Wallenberg grant to two mathematicians at the university
Stockholm University is awarded two grants within the Knut and Alice Wallenberg Foundation's mathematics program for recruiting prominent researchers in mathematics.
The Knut and Alice Wallenberg Foundation's mathematics program has been running since 2014. The program is of great importance for mathematics research in Sweden giving the best young Swedish mathematicians international experience by giving them the opportunity to travel abroad as postdocs. At the same time, both younger and more experienced mathematicians are being recruited to Sweden from abroad.
Within the framework of the program, 15 mathematicians now have to share in SEK 27 million in grants. Two of these grants go to Stockholm University.
More accurate simulations of ice sheets
Assistant Professor Josefin Ahlkrona will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, Stockholm University.
One of the most dramatic consequences of climate change is the melting ice sheets in Greenland and the Antarctic. The results will be rising sea levels that threaten coastal communities and ecosystems. However, predictions of how much the sea level will increase over the next few decades are very uncertain. The purpose of the planned project is to develop models for the structure of the ice sheets and to create more efficient algorithms for calculating ice melt.
One important reason for the models’ unreliability is that it is difficult to include all the internal stresses in the ice. If computer simulations are not to take several years to complete, or require memory in excess of today’s supercomputers, some stresses must either be entirely ignored or be included in the model at a very low resolution.
Need to simplify models
Another reason is the lack of understanding of the mathematics underlying the advanced models that include all the stresses. These models are so complicated that it has been difficult to know how to apply them without considerable numerical errors. This is particularly unfortunate at coastlines, where the ice is in contact with the sea and much of the melting occurs.
One way to use computing power optimally would be to simplify the model by only including all the stresses in the ice where they are of the greatest importance (such as close to the coast) and using a more efficient model for the other areas. However, it is also necessary to estimate the numerical errors this method entails. The results can then be used to improve an algorithm called ISCAL (Ice Sheet Coupled Approximation Level), so that simulations of the ice sheets will be 4-10 times faster.
Two modern theories in a productive cooperation
Matthew Kennedy is an associate professor at the University of Waterloo, Canada. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Department of Mathematics, Stockholm University.
Geometric objects and their symmetries have been studied since the ancient Greeks. Eventually, there was a move away from the objects themselves and studies of symmetry became increasingly abstract. Different symmetries were placed in different groups and, in the early 19th century, the famous French mathematician Évariste Galois developed group theory.
The concept of groups is now central to both mathematics and modern physics, with many new methods for dealing with groups being introduced over the past century. One of these is operator algebras, which was developed in the 1930s to provide the newly created quantum mechanics with a solid mathematical basis. An entirely different way of studying groups is by using boundary theory, which was created in the 1960s to study their large-scale behaviour.
Several breakthroughs over the last decade
A revolutionary insight about how to link these two relatively new areas of mathematics has led to several breakthroughs over the last decade. Boundary theory has become a fundamental tool for operator algebras, and vice-versa – several important problems in boundary theory have been illuminated by using operator algebras. The aim of the planned project is to further develop these methods and use ideas from operator algebras to investigate current problems in boundary theory for groups.
Matthew Kennedy is a world-leading researcher in operator algebras. He works at the University of Waterloo in Canada, which hosts the closely related multidisciplinary Institute for Quantum Computing. At the institute theoretical research is combined with quantum information theory and other areas of importance for future quantum computers, including operator algebras.
Last updated: March 23, 2022
Source: Communications Office