Dennis Hejhal

Dennis Hejhal is an American mathematician renowned for his profound contributions to analytic number theory, spectral theory, and the geometry of Riemann surfaces. His pioneering work centers on the deep interconnections between the Selberg trace formula, the distribution of zeros of the Riemann zeta function, and the spectral theory of Laplace–Beltrami operators on hyperbolic surfaces. Hejhal has held prominent positions at the University of Minnesota and the Royal Institute of Technology in Stockholm, and his research has significantly advanced understanding in automorphic forms and Teichmüller theory.

Biography

Born in Chicago, Hejhal completed his undergraduate studies at the University of Chicago before earning his Ph.D. in 1972 from the University of California, Berkeley under the supervision of Charles B. Morrey Jr.. His early academic career included positions at the Institute for Advanced Study in Princeton and Stanford University. He joined the faculty of the University of Minnesota in 1978, where he spent the majority of his career, while also maintaining a long-term association with the Royal Institute of Technology in Sweden. His research visits have included extended stays at institutions like the Institut des Hautes Études Scientifiques near Paris and the Max Planck Institute for Mathematics in Bonn.

Research and contributions

Hejhal's research is distinguished by its depth and technical power in connecting disparate areas of pure mathematics. A central achievement is his exhaustive, two-volume treatise on the Selberg trace formula, which provides a comprehensive foundation and extends the formula's applications to congruence subgroups and higher-dimensional settings. His investigations into the zeros of the Riemann zeta function and other L-functions have yielded critical insights into their statistical properties and connections to random matrix theory, influencing the work of mathematicians like Peter Sarnak and Zeev Rudnick. Furthermore, his work on the spectral theory of Laplace–Beltrami operators on Riemann surfaces has implications for quantum chaos and the geometry of moduli space. He has also made significant contributions to Teichmüller theory, particularly concerning the Bers embedding and the structure of universal Teichmüller space.

Awards and honors

In recognition of his influential work, Hejhal has received several prestigious fellowships and honors. He was awarded a Sloan Fellowship in 1976 and a Guggenheim Fellowship in 1984. He has been an invited speaker at major international congresses, including the International Congress of Mathematicians in Warsaw. His research has been supported by grants from the National Science Foundation and the Swedish Research Council. He is a fellow of the American Mathematical Society and his work is frequently cited in the fields of number theory and spectral geometry.

Selected publications

Hejhal's publications are noted for their detail and scope. His seminal books include *The Selberg Trace Formula for PSL(2,R)* (Volume I, 1976; Volume II, 1983), which remain definitive references. Key research papers encompass "Zeros of Epstein zeta functions and supercomputers" in the proceedings of the International Congress of Mathematicians, and "On the uniformization of Riemann surfaces" in the *Annals of Mathematics Studies*. Other important works include "Regular *b*-groups, degenerating Riemann surfaces, and spectral theory" in *Memoirs of the American Mathematical Society* and contributions to the *Journal d'Analyse Mathématique* on the asymptotic distribution of eigenvalues.

Academic appointments

Hejhal has held significant academic positions throughout his career. He is a Professor Emeritus at the University of Minnesota's School of Mathematics. Concurrently, he has served as a Professor of Mathematics at the Royal Institute of Technology in Stockholm since 2001. He has held visiting professorships and research memberships at numerous institutions worldwide, including the Institut des Hautes Études Scientifiques, the Max Planck Institute for Mathematics, and the Mathematical Sciences Research Institute in Berkeley. He has also supervised several doctoral students who have gone on to prominent careers in mathematics.

Category:American mathematicians Category:1947 births Category:Living people Category:University of Minnesota faculty Category:University of California, Berkeley alumni