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Kenneth Brown | |
|---|---|
 Kenneth Brown at Oberwolfach in 2004 | |
| Born | Kenneth Stephen Brown November 1945 (age 78–79) |
| Nationality | American |
| Other names | Ken Brown |
| Alma mater | |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Cornell University |
| Thesis | Abstract homotopy theory and generalized sheaf cohomology (1971) |
| Doctoral advisor | Daniel Quillen |
| Notable students | Susan Hermiller, David Webb |
| Website | https://pi.math.cornell.edu/~kbrown/ |
Kenneth Stephen Brown (born November 1945) is an American mathematician, and an emeritus professor at Cornell University. Brown has broad mathematical interests, centered around topology and group theory.
Education and career
editBrown earned his Ph.D. in 1971 from the Massachusetts Institute of Technology, under the supervision of Daniel Quillen. His thesis was titled Abstract homotopy theory and generalized sheaf cohomology.[1] He was hired directly after his Ph.D as an assistant professor at Cornell University, where he remained until his retirement in 2014. He served as chair of the department from 2002 to 2006.[2]
Brown has broad interests around topology and group theory, also extending to combinatorics, and probability theory. He is also known for his work in category theory, cohomology theory, and geometric group theory. He has published over 30 scientific articles and 2 books,[3] and advised 16 Ph.D. students.[1][2]
Significant contributions
editBrown's early work is in category theory and K-theory. He is known for Ken Brown's Lemma in the theory of model categories, which gives a sufficient condition for a functor to send weak equivalences to weak equivalences.[4][5] Brown is one of the authors for which the Brown-Gersten-Quillen spectral sequence is named.[6]
Brown discovered the main idea used for practical applications of discrete Morse theory, that of performing repeated simplicial collapse operations in various skeleta of a CW complex to replace the complex with a simpler complex.[7] This work generalizes methods used earlier in joint work with Ross Geoghegan;[8] the idea was later rediscovered (with the connection to the discrete Morse Theory of Robin Forman) by Manoj Chari.[9][10]
Later in his career, Brown worked on random walks in hyperplane arrangements and semigroups. Based partly on work with Persi Diaconis,[11] he developed a theory of random walks on left regular bands.[12][13]
Brown has written two graduate textbooks on group cohomology and on buildings. The book on buildings was (together with the book of Mark Ronan) one of the first textbook-level expositions of the topic;[14] an expanded second edition of this textbook was coauthored with Peter Abramenko.
Awards and honors
edit- Brown was named as a fellow of the American Mathematical Society in the inaugural class of 2013.[15]
- A conference titled "Approaches to Group Theory" was held in honor of Brown's 65th birthday in 2010.[16][17]
- Brown was an invited speaker at the International Congress of Mathematicians in 1978 at Helsinki.[18]
Books
edit- Abramenko, Peter; Brown, Kenneth S. (2008). Buildings : theory and applications. New York London: Springer. ISBN 978-0-387-78834-0. MR 2439729. OCLC 426513857.
- Brown, Kenneth (1989). Buildings. New York: Springer. ISBN 0-387-98624-3. MR 1644630. OCLC 42279289. (Reprinted in 1998.)
- Brown, Kenneth (1982). Cohomology of groups. New York: Springer-Verlag. ISBN 0-387-90688-6. MR 1324339. OCLC 8169670. (Reprinted with corrections in 1994.)
References
edit- ^ a b Kenneth Stephen Brown at the Mathematics Genealogy Project
- ^ a b "Curriculum Vitae, Kenneth Stephen Brown" (PDF). Retrieved September 26, 2019.
- ^ "Kenneth S. Brown author profile at MathSciNet". Retrieved September 26, 2019.
- ^ Hovey, Mark (2007), Model Categories, Mathematical surveys and monographs, vol. 63, American Mathematical Society, p. 6, ISBN 9780821843611, MR 1650134
- ^ ""Factorization Lemma"". nLab.
- ^ McCleary, John (2001). A user's guide to spectral sequences. New York: Cambridge University Press. ISBN 0-521-56759-9. MR 1793722. OCLC 44669736.
- ^ Brown, Kenneth S. (1992). "The Geometry of Rewriting Systems: A Proof of the Anick-Groves-Squier Theorem". Mathematical Sciences Research Institute Publications. Vol. 23. New York, NY: Springer New York. pp. 137–163. doi:10.1007/978-1-4613-9730-4_6. ISBN 978-1-4613-9732-8. ISSN 0940-4740. MR 1230632.
- ^ Brown, Kenneth S.; Geoghegan, Ross (1984). "An infinite-dimensional torsion-free group". Inventiones Mathematicae. 77 (2). Springer Science and Business Media LLC: 367–381. doi:10.1007/bf01388451. ISSN 0020-9910. MR 0752825. S2CID 121877111.
- ^ Chari, Manoj K. (2000). "On discrete Morse functions and combinatorial decompositions". Discrete Mathematics. 217 (1–3). Elsevier BV: 101–113. doi:10.1016/s0012-365x(99)00258-7. ISSN 0012-365X. MR 1766262.
- ^ Brown, Kenneth S. "Rewriting systems and discrete Morse theory" (PDF). Spring Southeastern Sectional meeting abstracts. American Mathematical Society. Retrieved September 27, 2019.
(See also the slides from the talk.) - ^ Diaconis, Persi; Brown, Kenneth S. (1998). "Random walks and hyperplane arrangements". The Annals of Probability. 26 (4). Institute of Mathematical Statistics: 1813–1854. doi:10.1214/aop/1022855884. ISSN 0091-1798. MR 1675083.
- ^ Brown, Kenneth S. (2000). "Semigroups, rings, and Markov chains". Journal of Theoretical Probability. 13 (3). Springer Nature: 871–938. doi:10.1023/a:1007822931408. ISSN 0894-9840. MR 1785534. S2CID 14565862.
- ^ Margolis, Stuart; Saliola, Franco; Steinberg, Benjamin (2015). "Combinatorial topology and the global dimension of algebras arising in combinatorics". Journal of the European Mathematical Society. 17 (12). European Mathematical Publishing House: 3037–3080. arXiv:1205.1159. doi:10.4171/jems/579. ISSN 1435-9855. MR 3429159. S2CID 118371503.
- ^ Humphreys, James E. (1989-10-01). "Book Review: Buildings". Bulletin of the American Mathematical Society. 21 (2). American Mathematical Society (AMS): 303–308. doi:10.1090/s0273-0979-1989-15836-9. ISSN 0273-0979. MR 1567805.
- ^ "Fellows of the AMS: Inaugural Class" (PDF). Notices of the American Mathematical Society. 60 (5): 631–637. May 2013. Retrieved September 26, 2019.
- ^ "Approaches to Group Theory conference webpage". Retrieved September 26, 2019.
- ^ Glaser, Linda (October 27, 2010). "Ken Brown mirrors the changing face of mathematics". Cornell Chronicle. Retrieved September 26, 2019.
- ^ "ICM Plenary and Invited Speakers". International Mathematical Union. Retrieved September 26, 2019.
External links
edit- "Ken Brown's homepage". Retrieved September 26, 2019.
Category:1945 births Category:Living people Category:20th-century American mathematicians Category:21st-century American mathematicians Category:Massachusetts Institute of Technology alumni Category:Cornell University faculty Category:Fellows of the American Mathematical Society Category:Place of birth missing (living people) Category:Category theorists Category:Topologists Category:Group theorists