Egbert Brieskorn

Egbert Brieskorn
Gert-Martin Greuel · CC BY-SA 2.0 de · source
Name	Egbert Brieskorn
Birth date	7 July 1936
Birth place	Rostock, Free State of Mecklenburg-Schwerin
Death date	11 July 2013
Death place	Bonn, North Rhine-Westphalia
Nationality	German
Fields	Mathematics
Alma mater	University of Göttingen, University of Münster
Doctoral advisor	Heinz Hopf
Known for	Brieskorn–Grothendieck singularities, Brieskorn spheres, work on Lie groups, singularity theory

Egbert Brieskorn was a German mathematician noted for foundational work in singularity theory, connections between algebraic geometry, differential topology, and Lie group theory, and the discovery of exotic differentiable structures on spheres known as Brieskorn spheres. His research linked concepts from Hirzebruch, Milnor, and Arnold to concrete examples that influenced subsequent developments in knot theory, symplectic geometry, and gauge theory. He held professorships in several German universities and played an influential role in fostering mathematical research communities centered on Bonn and Göttingen.

Early life and education

Brieskorn was born in Rostock in 1936 in the historical context of the Free State of Mecklenburg-Schwerin and grew up during the era shaped by events such as World War II and the postwar reorganization of Germany. He studied mathematics at the University of Göttingen and the University of Münster, where he came under the influence of figures associated with the Göttingen tradition, including contacts with researchers linked to David Hilbert's legacy and the mathematical circles surrounding Heinz Hopf and Hermann Weyl. Brieskorn completed his doctoral studies under the supervision of Heinz Hopf, producing work that already reflected intersections with differential topology and complex analysis as practiced in leading centers like Princeton University and Institute for Advanced Study.

Academic career and positions

Brieskorn held academic positions at several institutions, moving through the German university system in the tradition of scholars such as Felix Klein and Bernhard Riemann. He served as a professor at the University of Münster before taking a chair at the University of Bonn, where he succeeded colleagues in a department influenced by scholars like Heinz Hopf and Reinhard Selten—the latter known in different fields but representing the span of Bonn's scholarly environment. At Bonn, Brieskorn led research groups that collaborated with mathematicians from institutions including Harvard University, Princeton University, ETH Zurich, and University of Tokyo, fostering exchanges with contemporaries such as John Milnor, Pierre Deligne, and Vladimir Arnold. He supervised doctoral students and postdoctoral researchers who later joined faculties at universities like Cambridge University, University of California, Berkeley, and École Polytechnique.

Contributions to mathematics

Brieskorn's work established deep links between singularity theory and several areas of mathematics. He introduced explicit hypersurface singularities now called Brieskorn singularities and constructed exotic differentiable structures on spheres—commonly referred to as Brieskorn spheres—building on the discoveries of John Milnor concerning exotic spheres and connecting to classification results by Michel Kervaire and M. A. Kervaire and John Milnor's earlier topology work. Brieskorn identified relationships between isolated complex hypersurface singularities and representations of Weyl group symmetries associated with Lie algebras of type ADE, elaborating connections that invoked names like Élie Cartan, Hassler Whitney, and Claude Chevalley. His collaboration and exchanges with Michael Atiyah and Isadore Singer resonated with index-theoretic perspectives, while interactions with Beno Eckmann and Hermann Weyl-inspired geometry enriched topological interpretations. Brieskorn explored monodromy of singularities and the Milnor fibration, extending foundational ideas by John Milnor and René Thom. His analysis of deformation theory and resolution of singularities drew on methods related to work by Oscar Zariski, Alexander Grothendieck, and Heisuke Hironaka, establishing bridges to algebraic geometry topics such as moduli spaces studied by David Mumford and Alexander Grothendieck's school. The Brieskorn–Grothendieck perspective influenced later research in mirror symmetry, Frobenius manifolds following Boris Dubrovin, and interactions with string theory-inspired mathematics in venues such as Institut des Hautes Études Scientifiques.

Awards and honors

Brieskorn received recognition from German and international bodies. He was elected to academies including the Göttingen Academy of Sciences and Humanities and the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts, reflecting a career comparable to peers like Heinz Hopf and Günter Harder. He was awarded national honors and invited to deliver lectures at institutions such as International Congress of Mathematicians conferences and seminars hosted by Max Planck Society institutes. Colleagues commemorated his contributions in memorial volumes alongside mathematicians like John Milnor, Michael Atiyah, and Pierre Deligne.

Selected publications

Brieskorn authored influential papers and monographs that became central references. Notable works include publications on Brieskorn spheres and singularities, often cited alongside texts by John Milnor, Kervaire, and Michel Spivak. He contributed survey articles and research papers to proceedings of conferences at venues such as International Congress of Mathematicians and edited volumes from Springer Verlag series. His collected papers and lecture notes were disseminated through publishers associated with Springer, Birkhäuser, and university presses in Bonn and Göttingen, and were widely used by researchers at institutions like Princeton University and ETH Zurich.

Personal life and legacy

Brieskorn lived much of his career in Bonn and remained active in scholarly communities until his death in 2013 in Bonn, North Rhine-Westphalia. His legacy persists through the Brieskorn spheres that continue to inform studies in differential topology, contact topology, and low-dimensional topology areas engaged by researchers at University of California, Berkeley, University of Cambridge, and Institute for Advanced Study. Memorial conferences and special journal issues honored him alongside figures such as John Milnor and Michael Atiyah, and his influence is visible in the work of students and collaborators at institutions including University of Münster, University of Bonn, and ETH Zurich. He is remembered as a mathematician who bridged continental traditions exemplified by David Hilbert's and Élie Cartan's schools, leaving concrete examples and conceptual frameworks that continue to shape contemporary research.

Category:German mathematicians Category:1936 births Category:2013 deaths