Biography:Peter McMullen
Peter McMullen | |
|---|---|
| Born | 11 May 1942 |
| Nationality | British |
| Alma mater | Trinity College, Cambridge |
| Known for | Upper bound theorem, McMullen problem |
| Scientific career | |
| Fields | Discrete geometry |
| Institutions | Western Washington University (1968–1969) University College London |
Peter McMullen (born 11 May 1942)[1] is a British mathematician, a professor emeritus of mathematics at University College London.[2]
Education and career
McMullen earned bachelor's and master's degrees from Trinity College, Cambridge, and studied at the University of Birmingham, where he received his doctorate in 1968.[3] and taught at Western Washington University from 1968 to 1969.[4] In 1978 he earned his Doctor of Science at University College London where he still works as a professor emeritus. In 2006 he was accepted as a corresponding member of the Austrian Academy of Sciences.[5]
Contributions
McMullen is known for his work in polyhedral combinatorics and discrete geometry, and in particular for proving what was then called the upper bound conjecture and now is the upper bound theorem. This result states that cyclic polytopes have the maximum possible number of faces among all polytopes with a given dimension and number of vertices.[6] McMullen also formulated the g-conjecture, later the g-theorem of Louis Billera, Carl W. Lee, and Richard P. Stanley, characterizing the f-vectors of simplicial spheres.[7]
The McMullen problem is an unsolved question in discrete geometry named after McMullen, concerning the number of points in general position for which a projective transformation into convex position can be guaranteed to exist. It was credited to a private communication from McMullen in a 1972 paper by David G. Larman.[8]
He is also known for his 1960s drawing, by hand, of a 2-dimensional representation of the Gosset polytope 421, the vertices of which form the vectors of the E8 root system.[9]
Awards and honours
McMullen was invited to speak at the 1974 International Congress of Mathematicians in Vancouver ; his contribution there had the title Metrical and combinatorial properties of convex polytopes.[10]
He was elected as a foreign member of the Austrian Academy of Sciences in 2006.[11] In 2012 he became an inaugural fellow of the American Mathematical Society.[12]
Selected publications
- Research papers
- McMullen, P. (1970), "The maximum numbers of faces of a convex polytope", Mathematika 17 (2): 179–184, doi:10.1112/s0025579300002850.
- Survey articles
- Books
References
- ↑ Peter McMullen, Peter M. Gruber, retrieved 2013-11-03.
- ↑ UCL IRIS information system, accessed 2013-11-05.
- ↑ McMullen, Peter; Schulte, Egon (12 December 2002), Abstract and regular polytopes, ISBN 9780521814966, https://books.google.com/books?id=JfmlMYe6MJgC&pg=PA530, retrieved 2022-05-11
- ↑ Peter McMullen Collection, 1967-1968, Special Collections, Wilson Library, Western Washington University, retrieved from worldcat.org 2013-11-03.
- ↑ "Austrian Academy of Sciences: Peter McMullen". https://www.oeaw.ac.at/m/mcmullen-peter.
- ↑ Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate Texts in Mathematics, 152, Springer, p. 254, ISBN 9780387943657, https://books.google.com/books?id=xd25TXSSUcgC&pg=PA254
- ↑ Gruber, Peter M. (2007), Convex and discrete geometry, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 336, Berlin: Springer, p. 265, ISBN 978-3-540-71132-2, https://books.google.com/books?id=bSZKAAAAQBAJ&pg=PA265.
- ↑ Larman, D. G. (1972), "On sets projectively equivalent to the vertices of a convex polytope", The Bulletin of the London Mathematical Society 4: 6–12, doi:10.1112/blms/4.1.6
- ↑ "A picture of the E8 root system". American Institute of Mathematics. https://aimath.org/E8/mcmullen.html.
- ↑ ICM 1974 proceedings .
- ↑ Awards, Appointments, Elections & Honours, University College London, June 2006, retrieved 2013-11-03.
- ↑ List of AMS fellows, retrieved 2013-11-03.
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