CCA 2014 prospectus - PhD in mathematical analysis at the University of Cambridge by Cambridge Centre for Analysis

CCA Prospectus 2014-15 PhD studies in mathematical analysis

Key facts The CCA PhD in mathematical analysis at a glance   

Closing date for applications: 15 January 2014 Admissions code: MAPM211 Duration: three‐four years

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Up to 10 students per year admitted Up to six studentships available for 2014 entry Essential: a 4‐year undergraduate degree (or 3‐year undergraduate plus Masters) in mathematics or a mathematics‐related subject; evidence of scholarly excellence

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Desirable: previous experience studying mathematical analysis Mailing list for further information at http://eepurl.com/bCXz1 Based at the Centre for Mathematical Sciences, University of Cambridge Covers all aspects of mathematical analysis including: o Geometric analysis o Partial differential equations o Probability o High dimensional and non‐parametric statistics o Image analysis o Approximation theory o Compressed sensing o Applications

Introduction ............................................................................................................................................ 5 What is the CCA? ..................................................................................................................................... 6 What are the possible career directions following a CCA PhD? ................................................................ 6 CCA student facilities .................................................................................................................................... 7 Centre for Mathematical Sciences ............................................................................................................... 7 Mathematics at the University of Cambridge .............................................................................................. 7 Course structure ...................................................................................................................................... 9 How does the CCA PhD differ from a standard PhD? ................................................................................... 9 What is the admission process for CCA? ...................................................................................................... 9 First year training in CCA ............................................................................................................................ 10 CCA community and events ................................................................................................................... 13 Conference funding for CCA students ........................................................................................................ 13 Events, short courses and seminars ........................................................................................................... 13 Admissions, funding and colleges .......................................................................................................... 14 The admissions procedure ......................................................................................................................... 14 Funding ....................................................................................................................................................... 15 Colleges at the University of Cambridge .................................................................................................... 15 Directory of staff and students .............................................................................................................. 17 The CCA team ............................................................................................................................................. 17 CCA students: 2010 cohort ......................................................................................................................... 26 CCA students: 2011 cohort ......................................................................................................................... 30 CCA students: 2012 cohort ......................................................................................................................... 34 CCA students: 2013 cohort ......................................................................................................................... 37

Introduction At the Cambridge Centre for Analysis, we believe that excellence in mathematical analysis requires a broad base of knowledge. At their best, mathematical analysts (whether in academic or industrial setting) should be able and willing to deploy a very wide range of techniques across pure, stochastic, computational and applied analysis. Mathematical analysis does not lend itself to restricted practices, excessive specialisation and narrowness of vision! It calls upon personal effort and excellence, but also upon teamwork and communication, whether with fellow experts or with the user community. This is the spirit we seek to instil among our students and, indeed, the entire structure of studies is designed to foster breadth of knowledge and collaboration.

What is the CCA? Cambridge Centre for Analysis was established in 2010 with initial dedicated support from EPSRC within the Centres for Doctoral Training programme. From 2014, CCA will be supported wholly through the University of Cambridge as part of its PhD programme in Mathematics. The scope of research in CCA is wide, with a unifying thread of mathematical analysis. The main research groups participating in CCA are:  Geometric Analysis and Partial Differential Equations  Probability and Statistics  Applied and Computational Analysis

What are the possible career directions following a CCA PhD? Some CCA students will follow a career path into the academic sector and others into the industrial sector. Topics pursued in CCA include both fundamental mathematical questions and more applied ones. Some examples of real‐world problems which both motivate academic research and make CCA‐trained analysts attractive to industry employers are as follows:  Oil reservoir design involves fluid mechanics, computational analysis and stochastic analysis;  The design of transport networks involves stochastic analysis, operation research and nonlinear PDEs;  The design of modern aero‐engines involves a combination of computational analysis, physical insight, modelling and experimental testing;  Data mining and making sense of large amounts of data requires stochastic computational and harmonic analysis, and numerical algebra.

CCA student facilities There are three CCA students in each office. Offices are large, modern and airy. Each room is equipped with three workstations with PCs and wi‐fi/Ethernet connections for laptops, as well as with bookshelves, filing cabinets, a whiteboard and a noticeboard. Several members of the core CCA team have their offices in the CCA area, and all new students are housed in offices close to each other. Other members of the CCA team are easily accessible elsewhere in CMS. The building also has several shared facilities: photocopier, stationery cupboard, toilets, a shower room and perhaps most importantly, a common room. The latter is equipped with coffee and tea making facilities, a fridge, storage space, microwave and, vitally to impromptu brain‐storming sessions, large white board (even the common room coffee tables have been designed with glass surfaces that can be written on with whiteboard markers).

Centre for Mathematical Sciences The CCA is located in the Centre for Mathematical Sciences (CMS) which is also home to:  The Isaac Newton Institute  The Department of Pure Mathematics and Mathematical Sciences (DPMMS)  The Department of Applied Mathematics and Theoretical Physics (DAMTP)  The Gordon and Betty Moore Library1 CMS is a self‐contained research community with a full range of useful facilities from covered bicycle racks to a large common room, the Maths Café, amazingly well‐equipped Moore Library (with 24 hour access), lecture rooms, an endless range of seminars, plus the student‐run Happy Hour on Friday afternoons. The purpose‐built and award‐winning CMS buildings provide a range of facilities for study and research in a pleasant setting with outstanding integration of public and private space.

Mathematics at the University of Cambridge The University of Cambridge has been a world‐class centre of mathematical research since the dawn of modern science and its list of illustrious alumni and personnel commences with the greatest of them all, Sir Isaac Newton. The examinations of the Cambridge Mathematical Tripos (the undergraduate Cambridge exams) are the oldest continuously taken university examinations in the world2! The list of Cambridge mathematicians in the last two centuries includes Arthur Cayley, Joseph Sylvester, George Airy, Charles Babbage, George Green, Sir George Gabriel Stokes, James Clark Maxwell, John Couch Adams, Godfrey Harold Hardy, John Edensor Littlewood, Srinivasa Ramanujan, Abram Besikovitch, 1

Gordon Moore, one of the founders of Intel, might be familiar to you through the ‘Moore Law’. Until the mid‐Nineteenth Century all University of Cambridge students were obliged to graduate first in the Cambridge Mathematical Tripos ‐‐ thus, Cambridge classicists, biologists and historians had better knowledge of mathematics than many a mathematician elsewhere…

Geoffrey Ingram Taylor, Paul Dirac, Alan Turing, George Batchelor, Sir William Hodge, Sir James Lighthill, Alan Baker, John Thompson, Stephen Hawking, Sir Michael Atiyah, Andrew Wiles, Richard Borcherds and Timothy Gowers. Cambridge is widely acknowledged as one of the world centres of mathematical research and of the training of young mathematicians. Contemporary Cambridge mathematics comprises of two departments, Department of Applied Mathematics and Theoretical Physics (DAMTP) and Department of Pure Mathematics and Mathematical Statistics (DPMMS)3. These two departments together form the Faculty of Mathematics and are constituent departments of the School of Physical Sciences. There are important structural differences between mathematical studies in Cambridge and most other UK universities. For example, undergraduate courses are accompanied by supervisions, namely study in small groups (typically two students), instructed by a senior mathematician or an advanced research student. Cambridge is a collegiate university and much of student life in Cambridge, both undergraduate and postgraduate, is college‐based (for more information on colleges, please refer to the Admissions, funding and colleges section of this prospectus).

Both “DAMTP” and “DPMMS” are pronounced by experts as single‐syllable words. It isn't too difficult but, unless you are fluent Czech speaker, takes some training in puckering your lips.

Course structure The course structure at CCA emphasises a breadth of knowledge and experience of mathematical analysis, as well as community, communication and collaborative work.

How does the CCA PhD differ from a standard PhD? The main objective of the CCA PhD is exactly the same as that of a standard PhD, that is, research leading to a PhD thesis. CCA is distinctive through the following:  An initial training programme develops a wide range of skills across analysis. This training involves collaborative projects by student teams and student presentations to the cohort;  Students build quickly a supportive network for their work, both within the year cohort and among academic staff, post‐docs and other PhD students in CCA. CCA students run their own seminar in analysis and mentor incoming students;  The CCA course encourages you to develop numerous valuable transferable skills which will be vital to your career, whether you choose to work in industry or further your academic study.

What is the admission process for CCA? This differs from the standard PhD. You will need to apply by January 15th. Shortlisted students will be interviewed in February and offers made soon after. Successful applicants will therefore have an assured place at an early stage in the year. Before applying, you are encouraged to discuss informally with possible supervisors the areas in which you are interested in working. CCA supervisors will be pleased to outline potential research topics. It will help our consideration of your application to know with whom you are interested in working and in what fields. This does not necessarily have to be narrowed down to a single supervisor or research problem. CCA encourages research across traditional subject boundaries and many of our students are jointly supervised for this reason. On the other hand, some supervisors will want to work on a committed basis from the start ‐‐ hence the importance of an informal discussion. People to contact for advice prior to application: Dr Nathanael Berestycki Probability N.Berestycki@statslab.cam.ac.uk Professor Thanasis Fokas Applied & Computational T.Fokas@damtp.cam.ac.uk Analysis Dr Anders Hansen Applied & Computational A.Hansen@damtp.cam.ac.uk Analysis Dr Alexei Kovalev Geometric Analysis & PDE A.G.Kovalev@dpmms.cam.ac.uk Professor Arieh Iserles Applied & Computational A.Iserles@damtp.cam.ac.uk Analysis Professor Clément Mouhot Geometric Analysis & PDE C.Mouhot@dpmms.cam.ac.uk Dr Richard Nickl Statistics R.Nickl@statslab.cam.ac.uk Professor James Norris Probability J.R.Norris@statslab.cam.ac.uk Professor Nigel Peake Applied & Computational N.Peake@damtp.cam.ac.uk Analysis Dr Carola Schoenlieb Applied & Computational C.B.Schoenlieb@damtp.cam.ac.uk Analysis 9

Dr Alexei Shadrin Dr Neshan Wickramasekera

Applied & Computational Analysis Geometric Analysis & PDE

A.Shadrin@damtp.cam.ac.uk N.Wickramasekera@dpmms.cam.ac.uk

First year training in CCA The first year of studies incorporates three main components: i. Cohort‐based teamwork projects across a wide range of topics in analysis; ii. Two courses chosen from the extensive menu of over 80 postgraduate courses from the Cambridge Master of Advanced Study in Mathematics4; iii. One or two Beginning Research Projects. The main distinctive feature of training in CCA is the structured programme running over the first six months, when students spend 50% of their time learning new areas of analysis (considered broadly ‐‐ see the schedule below) and the other 50% of time working in small teams on project assignments which are presented to the whole cohort. Our students find this method of learning stimulating and enjoyable and the joint activity leads to an inclusive and well‐integrated cohort. Study groups in analysis Students are put in groups of 3—4 students for study groups. Study group projects are tailored individually to the interests of each cohort and each team is lead by either a postdoc or an advanced CCA student. Additional taught courses in analysis Students also take two lecture courses from the wide range of Masters and Graduate courses in Cambridge. For some this will be to deepen knowledge in their research area but others benefit from filling gaps in their mathematical education and use these courses to back up the work on teamwork assignments. The following Masters courses are particularly relevant: Advanced Probability, Introduction to Partial Differential Equations, Statistical Theory, Numerical Solutions of Differential Equations, Contemporary Sampling Techniques and Compressed Sensing. Depending on individual preferences some students have a research supervisor agreed in advance, others are given an opportunity to explore further different subject areas and potential research supervisors. All students have research supervision arrangements in place at the latest by the end of Lent term, in March of their first year. Beginning Research Projects Beginning Research Projects are an introduction to the original research you’ll do over the course of your PhD, leading to a thesis in a topic of mathematical analysis. If, upon applying, you have a very clear idea of what direction you would like your studies to take at CCA and a supervisor can be found for you, then you will take one Beginning Research Project during your first 4

http://www.maths.cam.ac.uk/postgrad/mathiii/descriptions.pdf (PDF)

year. This project will eventually become the basis of your thesis. Your work will be assessed at the end of the first year. If you are not sure about which direction you’d like to take during your time at CCA, you will take two shorter Beginning Research Projects during your first year. These will both be supervised by CCA personnel, or colleagues from DAMTP, DPMMS, industry or other University of Cambridge departments5. You will be encouraged to explore, in these projects, the areas of mathematical analysis which interest you. By the end of the first year, one of these projects will form the basis of your PhD thesis. Choosing a PhD topic Many applicants to CCA have a very clear idea of the direction they would like to take in their thesis; many applicants have no clear idea at all; and some applicants change their mind over the course of the first year. There is no right or wrong way to approach choosing a thesis topic, but the CCA directors and personnel are on hand to help you to decide. We will attempt to follow your preference for topic, subject to its suitability for a dissertation in mathematical analysis or its applications, and subject to the availability of a suitable supervisor. Academic Support Every student has two PhD supervisors. The primary supervisor is responsible for directing the PhD studies and is an expert in the underlying subject matter. He or she is typically a member of the Maths Faculty, but (depending on the topic of your dissertation) some primary supervisors may be drawn from other University of Cambridge departments or from industry. The role of the secondary supervisor is twofold. Firstly, as backup when primary supervisor is absent or unavailable. Secondly, by providing extra breadth and expertise, perhaps in the subject matter of the dissertation, perhaps on another relevant topic or application. This is particularly important in multidisciplinary or applications‐rich topics, which transgress standard subject boundaries. Support during your first year Every student at CCA is assigned a supervisor from amongst the senior personnel of the Maths Faculty. Before arriving at CCA, you will also be paired with a mentor from amongst the current CCA student body, to play a more informal advising role and to help you get oriented. This scheme also means you will know at least one person by the time you arrive. We also set up online resources for each cohort of students, during summer before you arrive, so you can all meet and talk to your future colleagues, albeit remotely.

Current students are working with Faculty members in Cancer Research UK Cambridge, Department of Engineering, and Department of Chemical Engineering. We also have students with supervisors in industry, at Microsoft Research and EADS.

Secondments & industrial placements Depending on the nature of your dissertation, it might be useful to second you for a while to industry, a research centre or another university department (in Cambridge or elsewhere) during your final year of studies. The CCA has many links with industry; companies such as Rolls Royce, Schlumberger, Microsoft, EADS, and BP. We encourage our students to benefit from these links. Your supervisors will be able to suggest other academic institutions that you might consider visiting. The benefit of taking an internship or academic visit in your final year is that when you apply for jobs after your PhD, either academic or industry, you will have proven and recent experience beyond Cambridge. Your internship will also provide you with another supervisor, and therefore the chance to provide a broader variety of references for job applications at the end of your PhD. Other activities Students are also encouraged to take part in other CCA activities, such as organising the C.A.K.E. seminar series, public engagement and the on‐going transferable skills courses, designed to equip you with a range of skills, competencies, knowledge and experience necessary to thrive as a mathematical analyst. Thesis list A list of our current thesis topics can be downloaded from our website: http://www.maths.cam.ac.uk/postgrad/cca/files/thesislist.pdf

CCA community and events The CCA brings together many academics working in all fields of analysis in a supportive and exciting academic community.

Conference funding for CCA students Some conference funding is available to students. We strongly encourage your participation in conferences, meetings, study groups etc., outside Cambridge to engage with the broader, international mathematic community. Conference and workshop opportunities are circulated to all CCA students regularly, and your supervisors will also be able to advise you on conferences, summer schools and other events that you might like to attend.

Events, short courses and seminars Alongside the thriving research community at Cambridge and the many talks open to all students at CMS throughout the year, we offer a number of seminars and courses specifically for CCA students and those interested in mathematical analysis. C.A.K.E. (Cambridge Analysts' Knowledge Exchange) Run by CCA students themselves, this weekly seminar series is a platform for graduate students and post‐ docs of the analytic persuasion to present their work to the wider analysis community. Discussion and collaboration form an integral part of the series to encourage the cross‐fertilisation of ideas between people working in the many different fields of analysis. You can find out more about C.A.K.E. at www.talks.cam.ac.uk/show/index/32175. Transferable Skills Training Throughout the academic year, the Faculty of Mathematics offers a comprehensive, wide‐ranging program of training in transferable and technical skills: supervising students; giving presentations; using LaTeX; academic writing; career development; communication skills; preparing a poster for conferences; even negotiation and persuasion. We encourage all our students to make use of these excellent training opportunities. Public engagement To further develop transferable skills, we expect all our students to participate in some form of public engagement at least once during their studies. In the past, this has taken the form of designing and presenting a display during the CMS open day and hosting seminars for non‐mathematicians on a range of mathematical topics that may be useful in their particular field. Further information about events at CCA:  CCA talks listings: http://talks.cam.ac.uk/show/index/33003  CMS talks listings: http://talks.cam.ac.uk/show/index/12900  Events at the Isaac Newton Institute: http://www.newton.ac.uk/events.html

Admissions, funding and colleges For our 2014 course, we will take applications from 1 September 2013. The deadline for applications is 15 January 2014.

The admissions procedure We are looking for candidates who already have strong foundations in mathematical sciences, inclusive of successful performance in either a Master‐level degree or a four‐year (or longer) undergraduate degree. The prerequisites for the course:  a good6 four year undergraduate degree in mathematics or a mathematics‐related subject; or a three year undergraduate degree plus Master’s degree in mathematics or a mathematics‐related subject;  Be able to demonstrate scholarly excellence;  If English is not your first language, you will need to demonstrate competence in English7. Prior experience studying analysis is an advantage but we are aware that knowledge can be acquired; talent and attitude are arguably more important! If you are unsure whether you meet our criteria, please feel free to email the CCA office (cca@maths.cam.ac.uk) and we will advise you, in confidence and outside of the formal application procedure. Making an application You must apply through the University of Cambridge Graduate Admissions website where you can find a step‐by‐step guide to submitting your application: www.admin.cam.ac.uk/offices/gradstudy/ Use the CCA course code MAPM211 where asked. If you wish to be considered for funding from the Cambridge Home and European Scholarship Scheme, the Cambridge Trusts and/or the Gates Scholarship, you can do so on the application form using the designated sections. Interviews The deadline for applications is 15 January 2014. After this date, we will review all the applications and contact those who have been shortlisted to arrange an interview. 6

It is often difficult to compare degrees and grades in different countries and university systems: if you are unsure, the CCA office will be happy to advise informally before you make your application. 7 Please visit the Graduate Admissions website for further details http://www.admin.cam.ac.uk/students/gradadmissions/prospec/studying/entryreq/index.html#english

These interviews will take place shortly after the application deadline, either in Cambridge or via Skype video call. During the interview, the CCA directors will be keen to ascertain the extent of your mathematical knowledge and experience so far. All our applicants will have gaps in their knowledge of mathematical analysis and one of the functions of the interview is to judge the size of these gaps. There will be technical questions asked during the interview, but not as you might expect in exam. Rather, any technical questions will be asked in order to gauge your ability and knowledge of mathematics. Offers We contact all interviewees within a week or two of interview. If we make you an offer, your application will be passed to the Graduate Admissions office to be processed. You will receive a formal offer letter from the Graduate Admissions office. This letter will also outline the academic or administrative conditions of the offer (if any).

Funding We expect to offer full support (fees and stipend) for up to six students for admission in October 2014. You are strongly encouraged to apply for all funding sources for which you are eligible. If you are an overseas‐ or EU‐based applicant and want to apply for the Gates Cambridge, CHESS or CISS scholarships, you must do so on your CCA application. There is no additional application form for these scholarships. You may also fund your place at CCA through private funding sources. Please refer to the Graduate Admissions website for comprehensive information about the funding and schemes available to EU applicants: www.admin.cam.ac.uk/students/gradadmissions/prospec/studying/funding/index.html Please bear in mind that the closing dates for the major scholarships are much earlier than the closing date for CCA applications.

Colleges at the University of Cambridge The University of Cambridge has 31 colleges, which are autonomous, self‐governing communities where students and academics live, work, learn and socialise. Colleges are independent of the University, but have a complex relationship with it. The University and departments provide teaching and research supervision for graduate students; the colleges provide pastoral support within a stimulating academic community. Every student at the University of Cambridge belongs to a college. Each individual college is responsible for selecting students (who have secured a place on a University of Cambridge course) in accordance with University regulations. 15

If you receive an offer of a place on a University of Cambridge course, you are guaranteed a place in one of the colleges. On the application form, you are invited to select up to two colleges. Your selection of colleges will not affect our decision on your admission. It may affect your eligibility for funding, where funding is offered by a college. All students admitted to CCA will be admitted to a college though not necessarily your chosen colleges. If we make you an offer, your application will be sent to your first choice of college for consideration. If unsuccessful it will then go to your second choice. If you are unsuccessful in applying to your second choice of college, your application will be circulated to other colleges. When choosing a college, you might want to consider factors such as:  How likely is it that I will get accommodation in college?  Is there a travel fund or any other grants?  Which colleges have accommodation for families or couples?  Where is the college located? Further information about the Colleges:  A guide to colleges (includes links to individual college websites): http://www.admin.cam.ac.uk/students/gradadmissions/prospec/studying/colleges/index.html  A guide to colleges for graduate students: http:\www.admin.cam.ac.uk\students\gradadmissions\prospec\whycam\benefits.html  A guide to the structure of the University, departments and colleges: http://www.admin.cam.ac.uk/offices/communications/services/cambridgeand/cambridgewaywor ks.pdf  FAQs about the college system: http://www.admin.cam.ac.uk/offices/communications/services/cambridgeand/cambridgecolleges .pdf

Directory of staff and students The CCA team The CCA team comprises its Directors, Administrator, two post‐docs and two CCA lecturers, as well as a larger number of CCA members: senior personnel, mostly from the Faculty of Mathematics, concerned with all aspects of running the Centre. Dr Anthony Ashton is a member of the Department of Applied Mathematics and Theoretical Physics and works in the Applied and Computational Analysis group. He did his PhD under the supervision of Professor A.S. Fokas. His research interests include: novel approaches to elliptic boundary value problems, Lie groups in PDE, new approaches to rigorous problems in Linear PDE theory and certain aspects of mathematical physics. http://www.damtp.cam.ac.uk/people/a.c.l.ashton/ Dr Jonathan Ben‐Artzi is a Research Associate at DAMTP. He is interested in analysis and partial differential equations. Primarily, he studies problems with a strong physical motivation. These include problems in kinetic theory, stochastic homogenization and hydrodynamic limits. Jonathan also has a particular interest in the spectral theory associated to these problems, with applications to ergodic theory and computational complexity. http://www.damtp.cam.ac.uk/user/jb792/

Dr Nathanael Berestycki is a Reader in the Statistical Laboratory within DPMMS. His research focuses on probability theory, which tries to predict the largescale behaviour of complex random systems. While the motivations for studying such systems come from areas as diverse as statistical physics, population genetics or theoretical computer science, their study often requires a combination of ideas from combinatorics, spectral analysis and PDEs, which are blended together with fundamental probabilistic tools such as Martingales. Recent topics of interest include in particular branching and coalescing particle systems, selfinteracting stochastic processes, random propagation phenomena in inhomogeneous media, and the geometry of random motion. He is an associate editor of the journal Theoretical Population Biology. http://www.statslab.cam.ac.uk/~beresty/

Professor Natalia Berloff leads the Quantum Fluids Group at DAMTP. She is an applied mathematician with a range of research interests which focus on nonlinear waves, superfluidity, quantum fluids, Bose—Einstein condensates, superfluid turbulence. http://www.damtp.cam.ac.uk/user/ngb23/

Dr Ed Brambley is a Royal Society University Research Fellow in the Department of Applied Mathematics and Theoretical Physics, and is a Fellow of Gonville Caius college. He has worked on several aspects of the mathematics of acoustics, stability, and fluid‐solid interaction, particularly with applications in aircraft engines. http://www.damtp.cam.ac.uk/people/e.j.brambley/

Dr Colm Caulfield is a Reader and holds a joint appointment in DAMTP and the BP Institute for Multiphase Flow. The BP Institute was established in 2000 by a generous endowment from BP, which has funded faculty positions, support staff and the Institute building, in perpetuity. The Institute research focuses on fundamental problems in multi‐phase flow and is highly interdisciplinary, spanning six University departments: Earth Sciences, Chemical Engineering & Biotechnology, Chemistry, Engineering and Physics as well as DAMTP. Colm’s research activity is in the broad area of fluid mechanics, and has three main strands: turbulent mixing, (generalized) stability theory, and plume dynamics. In general, his research problems are motivated both by industrial challenges and environmental or geophysical applications. http://www.damtp.cam.ac.uk/people/c.p.caulfield/ Professor Mihalis Dafermos researches the partial differential equations of mathematical physics, especially the celebrated “Einstein equations” governing general relativity. An important theme of his work is applying the methods of the rigorous non‐linear analysis of PDEs to mathematically resolve conjectures of physical interest. Two central topics of his current research are the nature of generic singularities in gravitational collapse and cosmology and the nonlinear stability properties of black hole space‐times. Mihalis has been awarded the Adams Prize, the Bodossaki Prize, the Whitehead Prize of the London Mathematical Society and the Early Career Award of the International Association of Mathematical Physics. http://www.dpmms.cam.ac.uk/~md384/ 18

Dr Sophia Demoulini works on partial differential equations, primarily on nonlinear evolution equations. One area of interest is the study of evolution equations associated to a non‐convex energy in which she has proved the existence of various types of weak solutions in which the oscillatory character of the solution is described by a Young measure; a particular case of applied interest is the system of dynamic viscoelasticity. A second area of research is the analysis of solitons in nonlinear field equations (such as those arising in Ginzberg‐Landau theory), questions o interest including the existence and regularity of topological solitons, the well‐posedness of the Cauchy problem and analysis of various singular limits. http://www.dpmms.cam.ac.uk/people/s.demoulini/ Dr Amit Einav is a Research Assistant in DPMMS under Dr Clément Mouhot’s ERC grant. His main interest lies in kinetic theory, the mathematical theory describing the time evolution of a system consisting of large amount objects (such as Dilute Gas, Plasma and Galaxies). In particular, Amit is interested in the famous Boltzmann Equation, and the study of it as a mean field limit of linear models, such as Kac’s and McKean’s. Recent work of Amit in the field was to show the validity of a conjecture y Villani on the entropy‐entropy production rather in Kac’s, and McKean’s models, proving that in the most general case, the entropy method doesn’t yield a reasonable relaxation rate, and thus more restriction on the data is needed. Amit’s current work is a continual investigation of the entropy and entropy production in Kac’s and McKean’s models. https://www.dpmms.cam.ac.uk/people/a.einav/ Professor Thanasis Fokas holds the chair of Nonlinear Mathematics at DAMTP. He is the author or co‐author of three monographs and of more than 250 papers, as well as the co‐editor of seven books. ISI Web of Science includes him in the list of the most highly cited researchers in the field of Mathematics. He has published in different areas of science, ranging from abstract areas such as differential geometry and quantum algebras, to applied areas such as models of chronic myelogenous leukaemia (with J.B. Keller) and protein folding (with I.M. Gelfand). His current interests include boundary value problems for linear and integrable nonlinear PDEs, as well as mathematical techniques for medical imaging. Among his awards are the Naylor Prize of the London Mathematical Society, the Aristeion Prize in Sciences of the Academy of Athens, the Excellence Prize of the Bodossaki Foundation, and a Guggenheim Fellowship. He has received honorary degrees from five Universities and has been decorated as the Commander of the Order of Phoenix by the President of the Hellenic Republic. http://www.damtp.cam.ac.uk/people/t.fokas/ 19

Dr Julia Gog’s research is in the mathematics of infectious diseases. Current projects include: models of influenza strain dynamics; within‐host dynamics of influenza; in vitro dynamics of Salmonella; bioinformatic methods to detect RNA signals in viruses. Julia is part of the Cambridge Infectious Diseases Consortium. http://www.damtp.cam.ac.uk/people/j.r.gog/

Geoffrey Grimmett is the Professor of Mathematical Statistics at the Statistical Laboratory of DPMMS. He works in probability theory and rigorous statistical mechanics, with special emphasis on the theory of large interacting systems including percolation and interacting particle processes. In addition to his research publications, he is the author of two student textbooks on probability, and three research volumes. http://www.dpmms.cam.ac.uk/people/g.r.grimmett/

Dr Anders Hansen is a Royal Society University Research Fellow and lecturer at DAMTP. His research interests are mostly in applied functional analysis, computational harmonic analysis, inverse problems and computability theory/complexity theory. This includes computational operator/spectral theory, sampling theory, compressed sensing, mathematical signal processing, medical imaging, as well as complexity theory for computational problems in infinite dimensions. One of his current focuses is sampling and sub‐sampling theory for infinite‐ dimensional problems with applications in medical imaging such as Magnetic Resonance Imaging and Computed Tomography. http://www.damtp.cam.ac.uk/user/na/people/Anders/ Professor Arieh Iserles holds the chair in Numerical Analysis of Differential Equations at DAMTP. His current research focusses on two themes: geometric numerical integration (the theory and practice of computational algorithms for differential equations that recognise and respect geometric features of the solution) and computation in the presence of high oscillation (in particular, highly oscillatory quadrature, computation of highly oscillatory differential equations and their applications in electronic engineering, and the investigation of spectra of highly oscillatory integral kernels and their applications in laser engineering). He is a past‐Chair of Society for Foundations of Computational Mathematics, Managing Editor of Acta Numerica and of Foundations of Computational Mathematics, Editor‐ in‐Chief of IMA Journal of Numerical Analysis. He was awarded the Lars Onsager Medal and in 2012 received the David Crighton medal. http://www.damtp.cam.ac.uk/people/a.iserles/ 20

Frank Kelly is Professor of the Mathematics of Systems at the Stats Lab and Master of Christ's College. His main research interests are in random processes, networks and optimization. He is especially interested in applications to the design and control of networks and to the understanding of self‐regulation in large‐scale systems. Frank has received several prizes for his work, inclusive of the Davidson Prize of the University of Cambridge, the Guy Medal in Silver of the Royal Statistical Society, the Lanchester Prize of the Institute for Operations Research and the Management Sciences and the Naylor Prize of the London Mathematical Society. He is a Fellow of the Royal Society. From 2003 to 2006 Frank Kelly served as Chief Scientific Adviser to the United Kingdom's Department for Transport. http://www.dpmms.cam.ac.uk/people/f.p.kelly/ Dr Chanwoo Kim received his B.S. from Seoul National University in 2006. He received his PhD in Mathematics from Brown University in May 2011. He joined the DPMMS at the University of Cambridge as the Herchel Smith Research Fellow in June 2011, as well as the Cambridge Centre for Analysis. Chanwoo's current research is concerned with partial differential equations and their applications, such as the boundary effects and external field effects of the kinetic equation (Boltzmann and Vlasov equations) and the stability/instability of free boundary problem in fluid dynamics. http://www.dpmms.cam.ac.uk/people/c.w.kim/ Dr Alexei Kovalev is a Lecturer in DPMMS. His research area is `special' differential‐geometric structures and their moduli spaces. These structures can often be expressed as solutions of partial differential equations, typically non‐linear and elliptic, on manifolds or vector bundles. At present I am concerned with Ricci‐flat 7‐manifolds of holonomy G2 and their calibrated minimal submanifolds. Other special geometries of interest include Calabi‐Yau and hyper‐Kähler manifolds and also aspects of anti‐self‐ duality in four dimensions.

Professor Clément Mouhot’s research at DPMMS focuses on partial differential equations from physics, especially the two main equations of kinetic theory: the celebrated ‘Boltzmann equation’ governing rarefied gas dynamics and ‘Vlasov‐‐Poisson equation’ governing plasmas and galaxies dynamics. He is using techniques from nonlinear analysis, spectral theory and probability in order to address questions and conjectures of physical interest. Recently he has been interested in several topics: the rate of convergence in the second principle of thermodynamics (hypocoercivity theory, spectral theory for non‐symmetric opera tors), the so‐called ‘Landau damping effect’ in plasma physics, and the derivation of nonlinear 21

PDEs from particle systems by mean‐field limit. http://cmouhot.wordpress.com/ Dr Richard Nickl is a Reader in the Statistical Laboratory of DPMMS. His work is about the mathematical foundations of nonparametric statistics, a field that lies at the intersection of statistics, probability, analysis and approximation theory. He uses modern tools from approximation theory, such as wavelets, to reconstruct infinite‐dimensional statistical parameters, such as densities, regression functions etc., which can then be estimated from a random sample. One of the key aspects of his research is to understand the interaction of these approximation theoretic tools with the data. He successfully applied modern tools from probability theory and functional analysis, the random fluctuations such as the ‘concentration of measure phenomenon’, to prove that certain nonparametric procedures possess optimality properties for statistical inference. http://www.statslab.cam.ac.uk/Dept/People/nickl.html Professor James Norris is a Director of CCA. He is Professor of Stochastic Analysis in DPMMS and Director of the Statistical Laboratory. He researches the formulation and analysis of mathematical models for random processes of coagulation and aggregation. His research interests also span stochastic differential equations, Malliavin calculus, analysis of heat kernels, fluid limits for Markov chains and applications, homogenization and stochastic computational algorithms. He is Associate Editor of Potential Analysis and Probability Theory and Related Fields and is Chair of the Committee on Stochastic Processes and their Applications. He is a recipient of the Rollo Davidson Prize. http://www.statslab.cam.ac.uk/~james/ Professor Gabriel Paternain is Professor of Mathematics at DPMMS. His research interests are in geometry and dynamical systems. https://www.dpmms.cam.ac.uk/~gpp24/

Nigel Peake is a Director of CCA and Professor of Applied Mathematics in DAMTP. His general research area is in the mathematical modelling of unsteady fluid flows, especially those found in aeronautics. He is particularly interested in noise generation by aeroengines, the vibration of fluid‐loaded structures and hydrodynamic stability. Current research projects include investigation of algebraic instability and transient growth in vortices, diffraction theory, flutter instability of elastic plates and noise generation by new open‐rotor aircraft engines. Nigel is an Associate Editor of the Journal of Fluid Mechanics, Vice‐President of the Institute of Mathematics and its Applications and is a member of the Council of the Smith Institute for Industrial Mathematics and Systems. http://www.damtp.cam.ac.uk/people/n.peake/ Professor Richard Samworth is a Professor in the Statistical Laboratory within DPMMS. His work covers theoretical and methodological aspects of Statistics, as well as computational issues and applications. He is interested in developing new statistical theory and methods to tackle the challenges posed by modern statistical applications, which may even involve situations where the number of `unknowns', such as parameters, is much larger than the sample size. Another area of interest is the use of convex analysis to study fully automatic methods for the estimation of a multidimensional probability density function from a sample of data. Richard was awarded the Royal Statistical Society Research prize for 2008. He is the Honorary Secretary of the Research Section Committee of the Royal Statistical Society, and an Associate Editor of the Journal of the Royal Statistical Society, Series B. http://www.dpmms.cam.ac.uk/people/r.j.samworth/ Dr Carola Schoenlieb is a Lecturer in Applied and Computational Analysis at DAMTP. Her research interests range from nonlinear partial differential equations to computational and convex analysis, with applications in digital image and signal processing. She studies fourth‐order equations and nonsmooth optimization problems, like the total variation functional, for image reconstruction, especially for so‐called image inpainting. Moreover, she works on computational methods for large‐scale problems appearing in 3‐ and 4‐D imaging. Within this context she is interested in both the theoretical and numerical analysis of the problems considered as well as their practical implementation and their use for real‐world applications like arts restoration and medical imaging. http://www.damtp.cam.ac.uk/user/cbs31/Home.html

Dr Alexei Shadrin is a Senior Lecturer at DAMTP and a member of the Numerical Analysis Group therein. His area of interests lies within Approximation Theory and includes, more specifically, various aspects of spline and polynomial interpolation, shape‐preserving approximation, Markov‐ and Landau‐Kolmogorov‐type inequalities between derivatives (which are closely related to problems of numerical differentiation). His current research topics are Karlin's conjecture, Zolotarev polynomials and exact constants in the Jackson‐Stechkin‐type inequalities. He is an Editor of Constructive Approximation and of East Journal on Approximations. http://www.damtp.cam.ac.uk/people/a.shadrin/ Dr Sumeet Singh is a Senior Lecturer in Engineering Statistics (Dept. of Engineering), an Affiliated Lecturer at the Statistics Laboratory and a Fellow of Churchill College. His primary research interest is Monte Carlo based computational statistics: theory, methodology and applications. http://www‐sigproc.eng.cam.ac.uk/~sss40/

Dr Perla Sousi is a Junior Research Fellow at Emmanuel College. She completed her PhD in Cambridge under the supervision of Professor James Norris. Her research interests lie in Probability theory and its applications. In particular, she works on problems involving spatial random processes, both continuous and discrete. This is an especially appealing area, because of its connections to other areas of mathematics, such as analysis, combinatorics and its applications to other sciences. Currently she is most excited by the topic of mixing times for Markov chains, an area on the interface of mathematics, statistical physics and theoretical computer science. In statistical physics, the mixing time represents how long it takes a physical system to reach equilibrium. In computer science, the mixing time is the main component in the running time of many important randomized algorithms. http://www.statslab.cam.ac.uk/~ps422/ Dr Ulrich Sperhake is a member of the Department of Applied Mathematics and Theoretical Physics General Relativity research group. His current research interests are Numerical Relativity, Black Holes as sources of Gravitational Waves, High‐Energy Collisions of Black Holes. http://www.damtp.cam.ac.uk/people/us248/

Dr David Stuart is a Reader in nonlinear PDE in DAMTP. His research is mainly directed towards the analytic study of solitons in nonlinear classical field theories (such as Yang‐Mills and Einstein equations), and related problems in nonlinear analysis. One class of problems under study arises in the analysis of various singular limits such as the adiabatic (or moduli space) approximation in self‐dual gauge theories, and the test‐particle and Newtonian limit in general relativity. Other problems of current interest include solitons in constructive quantum field theory, attempts to develop scattering theory for solitons in non‐integrable PDEs and the existence and properties of solitons by variational and heat flow methods. http://www.damtp.cam.ac.uk/people/d.m.a.stuart/ Professor Simon Tavaré is Senior Group leader at CRUK Cambridge Research Institute and a Professor at DAMTP. His research interests lie in statistics and computational biology, with particular emphasis on statistical inference in molecular biology; human genetics; population genetics; molecular evolution; evolutionary cancer genomics; microarray and second‐generation sequencing analysis; fly tracking; stochastic computation; probabilistic combinatorics. http://www.damtp.cam.ac.uk/people/s.tavare/

Dr Mike Tehranchi is a lecturer at the Statslab, within the Department o Pure Mathematics and Mathematical Statistics. His research interests are stochastic analysis and financial mathematics; interest rate and implied volatility models; utility maximization problems; stochastic evolution equations in infinite dimensions. http://www.statslab.cam.ac.uk/~mike/

Dr Tuomo Valkonen is a Research Associate at DAMTP. Ccurrent research concentrates on variational discontinuity‐preserving approaches to image processing, particularly a discontinuous transport equation for image interpolation, and higher‐order regularisation techniques. The earlier work focusses on optimisation methods for finite‐dimensional problems applied to clustering, and diff‐convexity. http://tuomov.iki.fi/

Dr Neshan Wickramasekera is a Reader in DPMMS. His research interests are in Geometric Analysis. In particular, he studies solutions to nonlinear geometric problems with variational structure, such as critical points of area (minimal submanifolds) in a given Riemannian manifold. These solutions typically carry small sets of unavoidable singularities. Neshan's recent work has focused on finding easy‐to‐check conditions for smoothness of stable critical points of the co‐dimension 1 area functional (stable minimal hypersurfaces), and on developing methods for understanding the nature of their singularities in the absence of these conditions. http://www.dpmms.cam.ac.uk/people/n.wickramasekera/ Dr Shiwu Yang is a postdoctoral research associate at CCA. https://www.dpmms.cam.ac.uk/people/s.yang/

CCA students: 2010 cohort

Marc Briant is from Bordeaux, France. After a scientific Baccalaureate (French equivalent to A‐level), he did the Preparatory Classes for admittance to the French Grandes Écoles. In 2006 he was accepted at Supaero (now part of Institute ISAE: Space and Aeronautics Superior Institute, based in Toulouse, France), an engineering school specialising in Space and Aeronautics. At the same time he did a Bachelor's Degree in Pure Maths followed by a Master's degree in Applied Maths at the University of Toulouse Paul Sabatier. In 2008‐2009 he took the Agregation of Mathematics. He would like his skills in mathematics to be useful (which is why he chose to study applied maths rather than pure maths). He would like to apply mathematics to real issues such as pole studies, animal behaviours, medicine, and to always apply mathematics to different problems, different topics in order to share knowledge with people for a real purpose. http://www.maths.cam.ac.uk/postgrad/cca/people/mbriant.html

Damon Civin is originally from Benoni, South Africa and went to High School at Benoni High, he then moved to Pretoria to study Mathematics at the University of Pretoria. He completed his BSc (Hons) in 2008 and MSc in Applied Mathematics in September 2010 before joining CCA at the end of that year. Damon is working on the analysis of the stability of solutions of the Einstein equations under the supervision of Professor Mihalis Dafermos. Beyond mathematics, he formerly played in the experimental band Sticky Antlers and worked with the KRNGY independent music label in South Africa. Damon is a member of the Sons of Da Gama team in the Mongol Rally 2012, driving from Cambridge, UK to Ulaan Bator, Mongolia to raise funds for Project Rhino KZN and the Lotus Children's Centre. http://damoncivin.wix.com/home Spencer Hughes is from the UK and completed both his BA degree and the Certificate of Advanced Study in Mathematics at Cambridge. His research interests are in geometric PDE and geometric measure theory. In particular, he is working on problems involving branched minimal surfaces under the supervision of Dr Neshan Wickramasekera. With his officemates, Bati and Kostas, Spencer blogs about mathematics: http://blameitontheanalyst.wordpress.com/ http://spencerthughes.wordpress.com/ http://www.maths.cam.ac.uk/postgrad/cca/people/shughes.html

Anastasia Kisil is originally from Odessa, Ukraine. She took her BA in Mathematics and Master of Advanced Study at the University of Cambridge in Trinity College. She is interested in all areas of mathematical analysis and has had work published in Advances in Applied Clifford Algebras and Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Currently she is working on Wiener‐Hopf methods in Partial Differential Equations. http://www.maths.cam.ac.uk/postgrad/cca/people/akisil.html http://www.damtp.cam.ac.uk/user/ak528/

Bernd Kuhlenschmidt is originally from Osnabrueck in Germany. He holds a Bachelor of Science in Information Systems from University of Muenster, Germany, and progressed to Studies in Mathematics at the same institution (including the vordiplom in Mathematics). He then took Part III (or the Certificate of Advanced Study in Mathematics) at the University of Cambridge. His main interests are Computational Statistics and Stochastic Calculus. In particular, he works on Monte Carlo methods (Particle Filters, Markov Chain Monte Carlo) for computation and statistical inference, and is also very interested in Mathematical Finance. http://www.maths.cam.ac.uk/postgrad/cca/people/bkuhlenschmidt.html Sara Merino is originally from Barcelona, Spain. Before coming to CCA she studied Mathematics and Statistics at the Technical University of Catalonia in Barcelona, Spain, and the completed an Engineer degree at the National School of Computer Sciences and Applied Mathematics in Grenoble, France. She also holds a Master of Research degree in Applied Mathematics from Joseph Fourier University, Grenoble, France. Her research interests are related to the study of Partial Differential Equations (PDE), in particular, Kinetic Theory and the use of Stochastic Analysis applied to PDE. She also enjoys learning didactics, philosophy and the history of science. http://www.maths.cam.ac.uk/postgrad/cca/people/smerino.html http://sara‐merino‐aceituno.blogspot.com/ Ed Mottram is from Lincoln, UK, and has studied Mathematics at the University of Cambridge since 2006: first as an undergraduate and then as a Part III student. His areas of interest are mathematical analysis and combinatorics. http://www.maths.cam.ac.uk/postgrad/cca/people/emottram.html

Kostas Papafitsoros, from Athens, Greece, took a Diploma in Applied Mathematics and Physics at the National Technical University of Athens, followed by a Postgraduate Diploma (Masters) in Pure Mathematics. He then studied for an MSc in Mathematical Modelling and Scientific Computing at the University of Oxford. His current work is on higher order regularisation methods on image processing, supervised by Dr Carola Schoenlieb. Kostas is working on using techniques from the areas of calculus of variations, geometric measure theory and I also do some numerics. Other areas of interest are real and functional analysis; measure theory; infinite combinatorics; numerical linear algebra. With his officemates, Bati and Spencer, Kostas blogs about mathematics: http://blameitontheanalyst.wordpress.com/ http://www.maths.cam.ac.uk/postgrad/cca/people/kpapafitsoros.html Florian Pinsker was born in Tuebingen, Germany, and raised in Vienna, Austria. Prior to arriving at CCA he studied for a Diploma in theoretical physics, alongside courses in maths and philosophy. He is doing research in nonlinear dynamics with fields of expertise are Exciton‐Polariton condensates, atomic Bose‐Einstein condensates and more generally quantum many body systems. Florian’s research invokes computational and rigorous analysis of e.g. nonlinear Schrödinger‐type equations or complex Ginzburg‐Landau‐type equations. In particular I am interested in the study of phase transitions of such systems. http://www.maths.cam.ac.uk/postgrad/cca/people/fpinsker.html Kolyan Ray grew up in France and Switzerland. He took an International Baccalaureate at the International School of Geneva, Switzerland, before studying BA Mathematics and Part III (the Certificate of Advanced Study in Mathematics) at the University of Cambridge. His area of interest is mathematical statistics and probability. http://www.maths.cam.ac.uk/postgrad/cca/people/kray.html

Bati Sengul was born in Turkey and has lived in England since 1998. He did an undergraduate degree at the University of Bath, after which he completed the Part III (Certificate of Advanced Study in Mathematics), at the University of Cambridge. His current work is on coalescent processes with my supervisor Nathanael Berestycki. It involves a mix of discrete and continuous techniques, such as viewing coalescent processes as a bunch of excursions of a Brownian motion. Bati is also interested in percolation and random graphs. There are many cute problems that arise from these fields that are interesting to answer. With his officemates, Kostas and Spencer, Bati blogs about mathematics: 29

http://blameitontheanalyst.wordpress.com/ www.batisengul.co.uk http://www.maths.cam.ac.uk/postgrad/cca/people/bsengul.html

CCA students: 2011 cohort

Luca Calatroni is from Cigognola, a little village near Pavia in the north of Italy. He completed his BSc in Mathematics (2009) and his MSc in Applied Mathematics (2011) at the University of Pavia. His research is related to non‐ smooth variational methods for image processing, under the supervision of Dr Carola‐Bibiane Schönlieb. He has been working on splitting dimensional methods for higher‐order imaging problems and is currently working also on optimal parameter estimation in total‐variation denoising under PDE constraints (joint work with Juan Carlos De Los Reyes, University of Quito). His interests are in applied analysis, calculus of variations, analysis of evolution PDEs and numerical methods for optimal control. Beyond mathematics, he likes every sort of music and is addicted to travelling and to playing the piano. http://lucacalatroni.weebly.com/ http://www.maths.cam.ac.uk/postgrad/cca/people/lc524.html Alberto Coca took the Licenciature en Matemáticas at Universidad Autónoma de Madrid (2006‐10). He then took an MSc in Mathematics and Finance at Imperial College London (2010‐11) and submitted his thesis on the use of Bayesian networks to model stress events in banking. Alberto enjoys any types of maths, but has a special interest in pure mathematics: probability, statistics, analysis and geometry. Despite his rather pure approach, Alberto enjoys solving real‐life problems and plans on researching topics with tangible applications. He has a strong belief in making mathematics (and science) understandable to everybody. Outside of maths, Alberto enjoys sports (windsurfing, snowboarding and football), music and socialising with friends and family (if possible, under the Spanish sun). http://www.maths.cam.ac.uk/postgrad/cca/people/ac776.html Kevin Crooks is from Preston, UK. He did an MMath at Warwick University from 2007‐2011 where he particularly enjoyed the PDE existence/uniqueness theory. His fourth year project looked at the mathematics behind Bose‐Einstein condensation. Outside of maths, Kevin enjoys rock climbing, hill walking and skiing. http://www.maths.cam.ac.uk/postgrad/cca/people/kmc47.html

Eoin Devane lives in West Wickham, just south of London, U.K. He studied for the MMath in Mathematics at the University of Oxford, from 2007 until 2011. He is particularly interested in the applications of mathematical analysis to problems of physical and industrial relevance. http://www.maths.cam.ac.uk/postgrad/cca/people/esmd2.html

Milana Gataric completed her BSc in Mathematical Engineering in 2009, and MSc in Applied Mathematics in 2010, both at the University of Novi Sad, in Serbia. For an\‐other year, she stayed at the same university working as a research assistant in a research group for numerical analysis, before joining the CCA in October 2011. Milana's mathematical interests vary across different fields of mathematical analysis, and discrete mathematics as well. Right now, she is focusing on expanding her theoretical knowledge in different areas of mathematical analysis, so she can eventually apply it in the real world. http://www.maths.cam.ac.uk/postgrad/cca/people/mg617.html Adam Jones is from Swindon, U.K. He read for the MMath at Balliol College, University of Oxford, between 2007 and 2011. In the fourth year Adam largely focused on probability theory and wrote his dissertation on some of the relationships between discrete random objects (in particular, trees and their encodings) and their continuous scaling limits. His main areas of interest are in probability theory. http://www.maths.cam.ac.uk/postgrad/cca/people/aj398.html Alex Jones is from Northampton, U.K. Prior to CCA, Alex took a BA and MMath at the University of Cambridge, from 2007‐2011. Recent studies have been in probability and analysis, although he has interest in all areas related to mathematical analysis. http://www.maths.cam.ac.uk/postgrad/cca/people/adj27.html

Natalia Kudryashova joined CCA after finishing Part III Mathematics at Cambridge. She has an interest in various areas of mathematical analysis and their applications to real world problems. http://www.maths.cam.ac.uk/postgrad/cca/people/nk375.html

Guolong Li is originally from China and has lived in Belgium since the age of 13. He took the Mathematical Tripos at University of Cambridge before commencing his studies at CCA. He is interested in various aspects of pure maths and probability related subjects, with his main interests being in stochastic analysis and numerical analysis. http://www.maths.cam.ac.uk/postgrad/cca/people/gl288.html

Kornel Maczyński is from Bielsko‐Biala, a city in southern Poland. He completed a Bachelor's course in Computer Science and Masters in Mathematics at the University of Warsaw. He has always been primarily interested in mathematical analysis. In summer 2008, he visited Dublin City University and worked on some problems in numerical integration of highly oscillating functions. Later, his interests shifted towards PDEs. In his Masters thesis he applied nonlinear semigroups approach to a singular weighted mean curvature flow which was described by a partial differential equation. Beyond Mathematics, Kornel enjoys wildlife photography, playing the piano and hiking in the mountains. http://www.maths.cam.ac.uk/postgrad/cca/people/km526.html Clarice Poon was born in Hong Kong and has lived in the UK since 2001. She completed the MMathComp in mathematics and computer science at the University of Oxford. Her areas of interest include mathematical signal processing, sampling theory and compressed sensing. She is currently investigating ideas related to infinite‐dimensional compressed sensing under the supervision of Anders Hansen. http://www.damtp.cam.ac.uk/user/cmhsp2/ http://www.maths.cam.ac.uk/postgrad/cca/people/cmhsp2.html

Alberto Gil Ramos was born in Porto, Portugal on December 30, 1986. He received the Licenciatura in Mathematics degree and the Master in Mathematics degree from the Faculty of Sciences of the University of Porto, Portugal, in 2007 and 2010, respectively, and has received scholarships from Fundação para a Ciência e a Tecnologia, Instituto de Telecomunicações and Fundação Calouste Gulbenkian. His mathematical areas of interest include asymptotic expansions, integral transforms and measure and probability. http://www.maths.cam.ac.uk/postgrad/cca/people/agcpr2.html Martin Taylor is from Carlisle in the north of England. He studied for an MMath at the University of Warwick between 2007 and 2011. His research interests include partial differential equations and harmonic analysis. http://www.maths.cam.ac.uk/postgrad/cca/people/mt546.html

Lukas Vermach is originally from Prague, Czech Republic. At Charles University, Prague, he took a BSc in Physics (2006‐‐2009) followed by a MSc in mathematical modelling in physics (2009‐‐2011). His Master's thesis was on modelling of ferromagnetic shape memory alloys. Lukas' main areas of interest are partial differential equations and calculus of variations, and also the didactics of physics. Outside of mathematics, he loves ice hockey and football. http://www.maths.cam.ac.uk/postgrad/cca/people/lv260.html Zipeng Wang received a Masters from Penn State University, USA, under the supervision of Professor Alberto Bressan. His main areas of interest are harmonic analysis, PDEs with objectives of nonlinear wave equations and hyperbolic conservation law. Zipeng has had his work published in the {\it Journal of Differential Equations and Analysis & Applications. Outside of mathematics, Zipeng enjoys music (especially classical and baroque), playing the piano, and mountain climbing. http://www.maths.cam.ac.uk/postgrad/cca/people/zw255.html

CCA students: 2012 cohort

Alex Bastounis grew up in the small town of West Wickham in Kent. He completed an MMath at Warwick where he studied courses ranging from PDE theory to Stochastic processes. His interests lie in the vast majority of topics that could be considered analysis but generally prefers applied analysis ‐ Alex enjoys seeing how the various abstract functional analytic theorems that mathematicians produce apply to model real life phenomena. Whenever he has spare time he spends it visiting new places with friends and is also an avid motorsport fan. http://www.maths.cam.ac.uk/postgrad/cca/people/ab2053.html Tom Begley was born in Bristol and grew up in Poole in the south of England. He studied for an MMath at the University of Bath (2008‐‐2012) focussing mostly on topics in pure mathematics and particularly those relating to analysis. His mathematical areas of interest are still fairly broad, but he is interested in PDE theory. Outside of mathematics, Tom loves to go skiing, hiking, diving and enjoys visiting new places. http://www.maths.cam.ac.uk/postgrad/cca/people/tcb33.html Helge Dietert is originally from Hildesheim in northern Germany. He has been studying Mathematics in Cambridge for his bachelor (2008‐‐2011) and masters (2011‐‐2012) degrees whilst keeping a strong connection to Physics. He is interested in a broad spectrum of Mathematics, including some physical applications, especially in kinetic theory, statistics and probability. http://www.maths.cam.ac.uk/postgrad/cca/people/hgwd2.html

Rob Hocking is from Calgary, Canada. His undergraduate degree was in Maths and Physics and his Masters was in Computer Science, focussing on Scientific Computing, both from the University of British Columbia. His interests are broad, including topics in pure mathematics/physics, computing and computer graphics. As an informal project, he is currently applying photon mapping techniques from computer graphics to study gravitational lensing. Outside of mathematics, Rob is a runner and enjoys hiking. He is also a huge fan of Thai and Indian food, which he enjoys cooking at home. http://www.maths.cam.ac.uk/postgrad/cca/people/lrh30.html 34

Tom Holding is working with Professor Clément Mouhot.

Henry Jackson studied for an MMath in Maths & Statistics at St. Peter's College Oxford, finishing in 2012. His main interests there were in probability theory and statistics. I'm really looking forward to the breadth of courses available at the CCA. Beyond maths, Henry enjoys playing the trumpet, listening to all sorts of music, and any form of comedy. http://www.maths.cam.ac.uk/postgrad/cca/people/hrj28.html

James Mathews is from East Grinstead in West Sussex. He did his MMath Warwick University from 2008‐‐2012 and enjoyed studying PDEs. He would like to apply the analysis he has learnt to industrial problems. Outside of mathematics, James sails (competing in the University finals) and enjoys cycling. He has spent the last two summers teaching Mathematics in secondary schools in South Africa and Tanzania as a volunteer for Warwick in Africa. http://www.maths.cam.ac.uk/postgrad/cca/people/jrm214.html

Kim Moore is from Manchester, UK. She has spent the last four years studying for an MMath at the University of Bath. During this time she mainly focused on pure maths, so is looking forward to broadening her knowledge with courses in applied maths and probability at the \CCA. She hopes to use technique from all subfields of analysis in her research, and see how analysis can be applied to other areas of maths and real world problems. Beyond mathematics, Kim enjoys reading hiking, listening to and playing music, and playing any sport. http://www.maths.cam.ac.uk/postgrad/cca/people/km492.html

Parousia Rockstroh is from the United States. He completed his BSc in Mathematics at Harvey Mudd College (Claremont, California) in 2008. Following this, he completed an MSc at Simon Fraser University in Vancouver, with a thesis on a computational method for solving intrinsic geometric PDEs on surfaces with singularities. Parousia's mathematical interests lie in PDEs and geometric analysis with a particular emphasis on geometric evolution and heat equations. He is particularly interested in applying and using methods from these areas to study techniques in image processing and related fields. http://www.maths.cam.ac.uk/postgrad/cca/people/pr367.html Giles Shaw was born near Cambridge but has lived in Worcestershire for the last ten years. He took his MMath degree at Worcester College, Oxford, between 2008 and 2012. In his third year he worked on a summer project with the aim of characterising gradient young measures on sets of four matrices. During his fourth year, he primarily studied functional analysis and its applications to PDE theory, but found time for some number theory too. Mathematically, he has so far been interested in functional analytic and variational methods for PDEs, especially nonlinear ones. At CCA, Giles is looking forward to improving his knowledge of Probability Theory and Numerical Analysis whilst deciding on areas for further research. Outside of Maths, Giles has a wide variety of interests: reading and playing guitar, debating on most issues and follow world events avidly. On the sporting side of things, he was a member of the Oxford University Shorinji Kempo club (a martial art) and has recently taken up powerlifting. http://www.maths.cam.ac.uk/postgrad/cca/people/gwhs2.html Vittoria Silvestri is from Rome, Italy. She completed her BSc degree with Honours in Mathematics at University of Rome “La Sapienza” in July 2012 with her dissertation in “Random continued fractions”. She then studied for a year at University of Birmingham, September 2011 ‐‐ June 2012 and completed her MSc degree with Honours at University of Rome in July 2012. Her dissertation was “Random walks on quasi one dimensional lattices with periodic heterogeneity”. Vittoria is mainly interested in stochastic processes and their applications to real‐world problems. http://www.maths.cam.ac.uk/postgrad/cca/people/vs358.html

Tim Talbot is originally from Derbyshire. Prior to CCA, Tim took the University of Cambridge Tripos in Mathematics. He is now working with Alexei Kovalev on gluing theorems for Ricci‐flat manifolds: given two complete such manifolds with sensible asymptotic behaviour, it is likely they can be joined together. Questions then arise such as "are there any Ricci‐flat metrics on the joined manifold that are not from this gluing?". At present, this is restricted to the simpler Kaehler case.

Marcus Webb is originally from originally from Bolton (near Manchester, UK). He studied for MMathCompSci at Worcester College, Oxford, 2008 to 2012, and won the Hoare prize for best overall performance. He concentrated on mathematics more than computer science. His general research interest is in numerical analysis and applied functional analysis. In layman's terms, He is interested in how mathematical problems can be solved using a computer. His PhD supervisor is Professor Arieh Iserles. For more specific interests, and materials that may be of interest to you such as his first year CCA miniproject reports, visit Marcus’s homepage. Outside of mathematics: main hobby is rowing, and rows for Jesus College in the inter‐college competitions (sometimes against other CCA students!). He loves to go for walks with his wife Yee Chien. http://www.maths.cam.ac.uk/postgrad/cca/people/mdw42.html

CCA students: 2013 cohort

Dominic Dold was born in southern Germany and went to university in Heidelberg, where he completed an undergraduate degree in Mathematics and Physics in 2012. Afterwards he changed to Cambridge and did Part III at Magdalene College. He is interested in the majority of topics that are considered analysis ‐ which is why he’s looking forward to the spectrum of courses available in the CCA. Other mathematical interests particularly lie in PDE theory and applications of analysis to physics. Outside of mathematics, he likes reading and discussing philosophy, listening to classical music and walking, and is a casual rower. http://www.maths.cam.ac.uk/postgrad/cca/people/dd413.html

David Driver previously studied at Warwick University where he enjoyed PDEs and stochastic analysis. In his spare time, he enjoys badminton, mountaineering and climbing. http://www.maths.cam.ac.uk/postgrad/cca/people/dd425.html

Sam Forster hails from Wiltshire, UK. Before coming to CCA he completed an MMath at Warwick University. His areas of interest are harmonic analysis, PDEs and geometry. Outside of maths he likes all kinds of sport, music, books and films. http://www.maths.cam.ac.uk/postgrad/cca/people/spf34.html

Eavan Gleeson is originally from Dublin, Ireland. In 2013 she completed Part III of the Cambridge Tripos (receiving an MASt in Mathematics). Prior to that, she read mathematics at Trinity College Dublin, where she was elected a Scholar of the University based on her exceptional academic performance. She has a broad range of interests in analysis, particularly PDE and existence/uniqueness theory. http://www.maths.cam.ac.uk/postgrad/cca/people/eg336.html After finishing school in Goettingen, Germany, Karen Habermann read Mathematics at Cambridge, obtaining her MMath and BA degrees in 2013. Her main research interests are in probability theory. http://www.maths.cam.ac.uk/postgrad/cca/people/kh457.html

Franca Hoffmann is originally from cologne, Germany, but has lived in Montréal, London and Lyon before coming to Cambridge. She took her MSci in Mathematics at Imperial College London and before that studied at École Normale Supérieure de Lyon. Her research interests lie in many areas of pure and applied mathematics, but she is keen to specialise in Applied PDES. Current interests are in kinetic theory and diffusive models in mathematical biology. In the future, she would like to tackle problems in analysis that involve challenging mathematics and which benefit society. http://www.maths.cam.ac.uk/postgrad/cca/people/fkoh2.html Ben Jennings is originally from Formby, near Liverpool. Before his studies commenced at CCA, Ben completed his MMath at Warwick University. Whilst at Warwick, he particularly enjoyed his work on PDEs, functional analysis and probability theory. On the applied side, he has an interest in epidemiology. Outside of maths, he is an amateur sportsman and avid reader. http://www.maths.cam.ac.uk/postgrad/cca/people/bj244.html

Adam Kashlak grew up in Bucks County, Pennsylvania which is just outside of Philadelphia. He completed a Bachelor of Science in Pure Mathematics from McGill University in 2008 focusing in analysis. Then, Adam began working with a government research group near Washington DC, and completed my Master of Science in Applied and Computational Mathematics from Johns Hopkins University in 2011 focusing in probability and statistics. His favourite area of mathematics is probability, and most of his recent research can be summed up as placing balls into cells in some random way. Other interests include cooking and experimenting with new recipes, running, coding in C and R, Canada, reading The Atlantic, and drinking tea. http://www.maths.cam.ac.uk/postgrad/cca/people/ak852.html Zhuo Min ‘Harold’ Lim is originally from Singapore, but has been a student at Cambridge since October 2009 when he commenced the Cambridge Mathematical Tripos. He has also engaged in summer undergraduate research in mathematics, at Caltech in 2011 (applying the theory of Riemann surfaces to study Hele‐Shaw flow), and at Oxford in 2012 (using Young measures to study a variational model of phase‐transitions in crystalline solids). Harold is hoping to specialise in the rigorous analysis of nonlinear PDEs from mechanics and physics, but is also fascinated by the study of rigorous issues in mathematical physics. http://www.maths.cam.ac.uk/postgrad/cca/people/zml21.html 39

Davide Piazzoli is originally from Milan, Italy, and he took his Bachelor degree at the University of Milan. His thesis there was on Analytic Number Theory. After this, he took a joint Masters degree from University of Milan and the Université Paris Sud, Orsay, where his work focussed on Harmonic Analysis and PDEs. Outside of mathematics, Davide enjoys classical music, with a focus on 19th century and pianistic literature ‐‐ even though I am trying to broaden my views. He’s also fond of cinema literary culture. He enjoys jogging, nice restaurants and ‐ last but not least ‐ Italian sun. http://www.maths.cam.ac.uk/postgrad/cca/people/dp478.html Ellen Powell is originally from Surrey but has been in Cambridge for the last 4 years completing my BA and MMath. She is interested in many different areas within analysis though as yet has not focused on a particular specialism. In her MMath she elected to take many probability courses and wrote my Part III essay on Walsh Fourier series and is now keen to broaden her knowledge in and beyond this domain. In her spare time, she is a triathlete and enjoys competing for the university in various events throughout the year. She also plays clarinet, and during her time at Cambridge has been a member of several chamber groups and orchestras. http://www.maths.cam.ac.uk/postgrad/cca/people/ep361.html

Visit our webpage at: http://www.maths.cam.ac.uk/postgrad/cca/ Email: cca@maths.cam.ac.uk Cambridge Centre for Analysis Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WA +44 (0)1223 760377 Centre directors: Professor James Norris Professor Nigel Peake 41 ©2014 Cambridge Centre for Analysis, University of Cambridge This version 08 January 2014