Edmund Whittaker Professor of Mathematical Sciences, University of Edinburgh
Professor of Mathematics, Heriot-Watt University
Artwork by Son Yein
Current Events
The Mathematics of Climate Tipping Points and their Impacts
This workshop will be part of the ICMS Mathematics for Humanity initiative. The workshop will provide a forum for the development of mathematical thinking applied to climate tipping points and their possible impacts. We will invite a variety of experts across the Mathematical Sciences research spectrum to deliver an assessment of the mechanisms and risks of tipping events in the Earth’s climate and ecosystems under anthropogenic forcing scenarios. This will help to understand the associated impacts, including implications for mitigation and adaptation. The proposed workshop aims to give a forum for discussion of state-of-the art developments in and applications of mathematical sciences to tipping-aware risk assessments as well as adaptation and mitigation strategies. It also aims to bring open questions of relevance to the attention of researchers in the mathematical sciences.
Recent Advances in Anabelian Geometry and Related Topics
The aim of this workshop is to discuss the recent advances and new developments in the research area of anabelian geometry and the theory of arithmetic fundamental groups. This includes among others the newly discovered versions of the Grothendieck anabelian conjectures for hyperbolic curves and finitely generated fields, new results on the section conjecture, new developments in the theory of multizeta values, and the recent developments in combinatorial anabelian geometry and Grothendieck-Teichmuller theory.
We aim to bring together experts in the field, as well as researchers who are interested in the theory of arithmetic fundamental groups and its applications, in order to discuss these developments and explore further research directions and possible applications.
Signatures and Rough Paths: From Stochastics, Geometry and Algebra to Machine Learning
The aim of this workshop is to discuss stochastic, geometric, and algebraic approaches to signatures and rough paths, including developments in machine learning applications. The study of signatures have highlighted interactions between these fields, including approximation theorems in path spaces, path development (parallel transport) based methods in ML, algebraic approaches to signature tensors, among many others. One focus of this workshop is the theory and applications of multi-parameter signatures, which builds upon these interactions. We aim to bring together experts in these fields, as well as researchers interested in the theory and application of signatures, in order to discuss these developments and explore further relationships across these disciplines.
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
Workshop on Mathematics and Literature
Lectures on the Mathematical Structure of Language
ICMS Director's Public Lecture: The ABC Mysteries
Multiscale Modeling: Infectious Diseases, Cancer and Treatments
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 ten 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)