Jan Bruinier

Jan Bruinier
Name	Jan Bruinier
Birth date	1970s
Birth place	Netherlands
Nationality	Dutch
Occupation	Mathematician
Fields	Number theory, Arithmetic geometry, Modular forms
Institutions	University of Cologne, University of Duisburg-Essen, Max Planck Institute for Mathematics
Alma mater	Leiden University
Doctoral advisor	Hendrik Lenstra

Jan Bruinier is a Dutch mathematician known for his work in analytic number theory and arithmetic geometry, especially on harmonic Maass forms, Borcherds products, and arithmetic intersections. He has held positions at prominent European institutions and collaborated with leading researchers in modular forms, elliptic curves, and automorphic representations. His research has influenced the study of special values of L-functions, arithmetic theta lifts, and the Gross–Zagier formula.

Early life and education

Born in the Netherlands, Bruinier studied mathematics at Leiden University where he completed undergraduate and graduate studies. He wrote a doctoral thesis under the supervision of Hendrik Lenstra, contributing to topics related to modular functions, complex multiplication, and computational aspects of algebraic number theory. During his doctoral and postdoctoral periods he worked in environments connected to Dutch Mathematical Society activities and seminars involving researchers from University of Amsterdam and Delft University of Technology.

Academic career

Bruinier's early appointments included postdoctoral positions and research fellowships that brought him into contact with groups at the Max Planck Institute for Mathematics and research networks around Institut Henri Poincaré. He later joined the faculty at the University of Cologne and was affiliated with the University of Duisburg-Essen for collaborative projects. Throughout his career he has participated in conferences organized by institutions such as the European Mathematical Society, the International Congress of Mathematicians, and the Association for Women in Mathematics (in program collaborations), and he has been invited to speak at seminars at the Institute for Advanced Study and the Mathematical Sciences Research Institute.

Bruinier has supervised doctoral students who have pursued research on harmonic weak Maass forms and arithmetic applications, and he has served on editorial boards of journals focused on Crelle's Journal-type publications and other outlets in number theory. He has collaborated with scholars affiliated with Princeton University, Harvard University, University of Cambridge, and researchers from the Max Planck Institute network.

Research contributions

Bruinier's work centers on the interplay between automorphic forms and arithmetic geometry. He made significant contributions to the theory of harmonic Maass forms and the construction of Borcherds products, linking these to arithmetic intersection theory on Shimura varieties and moduli spaces of abelian varieties. His research includes developments of arithmetic theta lifts that relate coefficients of modular-type objects to heights of algebraic cycles and to derivatives of L-functions, connecting to landmark results such as the Gross–Zagier theorem and conjectures of Beilinson and Bloch.

He has advanced explicit formulas for Fourier coefficients and developed modularity results that interact with the theory of Heegner points on elliptic curves and special cycles on orthogonal and unitary Shimura varieties. Bruinier's collaborations with researchers at Yale University, University of Chicago, and ETH Zurich produced work on regularized theta lifts and Green functions, providing tools for computing arithmetic intersection numbers and investigating relations with the Siegel–Weil formula and the Kudla program.

In analytic aspects, his studies touch on the spectral theory of automorphic forms, traces of singular moduli, and the arithmetic of modular curves, linking classical modular functions like the j-invariant to modern perspectives on mock modular forms and Ramanujan-type phenomena. His computational approaches have utilized algorithms in algebraic number theory associated with groups around Hendrik Lenstra and computational packages developed in collaboration with colleagues from Leiden University and other European centers.

Awards and honors

Bruinier has received recognition through invited lectures at major conferences including sessions organized by the European Mathematical Society and the International Congress of Mathematicians-related events. He has been awarded research grants from European research agencies and national science foundations supporting investigations into modular forms and arithmetic geometry. His contributions have led to invitations to visiting positions at institutes such as the Max Planck Institute for Mathematics and research stays at the Institute for Advanced Study and Mathematical Sciences Research Institute.

Selected publications

- Bruinier, J. with collaborators, papers on harmonic Maass forms, Borcherds products, and arithmetic theta lifts published in journals associated with Cambridge University Press and Oxford University Press series. - Bruinier, J.; works on the arithmetic of modular curves, Heegner divisors, and Green functions appearing in proceedings of conferences held by the American Mathematical Society and the European Mathematical Society. - Joint publications with authors from Princeton University, ETH Zurich, and Yale University developing explicit formulas in the context of the Kudla program and the Siegel–Weil formula.

Category:Dutch mathematicians Category:Number theorists Category:Living people