# Françoise Tisseur to Deliver Olga Taussky-Todd Lecture at ICIAM 2019

Françoise is a numerical analyst specializing in numerical linear algebra. She has contributed real-world applications to the fields of theoretical analysis, perturbation theory, and numerical methods and software development.

Françoise is at the forefront of research on the theory and numerical solution of nonlinear eigenvalue problems, particularly polynomial eigenvalue problems. She has made major advancements in the analysis, perturbation theory, and numerical solution of these problems. Polynomial eigenvalue problems arise in a wide variety of science and engineering applications, such as dynamic analysis of mechanical systems, linear stability of flows in mechanics, and electronic band structure calculations for photonic crystals.

Françoise’s work shows for the first time that from the point of view of numerical stability, the usual approach to solve these problems is very often not the best. She has made major contributions to a fundamental open problem in the field — the derivation of a method that works directly on polynomial eigenvalue problems. As an important step towards their solution, she developed a new class of transformations allowing one to treat the problems directly with numerical techniques.

Pervading much of Françoise’s research is the theme of exploiting structure in matrix problems. She has devoted significant time to the creation of tools for analyzing structured problems, derivation of new or improved algorithms that exploit structure, and execution of error analysis to reveal the numerical properties of structure-exploiting algorithms for comparison and improvement.

Françoise recently adopted tropical algebras, a tool from pure mathematics. When combined with a valuation map in the tropical setting, 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. Tropical algebra becomes a useful tool for numerical linear algebra because tropical analogues are usually cheaper to compute than those in conventional algebra. One can then use them in the design of preprocessing steps to improve the numerical behavior of algorithms, such as convergence and stability.

Françoise studied at the University of St.-Étienne in France, completing her Ph.D. in numerical analysis in 1997. Following a postdoctoral position at the University of Tennessee, she moved to the University of Manchester, where she is now a professor of numerical analysis and director of the Manchester Institute for Mathematical Sciences.

Françoise’s work has garnered her many honors, including the 2010 Whitehead Prize of the London Mathematical Society, the 2012 Adams Prize of the University of Cambridge, and a Royal Society Wolfson Research Merit Award. She is also a SIAM Fellow.

*Inaugurated in 2007, the Olga Taussky-Todd Lecture is an invited lecture at ICIAM. This honor is conferred on a “woman who has made outstanding contributions in applied mathematics and/or scientific computation.” The lecture is named for Olga Taussky-Todd, whose scientific legacy is in both theoretical and applied mathematics, and whose work exemplifies the aforementioned qualities.*

*Lecturers are selected by a committee established by the ICIAM President, with input 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 the following members: Barbara Lee Keyfitz (Chair, Ohio State University); Raymond Chan (Chinese University of Hong Kong); Sofia C. Ohlede (University College London, U.K.); Ruben D. Spies (Instituto de Matemática Aplicada del Litoral, Argentina); and Anna Karin Tornberg (KTH Royal Institute of Technology, Sweden).*