'd gone all the way to Minneapolis for a conference. My research involves waves; acoustic waves, to be precise. I seek to understand the behaviour of sound waves when they move through a random medium, (For example, when sound wave moves through a crowd of people, but you don't know exactly where the people are).

I also design numerical methods for quickly computing properties of these sound waves and I try to prove that these numerical methods work. My research tends to come under the umbrella of `Uncertainty Quantification' -  designing and analysing numerical methods for problems containing randomness.

Having arrived in Minneapolis, had (some) sleep, and been treated to a very large breakfast in the hotel (I never knew pancakes could be that big!), we made our way to the conference venue, the Coffman Memorial Union

The Coffman Memorial Union, our conference venue

Happily, I didn't have to wrestle with the conference timetable on day one - there was a minisymposium all day on "Seismic Waves: Uncertainty Quantification in Imaging/Inversion Across Scales." Most of the talks in the minisymposium came from researchers in seismic imaging. They're interested in reconstructing the rock structure underneath the earth using sound waves.

Seismic imaging is a major motivator for my own research. We're interested in problems surrounding wave propagation and developing fast, accurate algorithms. And yet those in the 'seismic world' have some different concerns to me. I didn't hear any talk of mathematically proving that methods work, rather, they're interested in methods that seem to work well in realistic scenarios. For example, did you know that salt can cause issues for seismic imaging, as it reflects lots of sound waves? It was a valuable experience chatting with them - their interests could well inform the direction of my PhD.

At the end of day one were treated to a public lecture by Michael Berry from the University of Bristol (it's a small world). After this, some people went out for a drink (in the fabulously named Dinkytown area of Minneapolis) but I made my slightly jet lagged way back to the hotel. Why? Because I was talking the next day!

My talk was in the last possible slot on Tuesday evening, before the conference dinner. I wasn't expecting a big crowd! However, there were around 15 people in the room. They heard me speak on "Bounds on the Helmholtz equation in heterogeneous and random media".

A slide from my talk

This is work with my supervisors Ivan Graham and Euan Spence; we have proved that there are certain types of heterogeneous and random media where you can guarantee you'll never experience `resonance'. Resonance is the phenomenon that means an opera singer can shatter a glass, or that you'll find certain notes ring louder than others when you sing in the shower. If you've not experienced this - try it next time you have a shower!

After my talk came the conference dinner, in the impressive yet architecturally quirky McNamara Alumni Centre. The roof is polyhedral and part of the wall is the old entrance to the sports stadium, which leans over the inside space in a mildly worrying fashion.

The wall of the McNamara Alumni Centre - it's an old gate for the football stadium

The banquet was wonderful - we had the fantastic setting, with good food to boot. It was also a fun- and laughter-filled reminder of how multinational the academic community is. At our table of eight, we had five different nationalities represented (British, French, Austrian, American and Mexican).

And it seems that my talk actually made an impact (besides meaning people had to rush to the conference dinner). I was able to have a conversation with one of the audience members later in the week. They work on problems in plasmas, and were interested whether our results could apply to their work.

The following three days of the conference passed in a mixture of talks attended, meals enjoyed and acquaintances made or strengthened. These last two points are interlinked. It's a privilege to be able to go for sushi with a group of people you've met during the week and get to know one of the leaders in your field over lunch!

I have to mention the drinks reception we had in the Weisman Art Museum - we had modern art (I'm still not sure I understand it), views towards downtown Minneapolis over the Mississippi and a jazz trio. However, I don't think we quite appreciated the architecture from the inside!

The Weisman Art Museum

The strengthening of relationships continued until the last evening. You can't help but get to know people better after you've crossed the light rail tracks with them and then spent twenty minutes walking down a largely empty road bordered by abandoned lorry trailers and derelict flour mills in search of a beer hall that one of the group visited once before. To be fair, he'd been there for a conference dinner, knew exactly where he was going, and we had a great evening.

Grain elevators, near our walk on the final evening

And before we knew it, the conference was over, and we were on a flight back home! It was a week filled with waves, maths and mathematicians.I think you'll find me at WAVES 2019, and we might have another blog post title inspired by a song. Can you guess where it's going to be?

Image Credits:

## Students organise brilliant first SAMBa conference

We welcomed in mid-summer with our first SAMBa conference. The conference was organised by students Ben Robinson and Adwaye Rambojun, with many more of our students presenting talks or posters over the two days. These presentations showcased the range of excellent research that is taking place across the continuum of statistical applied mathematics.

External speakers Anja Sturm (University of Göttingen), Colin Morice (Met Office), and Richie Gill (Mechanical Engineering) showcased their work on branching and coalescing particle systems, reconstruction of daily air temperature variations, and in silico clinical trials, respectively.

Our partners, GKN, Schlumberger, AstraZeneca, and BT, each sponsored a session, and we were pleased to welcome a number of staff and students from UK universities, and industrial organisations, with 80 people attending over the two days.

Paul Milewski, co-Director of SAMBa, said: “It is wonderful to see the breadth of research taking place in SAMBa, and how well it was presented. The combination of talented students, diversity of research, and a cohort approach, where students continuously discuss with each other, has worked out extremely well.”

Anja Sturm, one of the invited speakers, said: "I was very impressed with the SAMBa programme and the conference. The talks and presentations were excellent and I was particularly taken by the great enthusiasm the students showed for their projects - which were indeed quite diverse and very interesting both from a mathematical, as well as an application point of view."

The atmosphere during the conference was great, with lots of discussion and a real sense of celebrating the achievements of SAMBa. We are already looking forward to next year!

More photos can be viewed here on Flickr.

In late November 2016, 10 keen students and academics made the long journey to Ulaanbaatar, the capital of Mongolia, for a research trip aiming to build links between Mongolia and the University of Bath.

Upon arriving in temperatures reaching -30 degrees Celsius, a few wondered what they had let themselves in for. Even Andreas Kyprianou, who knew Mongolia well, had never visited before in winter and was a tad apprehensive.

Left: the long journey from Bath to Ulaanbaatar, involving a stop off in Beijing. Right: arriving at Chinggis Khaan airport in Mongolia.

The aim of the trip was to help develop the Mongolian industrial mathematics and statistics capability. It was hoped this would help the country form evidence-based policies that will drive economic, industrial and environmental development. A team from the University of Bath was hence formed of individuals that could help build collaborative links between policy makers in Mongolia to generate high impact research activity, and deliver a course in statistics to provide training for young academics and workers. This included representatives from SAMBa, the Statistics group, IMI, IPR, and four postgraduate students.

The course was primarily run by the postgraduate students and had a large amount of interest with hundreds of applications. A suitable venue was identified which allowed for 130 participants from Mongolia to attend. The material began with motivational examples of the use of statistical analysis such as the use of clustering methods on electricity usage data to better predict electricity demand. The participants were introduced to statistical software R, and shown how to use it for initial data analysis and data visualisation. The course moved onto methods for hypothesis testing including how to pick the right test for different types of data. It concluded with methods for linear regression and clustering. Many of the participants had their own data from academic or public sector projects, and a lot of queries related to importing and analysing this data.

On the first day of the course, a TV crew recorded a report for the state TV channel MNB. A 3-minute long segment involving interviews was broadcast on the news on 22nd November 2016. At the time of writing, the report is available to view on the MNB website (22:00 mins).

Given the language barrier, it was found necessary to speak relatively slowly, and pause for a translation after every phrase. This was useful in developing the skill to speak in a concise articulate way, and to avoid using serpentine sentence construction (which I for one was previously guilty of when giving talks!).

Logistical challenges arose including intermittent WIFI access due to the large amount of people in the course. This was countered by the downloading of relevant materials including R software and packages onto many memory sticks for circulation.

Delivering the course was an enjoyable and extremely beneficial experience for us. The participants of the course were extremely friendly and it was genuinely a joy to work with them.

Top left: Poster advertising the statistics course. Top right: Robbie Peck assisting a course participant with the installation of the relevant statistical software. Bottom: Aoibheann Brady, Matt Thomas, Robbie Peck, and Adwaye Rambojun preparing and delivering the statistics course.

The other half of the University of Bath team took the lead in meeting policy makers to build future potential collaboration links. This included representatives from the National University of Mongolia, and the Ministries of Health, Energy, National Strategy. This proved fruitful with many different leads for collaboration with academic and public sector projects.

One potential collaboration involved looking at air pollution and tuberculosis records within Mongolia. The burning of untreated coal to fuel the large heating cost in Ulaanbaatar meant that the PM10 concentration in the city was relatively high. A possible direction would be to fit a model to pollution levels across space and time to ‘fill in the gaps’ where there are not records. One could then cross reference this with the tuberculosis records to measure any association between air pollution levels and tuberculosis diagnoses. It is hoped research such as this will have weight in influencing public policy through the links established with the public-sector workers we met.

Furthermore, Professor Gavin Shaddick ran a workshop in air pollution which began with talks from academics from Bath and Mongolia. This then followed the style of a SAMBa Integrative Think Tank by having cross discipline group discussions to identify problems and research questions, and then short presentations about directions one would take to tackle them. For each problem, a contact in Mongolia was identified to be the catalyst for future work in that area.

Top left: Meeting at the Public Health Institute. Top right: Julie Barnett in a discussion during a workshop on Epidemiology and Public Health. Bottom left: Andreas Kyprianou working through some ideas during a workshop on Ecology. Bottom right: Meeting at the Economics Research Institute.

Once the week had finished, we celebrated all the new potential future collaborations with a Mongolian feast. The food was particularly delicious, involving large amounts of tender meat and traditional Mongolian salads and sides. To our new Mongolian friends, we said “Баярлалаа!”, and hope to return to Mongolia in 2017 to ensure the successful development of the ongoing collaborations and to perform further training courses.

## My first conferences: A SAMBa story

My first year at SAMBa has been quite an eventful one. I can definitely say that SAMBa has delivered on its promise to help me explore different areas of Mathematics. However, this post is not about maths at all (who are we kidding, it probably is), it rather concerns my experience of conference attendance. My very first one was a workshop on big models at the University of Warwick, which incidentally happens to be my undergraduate institution. The reason I went there was to see what the Institute of Data science was up to, and as expected, they were doing things that I was interested in. Statistics, applied mathematics, data science and machine learning.

Swisstech Convention Centre, Lausanne (courtesy of STCC)

My second conference was perhaps the most daunting one. In my quest to know more about uncertainty quantification (UQ), I took up a module with the local expert on it, Prof. Rob Scheichl. This led to the SIAM conference on uncertainty quantification in Lausanne. The venue was breathtaking, to say the least. It was in the Swisstech convention centre at the EPFL. I have never seen an auditorium with that much leg room during the plenary talks. To fund myself, I along with a fellow SAMBAlite, Gianluca, successfully applied for funding from MI-Net. Part of the deal of going there was to further inter university collaboration, and hence the day preceding the conference involved some informal chat with Fabio Nobile's research group. We exchanged ideas and research interests. The rest of the week involved us going to different sessions. They were quite daunting to be honest as most of the speakers were very, very good at what they did. This only increased my desire to actually start a research project and further my knowledge in a specialist area. The thing that I believe was most beneficial for me was to see the use of machine learning in UQ. This contributed to my decision to take up machine learning as my current research project as I could see that UQ would still be an option if I diverted away from it for a bit. I have to say though, my bilinguality helped a lot during the trip. I speak both French and English fluently, coming from a bilingual society (well, we're actually multilingual as most of us speak a third oriental language plus our local dialect, creole. Mauritius FTW right?).

Me, Gianluca and another SAMBa student Matt outside the conference in Lausanne

I went to my next conference after I had chosen my project (which is on automatic damage assessment in x-rays of Psoriatic Arthritis patients). It was a summer school on Gaussian Processes organised by the Machine Learning group at the University of Sheffield. It was the first year where they added the words "and uncertainty quantification" to it. I expected it to be full of computer scientists. To my surprise, the attendees were extremely diverse. There was an analytics team from formula 1; a guy working with Siemens (I think it was Siemens) on wind turbines; and wait for it.....my UQ lecturer from Warwick, Tim Sullivan (who is one of the most rigorous applied mathematicians I know) and my final year project supervisor, Mark Girolami. Uncertainty Quantification can mean many things! The summer school had practical sessions and talks from people who are very good at working with Gaussian Processes. One thing I got from the whole thing was that Gaussian Processes are used everywhere, from trying to optimise functions you cannot evaluate, to trying to fix the posteriors you get in Bayesian Inverse Problems. Is there a better alternative? Maybe. The search continues....

Antarctica as modelled using Markov Chain Monte Carlo, a key tool in Uncertainty Quantification (courtesy of the National Science Foundation)

The next conference I went to was very different from my two previous ones. It was actually one on Psoriatic Arthritis (PsA). No maths, just medical researchers and practitioners talking about, well, PsA. I did not get most of what was happening as they were talking about genes and things. They also mentioned "statistics" a lot of times. That was scary. I mean, really scary. When I asked them what kind of tests they were doing the answer was often "I don't know, I just press on a button in stata". It thus seemed to me that medical doctors in general need a better grasp of data science. Hence I tried to get some statistics training into their realm by suggesting we do a little session with consultants undergoing training. This was well received and it is hoped we can do it in the future during one of their training days.

You might be asking yourselves, how did you, a self proclaimed applied mathematician (please don't hate me, I know I did stats as a major) go to a medical workshop? Long story short: I was invited to a meeting in Bath on medical imaging, as I had now started working on this. There I met Prof. Neil McHugh, who works in pharmacology at the University of Bath. I mentioned my desire to know more about the PsA and he suggested I go there.

My English teacher always told me to put a concluding comment in my essays, and this is kind of an essay. The food at non-maths meetings, like the medical imaging one and the PsA one is way better. I had three course warm meals in both of them as opposed to the usual dried out sandwiches that repeat themselves n-times where n is the number of days the meetings stretch out for. Oh, and I'm writing this on a plane to Beijing where I transit before going to teach stats in Mongolia on SAMBa business. This one is for another time!

## SAMBa's 2nd cohort impress with talks introducing their PhD projects

Over two afternoons in October, our second cohort of students presented their research to the rest of the SAMBa cohort, staff from the Department of Mathematical Sciences and the wider University, and some of our external partners.  Topics presented ranged from Modelling of Host Parasite Dynamics (complete with increasingly disgusting pictures) to Random Walks in a Changing Environment (or how to get from the University to Combe Down via Po Na Na) and encompassed all aspects of the statistical applied mathematics portfolio.

Above, clockwise from top left, are Aoibheann Brady, Gianluca Detommaso, Anna Senkevich and Adwaye Rambojun presenting their research.

Our new students, who are just beginning their MRes year, were in the audience and we even managed to get a photo of almost the entire SAMBa cohort 3 years in.

An impressive array of SAMBa hoodies

The transfer day talks presented a breadth of research from students working in collaboration with industrial partners on clinical trial design or medical imaging, to those with projects involving branching processes, applications of nucleation theory, and finite element methods for elliptic PDEs. The presentations were of an excellent standard and it is great to see how much our students have developed both in mathematical expertise and presenting skill over the last year. More details on all our SAMBa projects can be found on our website.

We are looking forward to seeing the progress of our research students and working with our 3rd cohort as they move through their MRes year. Watch out for their Transfer Day presentations this time next year!

## Bridging “the gap” in Mongolian Mathematics: a Q&A with Andreas Kyprianou

Mongolia is a country nestled between Russia and China, 6 and half times bigger than the UK but with a population 21 times smaller. It is the most sparsely populated country in the world (with 45% of the population living in the capital Ulaanbaatar). Mongolia has a rich history including the powerful rule of Genghis Khan, who created the Mongol Empire – the largest contiguous empire in history. But how much do you know about Mongolia in the present day? Have you been there? Do you know anyone who has? It seems somewhat a forgotten place, but recent activity from the University of Bath’s department of Mathematics aims to change that.

SAMBa co-director, Andreas Kyprianou has a long-standing relationship with Mongolia and now this is bearing fruit in terms of building a research base for the future. This relationship is growing even further and as that will have an impact on my job managing the SAMBa centre for doctoral training, and may even mean I get to visit Mongolia someday, I wanted to find out from Andreas how it all started and how he sees things developing in the future.

Andreas modelling various Mongolian outfits

I did my undergraduate studies in Oxford and moved to Sheffield for a PhD, graduating in 1996. After a brief stint as a temporary lecturer at the London School of Economics, I went to work for Shell as a Mathematician in their research laboratories in Rijswijk, The Netherlands. However, Shell was not for me so I left after about a year and a half, finding my way back to academia in late 1998.

After a short stint at the University of Edinburgh I was offered a five-year research fellowship back in the Netherlands, at Utrecht. A growing family brought me back to the UK in 2005 to Readerships at Heriot-Watt University, and then the University of Bath in 2006. I became a Professor in 2008.

Moving to Bath was a massive career boost. The probability group was in excellent shape and ready to grow. I enjoyed very much the aspirations of the Department and the University. We founded Prob-L@B (Probability Laboratory at Bath) in 2007, which has more than doubled in size in the last 10 years with a strong focus on doctoral and postdoctoral research infrastructure. This experience led me to taking up a role in bidding for the EPSRC funded CDT SAMBa. This was founded in 2014, and I now co-direct the centre.

When did you first travel to Mongolia? What made you decide to go?

I first went to Mongolia in 1998 after leaving Shell. Although things turned out well career wise, at that time it was unclear what lay beyond my resignation that summer. I recall handing in my security pass at Shell and going straight to the airport, from where I flew to China - not quite sure what would happen next! I travelled in China for a short while, but when I found that it was possible to catch a train to Ulaanbaatar from Beijing, nothing could stop me getting on that train. I still have memories of being a lone traveller on the night train to Ulaanbaatar and waking up at 6 a.m. to the wonder of seeing the Gobi Desert with wild camels running along the side of the track. At the same time, I was scared at what I would find in Ulaanbaatar. I knew nothing about this country and its people, beyond that it had undergone quite significant economic and social collapse since the fall of communism in 1990. However, from the minute I stepped off the train, I fell in love with Mongolia and I ended up staying quite a lot longer than expected.

The Beijing to UlaanBaator train (http://tonywheeler.com.au)

How did your relationship with Mongolia develop over the years?

I have been married to a Mongolian for 16 years. I met her on the steps of the central post office in Ulaanbaatar the day before I left Mongolia that first time and now, many years later, we live happily with our three daughters in Bath. Because of this, Mongolia has become a big part of my life. Over the last 20 years, I have been back to Mongolia many times and have witnessed dramatic social and economic changes, both for my own extended family and also the Mongolian nation as a whole.

When did you first start working with the maths department at the National University of Mongolia (NUM)?

It was through my niece, who studied Mathematics and Economics at NUM. I visited her a few years ago, when she was in the middle of her masters’ studies, and she asked me to come and give some lectures and meet her teachers. It was then that I met several academics at the Department of Mathematics, including Tsogzolmaa Saizmaa (or Tsoogii). She described the plight of Mongolian mathematics to me. It was an impressive story and I learnt of the solid foundations of the mathematical community of Mongolia, supported by the old Soviet system, with good connections to Novosibirsk and Moscow. However, following the fall of communism, there was a “gap” in the continuum of expertise that now needs rebuilding. Having seen with my own eyes the difficulties that Mongolia has experienced, I quickly agreed to help Tsoogii and her colleagues to somehow put Mongolian mathematics back on the map.

Andreas with Tsoogii and his neice, Tungaa

So what did you do?

Together with a group of enthusiastic colleagues, both from Mongolia and other countries, I organised an enormous workshop on stochastic processes and applications. Although I met Tsoogii in 2012, it took until 2015 to get the necessary funding in place and to build the organisation necessary to hold such a large event. One of the central aims was to provide a panorama of modern topics in probability theory for the local audience. But the most beneficial and lasting outcome was the opportunity to create personal contacts between young Mongolians and the global community. We chose the theme of probability not just because both Tsoogii and I share an interest in this field of mathematics but also because NUM has a history of work in probability theory that dates back to the origins of the department in the 1940s. We raised nearly 60K Euros for the workshop and it was attended by around 120 individuals, the majority of which were students, from 20 countries.

Tsoogii is joining SAMBa on a Schlumberger Foundation fellowship in 2016, can you describe how that came about?

Tsoogii was a top student and, when graduating from her Masters some years ago, she was very keen to pursue a PhD in probability theory. This was at a time that Mongolia was going through significant economic difficulties and opportunities in Mongolia were few and far between. At this time, her husband was offered a scholarship to study for a PhD in Korea and she went with him. Unfortunately, she was not able to get a scholarship to do a PhD in Mathematics in Korea but, not wanting to waste her time there, she accepted a scholarship to do a PhD in computing science alongside her husband. When they returned to Mongolia, Tsoogii took up a position in the Department of Mathematics which she has held since 2010. However, her dream of pursuing research in probability theory remained. Hosting the SAMBa Centre for Doctoral Training meant that we could give Tsoogii the opportunity to pursue a PhD in this field here in Bath. However, funding students from outside of the EU to undertake a PhD is not easy. Luckily we discovered the Schlumberger Faculty for the Future fellowship scheme which supports women from developing countries to undertake a PhD abroad with the aim that they return to their home countries to build up research groups. This was an absolutely perfect fit for Tsoogii! Sure enough, from a competitive field of over 1000 applicants, she was one of 49 fellows awarded funding. This means that Tsoogii can now address both her personal ambitions; to get a PhD in probability theory and to ensure the continuation of probability theory in Mongolia. We are super excited about welcoming her to SAMBa in September and look forward to helping her to realise these goals.

What have you enjoyed about working with NUM?

Mongolia is a very remote country. Nonetheless, there is a generation of younger Mongolian mathematicians who are very aware of developments in the rest of the world and don’t want to miss out. It’s often easy to forget how privileged we are in the West, and the opportunities we take for granted so it is great to be able to share some of those opportunities with researchers at NUM. It’s wonderful to support young people who are prepared to work really hard to achieve their goals.

The National University of Mongolia

How do you see Mongolian mathematics growing in the future?

Globalisation is generally accepted as a good thing for scientific research and Mongolia provides an ideal example of a country that could benefit significantly from increased connectivity, building on the opportunities afforded by the internet and social media. I believe that Mongolian mathematicians can form closer ties with their counterparts around the world, and take advantage of the many opportunities that exist in terms of doctoral and postdoctoral training. Tsoogii returning to Mongolia with a SAMBa PhD should have real impact in helping to deliver this.

There are many research opportunities in Mongolia that align with our research agenda in Bath and more widely in the UK. As with many countries and institutions, Mongolians are increasingly finding that they have an abundance of data which could be used to answer substantive questions, and inform policy decisions, across a number of fields. The foundation for interaction is now established and I am now working jointly with SAMBa and the Bath Institute for Mathematical Innovation (IMI) to initiate a number of collaborative projects.

The director of the IMI, Jonathan Dawes, has recently visited Mongolia and met researchers at NUM. Since his visit, Jonathan and I have worked closely with Gavin Shaddick (deputy director of IMI and co-director of SAMBa) to identify some very clearly defined projects in data science and statistics, focusing on air pollution, healthcare, agriculture and mining. These projects ensure there will be a building of Mongolian research capacity and will enable growing confidence in manipulating big data. They will provide a springboard to working collaboratively with Mongolian mathematicians and scientists, whilst developing a wider programme of future research and lasting collaboration. I hope that in the future we will see the delivery of real life impact on local communities from these interactions.

The people, fermented horse milk, and eating dumplings in small little cafes; preferably all three combined.

Tell us something we probably don’t know about Mongolia.

Mongolia sent a man into space in 1981. Jügderdemidiin Gürragchaa spent a total of 7 days, 20 hours and 42 minutes in space on the Soviet Salyut 6 space station.

## Mathematicians meet the Health Industry - SAMBa ITT4

I am starting my PhD research at the interface of probability and analysis, which you might think is quite far removed from industrial applications.

So did I, until I participated in SAMBa ITT4.

In June, we students, along with academics from Bath and around the world came together with representatives from our industrial partners, the pharmaceutical company AstraZeneca and the NHS's Royal National Hospital for Rheumatic Diseases (RNHRD), for an intensive week-long workshop. The workshop is one of SAMBa's Integrative Think Tanks (or ITTs), which are highlights of the SAMBa Programme:

ITTs are ‘big events’, focal points in the calendar of SAMBa activity, and central to its goals. ITTs are facilitated workshops in which academic, industrial, and other external partners present problems requiring research solutions, with lectures on relevant background given by experts. Students are expected to define routes to the solution of these problems, identifying the new research that will be necessary to make this possible.

Representatives from both partners came to Bath in advance of the ITT to brief us on the work that they do and the problems that they are facing. These visits were a part of our Student Led Symposia, which you can read more about in Owen's blogpost. It was clear that both partners were working in exciting application areas, including developing personalised medication and improving the efficiency of clinical trials. At this point, however, none of the problems jumped out to me from a mathematical point of view. Once we got to the ITT I was proven wrong.

The mix of people in the room generated lively discussion on the problems at hand and a huge range of ideas from all areas of mathematics were put forward to tackle them. Once the scattered ideas had been brought together into coherent groups, I decided to tackle one of AstraZeneca's problems: optimising the process of designing drugs. This seemed to be a problem in medical statistics, quite far from my own research interests, but I was quite happy to try working in a new area for a few days, as I had enjoyed doing at ITT3.

However, once we got into the problem, we found that it could be considered as a stochastic optimisation problem bringing this close to my own area of interest, and not too far from my proposed PhD topic. In fact, an undergraduate student is now doing further research along these lines over the summer, and we hope to pursue this further in the future.

The chance to work on an interesting industrial problem was not the only highlight of the ITT for me. Mathematics is often thought of as a solitary activity, but the ITT really encourages teamwork. The working groups which form allow students to work together with leading academics and experienced industrial partners - a really exciting and productive collaboration. Combined with regular coffee breaks, a dinner and plentiful after work drinks, this week was a brilliant opportunity to get to know new people from academia and industry alike.

So all in all, I found the ITT to be a fantastic experience, resulting in an insight into working with industry, lots of new acquaintances, and possibly even an industrial application for my research.