“Since the prize is only awarded every three years and doesn’t have any geographical or age restrictions, receiving it is a great honour and at the same time a big encouragement for me ,” Jessica Fintzen says. The $5,000 prize money is definitely of secondary importance. Much more important, she feels, is to thank all those who, in numerous discussions over the past few years, have joined her in advancing her field — the representation theory of p-adic groups — and those who supported her at various stages of her career.

Jessica Fintzen is already considered among the world’s leading mathematicians in this area despite her tender age. She is being recognized for her research in this subdiscipline of algebra including her paper entitled “Types for Tame P-Adic Groups.” Published in the high-profile journal “Annals of Mathematics” in 2021, it unlocks a deeper understanding of the representations of p-adic groups with the help of some advanced techniques.

“Groups” in this context are sets whose elements can be composed such that certain rules such as associativity are satisfied. One example of such a group is the symmetry group of a cube, which contains all the operations that keep the cube invariant. Representation theory describes groups as matrices, i.e. as linear representations between vector spaces. Starting from the field of rational numbers, it is possible to extend and complete it in various different ways to obtain larger fields. One very well-known way of doing this yields the field of real numbers. Another route leads to the “p-adic” numbers for each prime number p. Jessica Fintzen’s research is about using matrices to describe groups over these fields of p-adic numbers and to “represent” them. There are still many open questions in the representation theory of p-adic groups, especially for small prime numbers p.

### Biography

**Jessica Fintzen** received a bachelor's degree in mathematics and one in physics from the international Jacobs University Bremen before completing her PhD at Harvard University. After holding postdoctoral positions at the University of Michigan, the Institute for Advanced Study in Princeton and Trinity College in Cambridge, she became a lecturer (equivalent of assistant professor) and Royal Society University Research Fellow at the University of Cambridge and an assistant professor (later full professor) at Duke University. In 2022 she took up a professorship at the University of Bonn.

About the award

Presented every three years, the €5,000 **Frank Nelson Cole Prize in Algebra** was established in honor of Professor Frank Nelson Cole (1861–1926), longstanding secretary of the American Mathematical Society. It was awarded for the first time in 1928 and recognizes an exceptional piece of work in the field of algebra published in the past six years by a researcher of any age and from anywhere in the world. The 2015 prize went to the HCM’s Peter Scholze, who would go on to win the Fields Medal and is currently Director of the Max Planck Institute for Mathematics.