Edmund Whittaker Professor of Mathematical Sciences, University of Edinburgh
Professor of Mathematics, Heriot-Watt University
Artwork by Son Yein
Current Events
Young Homotopy Theorists Meeting
This meeting is a week-long conference focused on recent developments in homotopy theory. Although its origins lie in algebraic topology, the language of homotopy theory has turned out to be a flexible framework for discussing derived phenomena in many areas of mathematics, from arithmetic geometry to physics. The goal of this conference is to give young homotopy-theorists the opportunity to share ideas, perspectives, and techniques.
Thematic Month by Young African Researchers: Topics in Arithmetic Geometry
This is a hybrid event organized within the framework of the African Network for Arithmetic Geometry and Applications (ANAGA) which aims to develop arithmetic geometry in Africa. It is funded by the International Centre for Mathematical Sciences (ICMS) through their Mathematics for Humanity programme. One of the main goals of ANAGA is to train a new generation of researchers who will serve as a lever for the training of future generations. This meeting is an important milestone in that training process.
This thematic month is a 4-week session that mixes advanced courses, research talks and working groups.
The goal of this workshop is to bring together researchers in computational materials science and mathematics to discuss mathematical models and algorithms essential for understanding and simulating materials at the atomic, molecular, and particle scales. Set against the backdrop of emerging high-performance computational resources, such as the UK’s forthcoming first exascale supercomputer to be sited in Edinburgh, the workshop will focus on the development of new mathematical and algorithmic methodologies aiming to make the most of the computational power of future computer architectures in materials simulation. The workshop will stimulate research collaborations between researchers from the UK, EU and USA, and will offer the opportunity for mathematicians to learn more about the new challenges and opportunities these computational platforms will bring. Topics to be discussed will include novel approaches to computational multi-tasking and sampling; optimisation methodologies such as numerical continuation and deflation; coarse-graining and model reduction; and the rigorous mathematical analysis of such methodologies.
Knowledge Exchange Event: Rewilding
Achieving sustainable human-wildlife coexistence in well-functioning ecosystems is a vitally important and major challenge under global change. In this context, Rewilding, an emerging paradigm in ecosystem restoration, is viewed by a growing number of scientists as central to the restoration agenda. Rewilding differs from more established conservation approaches as it de-emphasizes efforts towards preserving or bringing back certain focal species or habitats, in favour of prioritising the connectivity and health of the ecosystem as a whole. More precisely, the emphasis is on restoration of ecosystem services (such as pollination, water purification, carbon storage, etc) and their underpinning ecosystem functions. Other defining features of rewilding are the requirement of minimal ongoing management and viewing ecosystems as social-ecological systems. The latter point provides space for different scales of rewilding, from the most purist at one end of the spectrum, to small-scale urban rewilding at the other. While mathematics has played a key role in ecology for well over a century, its use in rewilding remains limited. This is in part due to the fact that the rewilding approach is still in the early phases of developing a rigorous scientific foundation.
The purpose of this KE event is to bring together academic and non-academic scientists in mathematics and ecology, in order to tackle some of the practical problems related to rewilding. The ICMS has previously funded a term long programme, Rewilding mathematics. The perspectives paper Mathematical Perspectives on Rewilding is the outcome of that programme and the theoretical premise of this KE event.
My main preoccupation at the moment is a new project of the ICMS with the name Mathematics for Humanity. It's main goal is to support mathematical activities around the world with potential for direct impact on the betterment of the human condition. A subsidiary goal is to provide a unifying umbrella for many things of this nature that mathematicians are already doing. By providing this unifying framework, I hope the value of such activity is better recognised and that the practioner can enjoy a greater sense of mission. Please look at the webpage linked above and submit proposals for activities. I hope especially to attract new ideas from young mathematicians as well as senior mathematicians interested in running their usual research programmes in parallel with contributions to global welfare.
Article in Geneva Science and Diplomacy Anticipator Science Breakthrough Radar
Other Recent Events
An ICMS Meeting for Peace: America-Europe-Middle East Webinar on Fundamental Physics
Diophantine Equations and the Theory of Computation: A Lecture Series
Workshop on Mathematics and Literature
Lectures on the Mathematical Structure of Language
ICMS Director's Public Lecture: The ABC Mysteries
Public Lecture at UNAM, Mexico City: What Kind of Story is Mathematics?
Summary
I am a mathematician working primarily on arithmetic geometry, the study of spaces built out of finitely-generated systems of numbers. My main contribution to mathematics is the discovery of the non-abelian method of Chabauty, a theoretical framework for applying ideas of topology, especially homotopy theory, to the algorithmic resolution of Diophantine equations. I am also interested in mathematical physics, the mathematical structure of matter and spacetime in general, and topological quantum field theory in particular.
I have a keen interest in public engagement. I have given numerous presentations since 2010 at schools, teacher training workshops, and corporate training programmes, as well as 'talk concerts' on a wide range of topics in mathematics and its interface with other domains of inquiry, especially physics and economics. If you are interested in having me at such an event, do not hesitate to contact me. I have published 15 books so far written for the general public. My interest in engagement is an important component of the way I've put together this site. I'm trying to make the material accessible and friendly to any curious person, even while providing standard information that might be useful for my colleagues in academia. I hope the style is not off-putting to the latter. However, I haven't anything like the energy and creativity that some of the serious communicators of science are able to put into their website. As a result, I fear that my modest effort here will look silly both to colleagues and to the general public. As an extension of public engagement, I am a consultant for WoongjinThinkbig, one of the oldest educational publishers in Korea. I am doing my best to help them develop educational software.
I work at the International Centre for Mathematical Sciences, a gathering place for mathematical scientists from all over the world, located in the beautiful city of Edinburgh. The city is surrounded by nature, as rugged as can be in a major city, even while it's steeped in history, including intellectual history. It's a real privilege to trace the footsteps of inspiring figures like David Hume, Adam Smith, Mary Somerville, James Clerk Maxwell, and Michael Atiyah on a daily basis.
I grew up in Seoul, Korea, studied mathematics at Seoul National University, then received my Ph.D. in Mathematics at Yale University under the direction of Igor Frenkel, Serge Lang, and Barry Mazur (Harvard). I moved on to faculty positions at MIT, Columbia University, the University of Arizona, Purdue University, the Korea Institute for Advanced Study, University College London, Pohang University of Science and Technology, Ewha Womans University, and the University of Oxford, where I was the head of the number theory research group. Most recently before moving to Edinburgh, I was Christopher Zeeman Professor of Algebra, Geometry, and Public Understanding of Mathematics at the University of Warwick.
It is perhaps not so well known that a mathematician's life involves a good deal of travel. In particular, I have held visiting professorships at numerous institutions including the University of Paris, University of Illinois, University of Kyoto, Seoul National University, ICTS Bangalore, and the University of Toronto.
I am a fellow of the Royal Society of Edinburgh and the American Mathematical Society.
From 'Relative Langlands Duality' by David Ben-Zvi, Yiannis Sakellaridis, and Akshay Venkatesh
What is Mathematics?
The part of physics where experiments are cheap. (V.I. Arnold, On Teaching Mathematics (1997)) [Maame Ama Bainson, a student of mathematical epidemiology and oncology, points out that this is wrong: computing costs for her modelling experiments are very high.]
It appears that mathematics as we know it arises from the nature of our brains and the embodied experience. (G. Lakoff and R. Nunez, Where Mathematics Comes From (2000))
The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical. (D. Gale and L. Shapley, College Admissions and the Stability of Marriage (1962))
If all mathematics disappeared today, physics would be set back exactly one week. (R.P. Feynman, source unknown)
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. (R.P. Feynman, The Character of Physical Law (1965))
Its Applications (M. de Unamuno)