# Françoise Tisseur, Olga Taussky-Todd Lecturer at ICIAM 2019

Challenges in the numerical solution of nonlinear eigenvalue problems

The International Council for Industrial and Applied Mathematics has selected

**Monday, July 15, 2019, at the “Palau de la Música”, 12:00h**The International Council for Industrial and Applied Mathematics has selected

**Professor Françoise Marie Louise Tisseur**of the School of Mathematics, University of Manchester, to deliver the Olga Taussky-Todd Lecture at the International Congress on Industrial and Applied Mathematics, ICIAM 2019, in Valencia, Spain. This Congress is the most important international event in applied and industrial mathematics, held once every four years under the auspices of the International Council for Industrial and Applied Mathematics.Françoise Tisseur is a numerical analyst specializing in numerical linear algebra. Her contributions cover the whole range of topics from theoretical analysis, perturbation theory, numerical methods and software development, to real-world applications.

She is at the forefront of research on the theory and numerical solution of nonlinear eigenvalue problems, in particular polynomial eigenvalue problems. These problems arise in a wide variety of science and engineering applications, such as the dynamic analysis of mechanical systems (where the eigenvalues represent vibrational frequencies), the linear stability of flows in mechanics, and electronic band structure calculations for photonic crystals.

Françoise has made major contributions in the analysis, perturbation theory, and numerical solution of polynomial eigenvalue problems, an emerging topic when she began working on it. Her work marks the first analysis showing that the usual approach to solve these problems is very often not the best from the point of view of numerical stability. She has made major contributions to a fundamental open problem in the field, the derivation of a method that works directly on the polynomial eigenvalue problems. An important step towards solving this problem was the development of a new class of transformations allowing one to treat the problem directly with numerical techniques.

Pervading much of Françoise‘s work is the theme of exploiting structure in matrix problems. She has devoted a major effort to developing tools for analyzing structured problems, deriving new or improved algorithms that exploit structure, and carrying out error analysis to reveal the numerical properties of structure-exploiting algorithms, to enable comparison and improvement.

More recently, she adopted a tool from pure mathematics, tropical algebras. In the tropical setting, when combined with a valuation map, roots of polynomials, eigenvalues and singular values of matrices, and matrix factorizations offer order of magnitude approximations to the corresponding objects in the usual algebra. What makes tropical algebra a useful tool for numerical linear algebra is that these tropical analogues are usually cheaper to compute than those in the conventional algebra. They can then be used in the design of preprocessing steps to improve the numerical behaviour of algorithms such as convergence and stability.

Professor Tisseur studied at the University of St.-Etienne, completing her Ph.D. in Numerical Analysis at the University of St.-Etienne in 1997. Following a postdoctoral position at the University of Tennessee she moved to the University of Manchester, where she is now Professor of Numerical Analysis and Director of the Manchester Institute for Mathematical Sciences.

### Awards and honors

Tisseur’s work has garnered her many honors, among them the 2010 Whitehead Prize of the London Mathematics Society, the 2012 Adams Prize of the University of Cambridge, and a Royal Society Wolfson Research Merit Award. She is a Fellow of the Society for Industrial and Applied Mathematics.

### The Olga Taussky-Todd Lecture

The Olga Taussky-Todd Lecture is one of the invited lectures at the International Congress on Industrial and Applied Mathematics. This honour is conferred on a "woman who has made outstanding contributions in applied mathematics and/or scientific computation". The lecture is named in tribute to the memory of Olga Taussky-Todd, whose scientific legacy is in both theoretical and applied mathematics, and whose work exemplifies the qualities to be recognized. The Olga Taussky-Todd Lecture series was inaugurated in 2007 with a lecture by Pauline van den Driessche at ICIAM 2007 in Zurich. The lecturers since then have been Beatrice Pelloni (Vancouver, 2011), Éva Tardos (Beijing, 2015) and Françoise Tisseur (Valencia, 2019).

### The Olga Taussky-Todd Lecture for ICIAM 2019

Lecturers are selected by a committee established by the ICIAM President, with advice from the Association for Women in Mathematics and European Women in Mathematics. Nominations are solicited from the mathematical sciences community. The Committee for the 2019 Lecture consisted of:

She is at the forefront of research on the theory and numerical solution of nonlinear eigenvalue problems, in particular polynomial eigenvalue problems. These problems arise in a wide variety of science and engineering applications, such as the dynamic analysis of mechanical systems (where the eigenvalues represent vibrational frequencies), the linear stability of flows in mechanics, and electronic band structure calculations for photonic crystals.

Françoise has made major contributions in the analysis, perturbation theory, and numerical solution of polynomial eigenvalue problems, an emerging topic when she began working on it. Her work marks the first analysis showing that the usual approach to solve these problems is very often not the best from the point of view of numerical stability. She has made major contributions to a fundamental open problem in the field, the derivation of a method that works directly on the polynomial eigenvalue problems. An important step towards solving this problem was the development of a new class of transformations allowing one to treat the problem directly with numerical techniques.

Pervading much of Françoise‘s work is the theme of exploiting structure in matrix problems. She has devoted a major effort to developing tools for analyzing structured problems, deriving new or improved algorithms that exploit structure, and carrying out error analysis to reveal the numerical properties of structure-exploiting algorithms, to enable comparison and improvement.

More recently, she adopted a tool from pure mathematics, tropical algebras. In the tropical setting, when combined with a valuation map, roots of polynomials, eigenvalues and singular values of matrices, and matrix factorizations offer order of magnitude approximations to the corresponding objects in the usual algebra. What makes tropical algebra a useful tool for numerical linear algebra is that these tropical analogues are usually cheaper to compute than those in the conventional algebra. They can then be used in the design of preprocessing steps to improve the numerical behaviour of algorithms such as convergence and stability.

Professor Tisseur studied at the University of St.-Etienne, completing her Ph.D. in Numerical Analysis at the University of St.-Etienne in 1997. Following a postdoctoral position at the University of Tennessee she moved to the University of Manchester, where she is now Professor of Numerical Analysis and Director of the Manchester Institute for Mathematical Sciences.

### Awards and honors

Tisseur’s work has garnered her many honors, among them the 2010 Whitehead Prize of the London Mathematics Society, the 2012 Adams Prize of the University of Cambridge, and a Royal Society Wolfson Research Merit Award. She is a Fellow of the Society for Industrial and Applied Mathematics.### The Olga Taussky-Todd Lecture

The Olga Taussky-Todd Lecture is one of the invited lectures at the International Congress on Industrial and Applied Mathematics. This honour is conferred on a "woman who has made outstanding contributions in applied mathematics and/or scientific computation". The lecture is named in tribute to the memory of Olga Taussky-Todd, whose scientific legacy is in both theoretical and applied mathematics, and whose work exemplifies the qualities to be recognized. The Olga Taussky-Todd Lecture series was inaugurated in 2007 with a lecture by Pauline van den Driessche at ICIAM 2007 in Zurich. The lecturers since then have been Beatrice Pelloni (Vancouver, 2011), Éva Tardos (Beijing, 2015) and Françoise Tisseur (Valencia, 2019).### The Olga Taussky-Todd Lecture for ICIAM 2019

Lecturers are selected by a committee established by the ICIAM President, with advice from the Association for Women in Mathematics and European Women in Mathematics. Nominations are solicited from the mathematical sciences community. The Committee for the 2019 Lecture consisted of:- Barbara Lee Keyfitz, The Ohio State University, USA (Chair)
- Raymond Chan,The Chinese University of Hong Kong, Hong Kong
- Sofia C. Ohlede, University College London, UK
- Ruben D. Spies, Instituto de Matemática Aplicada del Litoral, Argentina
- Anna Karin Tornberg, KTH, Stockholm, Sweden