Bakker received her PhD degree at VU Amsterdam last college year, supervised by VU Professors Jan Bouwe van den Berg and Rob van der Vorst, for her thesis ‘Nonlinear waves in local and nonlocal media: a topological approach’.
Bente Bakker obtained her bachelor’s and her master’s degree in mathematics at the VU. She is currently working as a postdoc in Leiden. The PWN awards the Stieltjes Prize every year. The winner receives 2,500 euros. The jury selected the winner from a total of 76 candidates. The jury praises the high quality of the PhD thesis: “Bakker’s PhD thesis is at a level that one only sees once a decade”.
In her thesis, Bakker explores the ways in which algebraic-topological machinery, originating in the Calculus of Variations, can be used to study the existence and multiplicity of traveling wave solutions to a large class of Reaction Diffusion Equations that take nonlocal interactions into account. Inspired by Floer homology and Conley’s earlier theory of isolated invariant sets, she uses topological information to count traveling waves in Morse theoretic spirit. In addition, by adapting Noether’s theorem to a nonlocal setting she identified new conserved quantities. The abstract theory relies on technical conditions (such as ‘transversality’) and to verify these involves hard PDE analysis, in particular Carleman estimates.
Breaking down barriers
The jury says: “It was absolutely unclear that such estimates could be derived for equations with nonlocal terms, but Bakker managed, thus showing impressive technical skills. Bakker’s very general and imaginative adaptation of the Floer-Conley methods provides a new framework for thinking about traveling waves that is bound to spawn many new investigations. She deserves the prize for the abstract approach, both elegant and efficient, for the astonishing creativity in breaking down barriers previously thought impenetrable, and, last but not least, for the potential future impact on the description and understanding of coherent structures, with applications spanning nonlinear optics, fluid dynamics, and self-organized structures in biology or sociology.”