# Institute for Mathematical Sciences About IMS

# Tenth Anniversary: Speeches

### Speech by Professor Louis Chen, IMS Director

Professor Tan Chorh Chuan

Professor Roger Howe

Professor Chong Chi Tat

Distinguished Guests

Ladies and Gentlemen

A warm welcome to the 10th anniversary celebration of the Institute for Mathematical Sciences and many thanks to Professor Tan Chorh Chuan for gracing this occasion as our Guest of Honor.

Ten years have passed like a blink of an eye. The establishment of the IMS seems to have taken place only yesterday. But much has happened in the past ten years. And many events are still vivid in the mind.

The establishment of the Institute is a collective effort of the Department of Mathematics in pursuit of a common dream. It was approved in 2000 after three attempts made over a span of ten years. The Institute received start-up funding from MOE and NUS for its first five years of operation and is now primarily funded by NUS.

Modeled after successful mathematical institutes in the west, the IMS provides a platform for research interaction without hiring in-house researchers. Given Singapore’s geographical isolation and its small scientific community, the Institute faced many odds in achieving its mission. Fortunately, the IMS has been able to overcome most of the odds through the support of the Management Board, the advice of the Scientific Advisory Board and the active participation of the local and international scientific community.

The Management Board provides a framework for the Institute’s operations. In particular, the Chair of the Board, Professor Chong Chi Tat who was also the Provost during the Institute’s first five years, had provided it with the kind of flexibility that it needed during its initial years of development.

The Scientific Advisory Board, which helps in reviewing proposals for programs and workshops, also shares its wisdom with the Institute, and has guided and nurtured the Institute to what it is today. The local scientific community has taken an active interest in working with the Institute in fostering mathematical research in Singapore by organizing many programs and workshops and actively participating in many of them.
Mathematics is the underlying thread weaving through many disciplines in science and technology. It plays an important role in the formulation and analysis of today’s complex and multi-disciplinary scientific problems. By providing a platform connecting the mathematical sciences with the other disciplines the IMS has been able to contribute in a significant way to research vibrancy in the mathematical sciences in Singapore. It has also brought about greater interaction and research collaboration between mathematicians and scientists of different disciplines and between the local and the international scientific communities.

Over the years the IMS has benefited from the help and friendly cooperation of World Scientific which publishes its Lectures Notes Series and prints its newsletter *Imprints*.
In commemoration of the Institute’s 10^{th} anniversary, World Scientific has helped in designing and printing a booklet with the theme of this celebration as title, “Celebrating 10 Years of Mathematical Synergy”. It has also published a book entitled “Creative Minds, Charmed Lives”, which is a collection of interviews with 38 mathematicians and scientists who have visited IMS in the past 10 years. These interviews were conducted by my colleague Professor Leong Yu Kiang who has also provided invaluable contributions to the conceptualization of the newsletter as its founding editor.

On funding, the IMS has recently received a gift of about 1 million US Dollars from the John Templeton Foundation to establish the Asian Initiative for Infinity (or, in short, AII) at the Institute. The AII, which will focus on activities related to mathematical logic, was conceived by Professor Hugh Woodin and Professor Ted Slaman of UC Berkeley and Professor Chong Chi Tat of NUS, who also wrote a proposal for the Templeton Foundation grant. This gift is eligible for a dollar-for-dollar matching fund from the Singapore Government.

Since the inception of the IMS, I have had a total of five Deputy Directors. This is probably a record among all mathematical sciences institutes in the world. My Deputy Directors in chronological order of service are Chen Kan, Yeneng, Denny, Ka Hin and Ser Peow. With their different working styles and different strengths, they have all helped me significantly, particularly in those areas where I needed help the most.

Until recently I have had a fairly frequent turn over of support staff. But I have kept in touch with some of those who have left the Institute and I am happy to know that some of them are here today. The support staff is undoubtedly important for the smooth running of the day-to-day operations. They have done remarkably well under my demanding and fastidious style.

In closing, I would like to thank everyone who has, in one way or another, helped the IMS in its development or contributed to its success. In particularly, I would like to thank those members of the Management Board who have served on the Board continuously in the past ten years: Professor Chong Chi Tat, Chair, Mr Ng Kok Lip and Dr K K Phua. I would also like to thank the founding members of the Scientific Advisory Board: Professor Jacques-Louis Lions, who passed away in 2001 and is sadly missed by all of us; Professor Hans Föllmer, Professor Avner Friedman and Professor Keith Moffatt, whose term ended two years ago; and Professor Roger Howe, Chair, Professor Lui Pao Chuen and Professor David Siegmund, whose term will end in a few days.

I must thank our musical colleagues who will be adding a touch of culture to make this celebration a memorable one: Professor Bernard Tan who composed a piece, entitled “Remembrance”, for the occasion, and Ms Kelly Loh and Ms Mifiona Quah who will enchant us with the flute and the harp. Thanks also go to the Center for Instructional Technology for their professionalism and friendly cooperation in producing the video presentation for us and in video shooting this celebration.

I should also thank three scientific colleagues for the highlights that await us after the reception. They are Professor Tony Chan who has kindly taken time off from the busy schedule of being the President of the Hong Kong University of Science and Technology to share with us his rich US experience in research organization; Professor Hugh Woodin who has travelled half the world to bring to earth a mathematical universe only the initiated few have seen; and our former deputy director Professor Sun Yeneng who will cast some light on some basic questions about the nature of economics.

Last but not least, I would like to thank all of you for coming to IMS to join us in this celebration of our 10^{th} anniversary.

Thank you.

Copyright @ 2010 Institute for Mathematical Sciences. All Rights Reserved.

### Speech by Professor Chong Chi Tat, Chairman of Management Board

Professor Tan Chorh Chuan

President of NUS

Distinguished guests, colleagues and friends

Ten years is a period that is not too short for a review or summary, nor too long for recollection by those who saw it from the very beginning. In the case of the IMS, its conception, though certainly not its creation, goes back to the 1980’s. Those of us in the Auditorium this morning who call mathematics their profession, will each have a perception of what constitutes an ideal environment conducive to mathematical research. In my case three experiences shaped my view of this. The first was the time spent as a graduate student. The second took place when I attended my very first mathematical meeting at the Oberwolfach in Germany in 1984. The Institute is perched on a hillside in a lovely valley amidst the Black Forest. Every week, arriving on Sunday and leaving the following Saturday, a group of mathematicians who share common interest in a particular mathematical subject, get together, take walks, do hikings in the Forest, attend lectures, discuss ideas and perhaps exchange gossips almost continuously for six days. The third occasion took place in 1990 when I spent half a year at the Mathematical Sciences Research Institute in Berkeley. Here again is a mathematical institute located on a hilltop overlooking the striking San Francisco Bay, a short bus ride from Evans Hall, home of the Mathematics Department of UC Berkeley. In the MSRI, or Misery as some would call it, graduate students have plenty of opportunities to talk to young postdoctoral researchers and established mathematicians, down the corridors, on a blackboard or in the lecture theatre. The experience was inspiring, and the environment exciting.

Many of us in Singapore who have had the fortune of such encounters dreamt about something similar here. It started off as idle canteen talks, and later evolved into serious but failed attempts. However, time was moving fast. In 1998/99 we found ourselves submitting a proposal to the Ministry of Education on the establishment of an institute for mathematical sciences. To our surprise and great delight, the proposal was taken up with great interest and our dream and vision in the canteen became reality at the turn of the Century.

So what has IMS achieved in the past ten years? A quick count shows that it has organized, since activities began in 2001, 37 specialized programs and 35 other activities, including workshops, conferences and summer schools. According to my estimate, close to 2500 scientists, mathematicians, engineers, clinician, scientists and other professionals have participated in these activities. And the subjects featured covered a wide range of topics. They include the most fundamental of mathematics, the Foundations of Mathematics, to such diverse areas as cryptography, finance and economics, climate change, genomics, and communications. It is said that mathematics permeates through all subjects of human endeavor. The programs and activities at the IMS is a testimony to this. Through the time spent at the IMS, many have come to notice the work done in Singapore and the vibrant environment Singapore provides to researchers. Some have chosen to pursue graduate studies at the NUS; some have chosen to take up a career in Singapore, and many research collaborations have ensued. In my view, IMS has contributed not in a small way to the research vibrancy and international visibility of the University and perhaps of Singapore.

Of course the success of IMS was not due to the efforts of the Institute alone. Every program, every workshop that was organized involved people from either departments in the NUS, A*STAR institutes, NTU or SMU. In that sense, IMS success is the collective effort of many in Singapore, and their overseas colleagues.

The dream and vision that originated from canteen talks has a nice ending. But in comparison with MSRI and the Newton Institute in Cambridge, IMS is still relatively modest. The next ten years will probably call for an even bolder vision and bigger dreams. Perhaps it’s time to start another round of idle canteen talks. Many of us will be happy to participate in this exercise.

Thank you for your attention.

Copyright @ 2010 Institute for Mathematical Sciences. All Rights Reserved.

### Speech by Professor Roger Howe, Chairman of Scientific Advisory Board

It is a delight to be here today to help celebrate the 10th anniversary of the Institute for Mathematical Sciences. It has been a pleasure for me to be part the Scientific Advisory Board (SAB), and wonderful for all of us to work with Louis Chen, whose energy and devotion to the goals and activities of IMS have been inspirational. And also, very successful. Under Louis’s direction, the IMS has supported many excellent programs that have enhanced local expertise in a wide variety of areas. Louis has been especially careful to recruit programs related to Singapore’s strategic technological goals. It is an enviable record. There have been series of programs supporting the country’s efforts in biomedical science, imaging science, and hydrodynamics, and a variety of other programs in pure and applied mathematics that reflect and strengthen the research of local mathematical scientists. You don’t have to take my word for it; just go read the already 19 volumes of the IMS Lecture Note Series, published by World Scientific. Here I will use just three for examples: *Gabor and Wavelet Frames, Markov Chain Monte Carlo, and Braids.*

I would like to relate these volumes to a model of progress in mathematics. It seems useful to distinguish at least three types of mathematical activity. The most dramatic is the big breakthrough that revolutionizes a field and leads to striking applications. Let’s call this a type 1 event. We all love this kind of event, but there are two problems with it:

1) it is relatively rare; and

2) it is almost completely unpredictable.

Sometimes of course, a breakthrough doesn’t affect theory and applications equally. Sometimes a theoretical breakthrough has little or no practical ramifications, at least not in the near term, and sometimes a breakthrough just uses off-the-shelf mathematics in a new way. Even these one-sided breakthroughs tend to generate a lot of excitement.

The second kind of activity is the feverish period of dissemination, elaboration and consolidation after the first type of event. Lots of conferences, lots of papers with corollaries, or parallel results in a different context, or applications, or elaborations, or refinements.

The third kind of activity is what happens the rest of the time, which in most fields is most of the time. People are working out programs of investigation. They may be working on still unsolved problems, of older or more recent vintage, or trying to refine further or clarify how ideas in their field fit together, or elaborate concepts to adapt them to more complex situations, or investigating examples, or formalizing results, a kind of axiomatization to distill the key ideas in a particular area. During this kind of activity, it may seem to the outsider that not much is happening.

Policymakers and funders of course love the first kind of event. Everybody does. It is obvious that we can now do things better than in the past, or at least understand something much better; and if the breakthrough has an applied aspect, someone (probably __not__ mathematicians!) will save or make a lot of money. Policymakers tend also to feel pretty favorable about the second kind of activity, because the excitement is still there, and they can still remember the difference between before and after the event. These events are natural candidates for IMS programs.

The true test of policymakers is in supporting the third kind of activity. In this activity, which I believe characterizes most of mathematics most of the time, it may seem that mathematicians are wasting their time, becoming overly refined, not keeping their eyes on the main prize. But I submit that this is in fact the most important kind of mathematical activity. It is out of the ferment of exploration, or turning over ideas, subjecting them to critiques and “what if”s, mixing them together and seeing what happens, that the big breakthroughs come. In particular, this type of work is also suitable for IMS programs. I would like to use some IMS Lecture Notes to illustrate this claim, by briefly sketching how complex the history was that led to a few type 1 events.

**Volume 10: Gabor and Wavelet Frames**

In imaging science, a major revolution came in the 1980s, with the advent of wavelet methods, a superb example of a type 1 event. Wavelets have become an essential part of the toolkit of signal processors, including being incorporated in the JPEG standards. Wavelets have figured strongly in the image processing activities at IMS, and have been a central topic of research of several members of the NUS Department of Mathematics.

What led to the wavelet revolution? The complete history is very complex, but here I simply want to emphasize its long pedigree. Fourier analysis has been a heavily used tool in mathematics and physics since the late 18th century, and the first serious studies of the major linear partial differential equations of physics: the wave equation, the heat equation, and Laplace’s equation. Desire to understand what the Fourier Transform does led to intense study. Speaking very loosely, it was learned that Fourier Transform takes spatial information and converts it into frequency information. The standard, spatial representation of a function does not exhibit very plainly its frequency behavior, and vice versa.

The advent of quantum mechanics forced the realization that we cannot arbitrarily specify both the spatial behavior and the frequency behavior of a function. This is the celebrated Heisenberg Uncertainty Principle. Also with the advent of quantum mechanics, we got what mathematicians call the Heisenberg group, since it is the group-theoretic embodiment of the Heisenberg Canonical Commutation Relations. The Heisenberg group embodies both the spatial and frequency aspects of a function at the same time, at the price of being non-commutative.

When these ideas had been sufficiently digested, it occurred to some people to ask if there could be ways to represent functions that are partially localized in both position and in frequency, and also have good properties with respect to scaling. One of the early attempts to create bases of such functions was made by D. Gabor, but it was only in the 1980s, after several decades of development of ideas from the Calderon- Zygmund school of harmonic analysis that Gabor’s ideas were combined systematically with considerations based on scaling, giving rise to the bases known as wavelets, and associated multi-resolution analysis. This brief sketch will suggest how much history and patient investigation lay behind the dramatic advent of wavelets.

**Volume 19: Braids**

Another type 1 event of the 1980s was the discovery by Vaughan Jones of a connection between von Neumann algebras and knot theory. Each of these areas had a long history, with knot theory going back to the 19th century, and von Neumann algebras having their roots in von Neumann’s papers on operator algebras in the 1930s. They had been completely separate areas, but in his thesis, Jones found some algebraic structures that eventually led him to a connection with knots. This led to a tidal wave of new results in knot theory, including applications to DNA. (It has been discovered that nature has designed enzymes whose job is to perform basic operations of knot combinatorics!)

A more classical approach to knot theory, developed by Artin, is through the study of braids. A few years ago, a surprising discovery (a type 1 event in pure math) by members of the Mathematics Department at NUS linked braids to some of the classic questions in topology, especially the homotopy groups of spheres. IMS sponsored a program to highlight this new discovery, and followed it up with a broader program to integrate the new discoveries into the already existing fabric of algebraic topology.

**Volume 7: Markov Chain Monte Carlo**

Finally, let me mention the volume on Markov Chain Monte Carlo (MCMC) methods. Markov chains were invented by Andrei Markov in the early 20th century, apparently motivated by theoretical probability questions. They are a simple model of probabilistic dynamics. They envision a collection of possible states, and a fixed rule governing the chance of moving from one state to another. They have a clean and elegant theory, and are sometimes the subject of a tidy section in a chapter on eigenvalues and eigenvectors in a textbook on linear algebra. However, over the years, many people have applied them to many kinds of phenomena. For example, random walks are Markov chains.

MCMC is part of this roll call of applications, and has itself become a major type of application. MCMC is really not a type 1 event in the strict sense. Rather it is a long, rolling development, in which a particular approach to some hard problems has been found to be applicable in more and more areas. Yet the cumulative effect is like a revolution. Thus we have the article of P. Diaconis in the April, 2009 Bulletin of the American Mathematical Society, with title *The Markov chain Monte Carlo revolution*.

MCMC started in a 1953 paper by Metropolis, Rosenbluth and Rosenbluth, Teller and Teller. The basic idea, now frequently called simply the Metropolis algorithm, or Metropolis–Hastings algorithm, is to create a Markov Chain to sample approximately a probability distribution which is not easily computable directly. This was a new idea for using Markov chains. Over time, this idea itself has found many variations and new applications, most recently in biostatistics and mathematical finance.

Perhaps the epitome of an applied breakthrough is the rise of Google. Their fabulously successful Internet search engine is also based on a Markov chain, made from all the nodes in the internet! In the last ten years, Google has gone from non–existent to one of the biggest companies on the world in terms of market capitalization. I still cannot quite get my head around the possibility that one can perform a Markov chain on several billion variables, and come out with anything meaningful. Google doesn’t prove any theorems, but it shows by example that its methods work, millions of times every day, Few examples show better the power of pure mathematics when used in an opportune way. Let me highlight the fact that Markov chains had been sitting around for a long time, and had been used in a variety of ways that are not so far removed from their use by Google. First their invention, but also the ways they had been applied, reduced the potential barrier to their application to the internet.

These examples underline the importance of maintaining a level of mathematical expertise, so that such technologies can be understood and used adaptively. The IMS has clearly been a positive force in bringing understanding of such new developments to Singapore, and raising the capacity of its mathematical community to adapt to and utilize the new ideas, wherever they arise.

In closing, I would like to say a little about the future of IMS. In its first ten years, IMS has amply demonstrated its value for supporting the mathematical infrastructure of Singapore. I believe I speak for all my colleagues on the SAB, when I marvel at the effectiveness with which Louis Chen has spent the dollars he has been allocated. But I also believe that we have all wished those dollars could have been more. In particular, we have wished that the government had a mechanism for funding IMS, rather than having it be funded as an internal activity of NUS. We are grateful to NUS for taking on that burden, and salute the vision of both Deputy President for Research and Technology Barry Halliwell and Provost Eng-Chye Tan in providing ongoing funding for IMS. But in fact, IMS is, and should be thought of as, a national resource. In a country such as Singapore, with its reliance on technological progress, but with a modest number of mathematical scientists, and where anyone can get anywere in under and hour, it makes eminent sense to have an Institute for Mathematical Sciences, but it does not make sense to have two, or to have one attached to a particular institution, except as providing a physical home. I note that one of the planned programs of IMS is primarily coming from the School of Physical and Mathematical Sciences at NTU, and an earlier program was also. Programs have also been initiated by other institutions, and participants have come from many organizations in Singapore. I regard this as healthy. It is how IMS should work; but when IMS itself is funded through NUS this raises questions of financial responsibility. I hope that, as the challenge of finding a successor to Louis Chen as Director of IMS is addressed, the question of the funding mechanism that is commensurate with Singapore’s dependence on mathematical infrastructure and its physical size, will also be addressed.

Thank you.

Copyright @ 2010 Institute for Mathematical Sciences. All Rights Reserved.

### Speech by Professor Tan Chorh Chuan, NUS President

Professor Roger Howe, Chairman, IMS Scientific Advisory Board

Professor Chong Chi Tat, Chairman, IMS Management Board

Professor Louis Chen, Director, IMS

Distinguished guests

Ladies and Gentlemen

Good morning.

We at NUS have much to celebrate as our Institute for Mathematical Sciences (IMS) marks its 10th anniversary today. My warmest congratulations to the IMS team lead by Director Professor Louis Chen, Management Board Chair Professor Chong Chi Tat and Scientific Advisory Board Chair Professor Roger Howe, on reaching this key milestone!

**The value of mathematics to society**

Mathematics is the foundational discipline that underpins a wide range of disciplines, from physical and biological science, to engineering, to finance. This is beautifully captured in the title of a 1960 article by the Physics Nobel laureate Eugene Wigner called: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. The paper expounds the remarkable role that mathematical structure and concepts have in predicting and advancing physical theory. It is true that important research in mathematics is often motivated by finding solutions to real and practical problems that are multi-dimensional in nature. Equally important is fundamental curiosity-driven research in some of the more abstract and pure areas of mathematics, which sometimes leads to surprising and important applications to practical problems.

These observations are of even greater relevance in the current global landscape, where a growing number of countries are transforming themselves into knowledge-based economies and societies. For them, research, development and innovation - particularly in science and technology - are key drivers for positive change. It is not surprising that mathematics has an even more crucial role for such countries seeking to thrive in a new, globalised and diversified economy.

**IMS’ achievements in the last 10 years**

Turning to Singapore - we are at an exciting phase of growth, transiting from an efficiency-focused, manufacturing-based economy to one which is also powered by knowledge and innovation. In this regard, NUS has a critical role to play, as a key driver of knowledge creation, transmission and application. The quality and impact of our research are on a steeply rising trajectory, and there are several areas where we are doing high impact work in the global arena. IMS, set up in the year 2000, is a key part of our plans to put NUS on the world map for mathematics education and research. Let me highlight a few of IMS’ notable accomplishments.

First, harnessing synergies within NUS departments, IMS has developed innovative programmes that are broad-based and interdisciplinary, covering a wide range of mathematical fields, including mathematical applications in finance, biology, modelling of infectious diseases, climate change, imaging and digital media, and data analysis. These programmes, including activities such as summer schools, workshops, symposia and conferences, demonstrate both the breadth of IMS’ activities, as well as the ubiquity and relevance of mathematics across a range of disciplines.

Second, IMS has attracted a pool of talented scholars and researchers, offering them opportunities to pursue exciting ground-breaking work. Augmenting our local researchers and academics are leading world experts - including Nobel laureates, Fields medallists and members of the Academies of Sciences - as well as promising young scientists, who are regular visitors at IMS. It is a highly encouraging sign of success that IMS is fast becoming a magnet for talent and has built up a critical mass of top-rate scholars.

Third, IMS is actively building up synergistic partnerships with renowned institutions in the US, Japan and Canada, including the US National Science Foundation. In this regard, I am delighted to share that the IMS team - comprising Professor Chong Chi Tat and Professors Hugh Woodin and Ted Slaman - successfully secured a US$1million grant from the John Templeton Foundation, to support the Asian Initiative for Infinity, a programme that promotes the research of Mathematical Logic in Asia. Through such partnerships and collaborations, IMS has been able to build synergies, enhance its research impact and grow the critical mass of top-class talent in Mathematical Sciences for Singapore and beyond.

**Closing**

Let me now close by expressing, on behalf of the University, our heartfelt appreciation to all our researchers and scholars at IMS for your many and substantial achievements. I applaud the contributions of each one of you in making IMS what it is today. As IMS blazes new trails, I am confident that it will continue to be one of the pace setters for innovative education and cutting edge research in mathematical sciences.

Thank you, and please have an enjoyable conference.

Copyright @ 2010 Institute for Mathematical Sciences. All Rights Reserved.