Awarded to Annalisa Buffa (Institute for Applied Mathematics and Information Technologies, Pavia–Genoa–Milan, Italy) in recognition of her spectacular use of deep and sophisticated mathematical concepts to obtain outstanding contributions to the development of computer simulations in science and industry.
Annalisa Buffa graduated in Computer Engineering at the University of Pavia in 1996, and got her PhD in Mathematics at the University of Milan, in 2000. In 2004 she became Research Director at the Institute for Applied Mathematics and Information Technologies (Pavia–Genoa–Milan), and (overall) Director of the Institute in 2013. She has received important grants, including an ERC Starting Grant in 2008, and prestigious awards, including the Bartolozzi Prize and the John Todd Fellowship Prize in 2007.
In a relatively short amount of time she has been able to bring fundamental contributions to a number of different aspects of scientific computing, with an incredible range both in the type of applications and in the type of mathematical instruments.
One of her major achievements is the characterization of traces of vector fields for Sobolev spaces relevant in electromagnetics: in a series of fundamental papers with Patrick Ciarlet she produced a complete characterization of the traces on the boundary of polyhedral domains. This has been a breakthrough for the understanding of the integral equation formulation of electromagnetic scattering.
Another masterpiece was the construction, together with Snorre Christiansen, of an optimal preconditioner for electromagnetic integral equations. This problem was open for a long time, and the result finally came thanks to the combination of mathematical knowledge and engineering conception that she had acquired over the years. The preconditioner is already widely used in industrial practice.
More recently, with Giancarlo Sangalli she initiated research activity on the mathematical understanding of isogeometric analysis, where she played a fundamental role in providing a mathematical foundation. She studied the mathematical structure of non-tensor-product extensions of multivariate splines addressing deep theoretical questions which will impact enormously the development of adaptive isogeometric methods. She extended the theory of exterior calculus to splines, showing how this leads to unexpected schemes for several important problems, and she has also promoted the development of free software which is now widely used in the isogeometric community.
In brief, the trademark of her work is the use of highly sophisticated mathematical techniques to produce fundamental breakthroughs that are applied to computer simulations in industry. For this she can be considered as a worthy recipient of the 2015 Collatz Prize.
Subcommittee for the 2015 ICIAM Collatz Prize
- Donatella Marini (University of Pavia, Italy), chair;
- Tom Hou (California Institute of Technology, USA);
- Hisashi Okamoto (Kyoto University, Japan);
- Mete Soner (ETH Zürich, Switzerland);
- Andrew Stuart (University of Warwick, UK);
- Steve Wright (University of Wisconsin, USA).