Günter Harder

Günter Harder
Gert-Martin Greuel, Copyright is MFO · CC BY-SA 2.0 de · source
Name	Günter Harder
Birth date	1938-12-02
Birth place	Lindenfels, Hesse, Germany
Nationality	German
Fields	Mathematics, Number theory, Algebraic geometry, Automorphic forms
Alma mater	University of Freiburg, University of Göttingen
Doctoral advisor	Hans-Joachim Stender
Doctoral students	Josef Teichmann, others

Günter Harder (born 2 December 1938) is a German mathematician known for contributions to number theory, algebraic geometry, and the theory of automorphic forms. He has held professorships at prominent institutions and collaborated with leading figures in arithmetic geometry, influencing work on motives, L-functions, and the cohomology of arithmetic groups. His research interconnects with developments in Langlands program, Shimura varietys, and the study of special values of zeta functions.

Early life and education

Harder was born in Lindenfels,Hesse, and received his early schooling in Hesse. He studied mathematics and physics at the University of Freiburg and later at the Georg-August University of Göttingen, where he completed his doctorate under the supervision of Hans-Joachim Stender. His doctoral work placed him in the mathematical lineage extending through David Hilbert and Felix Klein to earlier German schools of algebraic geometry and number theory.

Academic career and positions

Harder held positions at several German and international institutions, including the University of Göttingen and the University of Bonn, where he served as a professor in the Mathematics Department. He has been a member of the Deutsche Forschungsgemeinschaft review panels and has participated in programs at the Institute for Advanced Study and the Max Planck Institute for Mathematics. He lectured at conferences organized by the European Mathematical Society, the International Mathematical Union, and the Mathematical Congress of the Americas and has been associated with collaborative projects involving the Institute Henri Poincaré, the Courant Institute of Mathematical Sciences, and the University of Chicago.

Research contributions and mathematical work

Harder's work spans interactions among modular forms, Eisenstein series, and the cohomology of arithmetic groups. He made influential contributions to the theory of Eisenstein cohomology and the study of special values of L-functions attached to automorphic representations, connecting to questions raised in the Langlands program. His investigations of boundary cohomology for locally symmetric spaces built on methods related to Borel–Serre compactification and were informed by work of Armand Borel, Jean-Pierre Serre, and Harish-Chandra. Harder explored congruences between modular forms and formulated results analogous to conjectures by Deligne and Bloch–Kato concerning periods and regulators of motives. His research influenced studies by Gerd Faltings on arithmetic of abelian varietys, by Richard Taylor and Andrew Wiles in modularity, and by Don Zagier in special values of L-series. Collaborations and interactions connected his methods to advances by Pierre Deligne, Robert Langlands, George Lusztig, and David Kazhdan in representation theory and arithmetic. He also contributed to the theory of algebraic stacks and integral models for Shimura varietys, engaging with approaches developed by Jean-Marc Fontaine, Kazuya Kato, and Michael Harris.

Awards and honors

Harder has received recognition from national and international bodies, including honors from the German Mathematical Society and invitations to speak at major gatherings such as the International Congress of Mathematicians and meetings of the European Mathematical Society. He has been named to editorial boards of leading journals and elected to academies such as the Academy of Sciences Leopoldina and the Göttingen Academy of Sciences and Humanities. His work has been cited in award contexts related to breakthroughs in arithmetic geometry and the Langlands program.

Selected publications

- "Eisenstein cohomology of arithmetic groups: the case GL_2", in collections honoring advances in automorphic forms and number theory; appeared alongside contributions by Armand Borel and Jean-Pierre Serre. - Papers on congruences between modular forms and the arithmetic of Shimura varietys, cited by researchers such as Gerd Faltings and Richard Taylor. - Expository articles on the cohomology of locally symmetric spaces and applications to special values of L-functions, appearing in volumes edited for the International Congress of Mathematicians and the European Mathematical Society.

Students and academic lineage

Harder supervised doctoral students who went on to positions in mathematical research and higher education, including noted mathematicians such as Josef Teichmann. His academic descendants form part of a lineage that connects through Hans-Joachim Stender to earlier scholars in Göttingen; this lineage intersects with students and collaborators of David Hilbert, Hermann Weyl, and Emmy Noether.

Category:German mathematicians Category:1938 births Category:Living people