Draft:Ragnar-Olaf Buchweitz

Ragnar-Olaf Buchweitz (18 March 1952 – November 2017) was a German-Canadian mathematician known for his work in commutative algebra, algebraic geometry, and singularity theory. He was a professor at the University of Toronto Scarborough and made foundational contributions to the homological theory of maximal Cohen–Macaulay modules and deformations of singularities.

Early life and education

Buchweitz was born in Neuruppin, Germany. He studied mathematics and physics at the University of Hannover, where he earned a Diplom (1972), PhD (1976), and Habilitation (1982).^[1]

Academic career

Following positions in Germany, the United States, and France, Buchweitz joined the University of Toronto in 1987, where he remained until his death.^[2] At Toronto, he served as professor and chair in the Department of Computer and Mathematical Sciences and was active in mentoring students in algebra and geometry.

Research

Buchweitz’s research focused on homological methods in algebra and geometry, particularly maximal Cohen–Macaulay modules, matrix factorizations, and Hochschild cohomology. His collaboration with Maurice Auslander, The homological theory of maximal Cohen–Macaulay approximations (1989), became foundational in the study of Gorenstein rings and singularity theory.^[3]

Together with Hubert Flenner, Buchweitz developed the theory of global Hochschild (co-)homology for singular spaces and introduced general semiregularity maps for modules and deformations.^[4] He also worked on non-commutative resolutions of discriminants and determinantal varieties, connecting algebraic geometry to representation theory and mathematical physics.

Awards

Buchweitz received the Humboldt Research Award in 2010 from the Alexander von Humboldt Foundation.^[5]

Legacy

A 2012 conference at Syracuse University celebrated his 60th birthday and his influence in commutative algebra and representation theory.^[6] After his death in 2017, colleagues and students highlighted his ability to bridge multiple mathematical disciplines and his deep influence on singularity theory and non-commutative geometry.^[2]

Selected publications

• Buchweitz, R.-O.; Greuel, G.-M. (1980): The Milnor number and deformations of complex curve singularities. Invent. Math. 58. doi: [10.1007/BF01390261](https://doi.org/10.1007/BF01390261)
• Auslander, M.; Buchweitz, R.–O. (1989). The homological theory of maximal Cohen–Macaulay approximations. Mémoires de la Société Mathématique de France 38: 5–37. doi:[10.24033/msmf.339](https://doi.org/10.24033/msmf.339)
• Buchweitz, R.–O.; Flenner, H. (2008). Global Hochschild (co-)homology of singular spaces. Advances in Mathematics 217 (1): 205–242. doi:[10.1016/j.aim.2007.06.012]
• Buchweitz, R.–O.; Flenner, H. (2008). The global decomposition theorem for Hochschild (co-)homology of singular spaces via the Atiyah–Chern character. Advances in Mathematics 217 (1): 243–281. [dot: 10.1016/j.aim.2007.06.013](https://doi.org/10.1016/j.aim.2007.06.013)
• Buchweitz, R.–O. (2021). Maximal Cohen–Macaulay Modules and Tate Cohomology over Gorenstein Rings, AMS Mathematical Surveys and Monographs, 262, doi:[10.1016/j.aim.2007.06.012](https://doi.org/10.1090/surv/262)

See also

• Cohen–Macaulay ring
• Singularity theory (mathematics)
• Homological algebra

References

Category:1952 births Category:2017 deaths Category:20th-century mathematicians Category:21st-century mathematicians Category:German mathematicians Category:Canadian mathematicians