David Harbater

David Harbater
Name	David Harbater
Birth date	1952
Nationality	American
Fields	Mathematics
Workplaces	University of Pennsylvania, Massachusetts Institute of Technology, Harvard University
Alma mater	Princeton University
Doctoral advisor	John Tate
Known for	Galois theory, patching methods, inverse Galois problem

David Harbater is an American mathematician noted for breakthroughs in algebraic geometry and Galois theory. He made influential contributions to the inverse Galois problem and developed patching techniques that connected arithmetic geometry, number theory, and algebraic topology. Harbater has held faculty positions at major research universities and has been recognized by leading scientific organizations.

Early life and education

Harbater was born in 1952 and pursued undergraduate and graduate studies that led him to advanced research in algebra. He completed his Ph.D. at Princeton University under the supervision of John Tate, a prominent figure associated with Harvard University and Harvard College. During his graduate training he interacted with researchers connected to Institute for Advanced Study, Massachusetts Institute of Technology, and contemporaries from University of Chicago and University of California, Berkeley.

Academic career

Harbater held academic posts at institutions including Massachusetts Institute of Technology and later at the University of Pennsylvania, where he served as a professor in the Department of Mathematics. He collaborated with mathematicians affiliated with Harvard University, Yale University, Columbia University, and international centers such as the École Normale Supérieure, Université Paris-Sud, and the Max Planck Institute for Mathematics. Harbater has been invited to speak at conferences organized by groups like the American Mathematical Society, the Mathematical Sciences Research Institute, and the Clay Mathematics Institute.

Research contributions and notable results

Harbater is best known for advancing the application of patching methods to problems in algebra and arithmetic geometry. Building on ideas related to Alexander Grothendieck's work and techniques from Gerritzen–van der Put theory and Rigid analytic geometry, he adapted patching to the context of Galois cohomology and branched covers. His work contributed to resolving cases of the inverse Galois problem over function fields and to the construction of Galois extensions with prescribed group via geometric methods related to Riemann surfaces, Belyi's theorem, and Hurwitz spaces.

He introduced and refined techniques that connected the deformation theory used by researchers like Michael Artin and Grothendieck with explicit construction techniques reminiscent of classical results by Évariste Galois and later algebraists such as Emil Artin and Emmy Noether. Harbater's methods influenced subsequent developments in field arithmetic, local-global principles akin to those studied by John Tate and Jean-Pierre Serre, and in the study of Brauer groups and Galois cohomology.

Notable results include solutions to embedding problems and the demonstration of the existence of Galois extensions with particular finite groups as Galois groups over rational function fields, connecting to work by Shafarevich, Igor R., Shankar Sen, and contemporaries studying the absolute Galois group of function fields. His approaches have been applied in research areas involving algebraic curves, moduli spaces, and interactions with number fields and local fields.

Awards and honors

Harbater's research has been recognized by awards and fellowships from organizations such as the National Science Foundation and election to professional societies including the American Academy of Arts and Sciences and the National Academy of Sciences. He has been an invited speaker at major events like the International Congress of Mathematicians and has held visiting positions at institutions including the Institute for Advanced Study and the Simons Foundation-affiliated centers.

Selected publications

- "Patching and Galois theory" — articles and lecture notes that developed patching techniques influencing later work in Galois theory and algebraic geometry. - Papers on the inverse Galois problem over function fields and related embedding problems published in journals connected to the American Mathematical Society and Elsevier-hosted periodicals. - Collaborative works with researchers from University of Michigan, University of Toronto, and European universities addressing applications to moduli problems and field arithmetic.

Personal life and legacy

Harbater's mentorship and collaborations have shaped generations of researchers associated with departments at University of Pennsylvania, Massachusetts Institute of Technology, and other institutions across North America and Europe. His legacy includes the propagation of patching methods into diverse areas of pure mathematics and the enrichment of the community studying the inverse Galois problem, continuing influences visible in contemporary research by mathematicians affiliated with Princeton University, Stanford University, and the University of Cambridge.

Category:American mathematicians Category:1952 births Category:Living people