Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at

University College London University College London (Trade name, branded as UCL) is a Public university, public research university in London, England. It is a Member institutions of the University of London, member institution of the Federal university, federal Uni ...

Education and career

McMullen earned bachelor's and master's degrees from

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, and studied at the

University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...

, where he received his doctorate in 1968. He taught at

Western Washington University Western Washington University (WWU or Western) is a public university in Bellingham, Washington, United States. The northernmost university in the contiguous United States, WWU was founded in 1893 as the state-funded New Whatcom Normal School, s ...

from 1968 to 1969. In 1978 he earned his Doctor of Science at

where he still works as a professor emeritus. In 2006 he was accepted as a corresponding member of the Austrian Academy of Sciences.

Contributions

McMullen is known for his work in

polyhedral combinatorics Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes. Research in polyhedral co ...

and

discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geom ...

, 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. 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. 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 In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, ...

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. 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.

Awards and honours

McMullen was invited to speak at the 1974

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

; his contribution there had the title ''Metrical and combinatorial properties of convex polytopes''. He was elected as a foreign member of the

Austrian Academy of Sciences The Austrian Academy of Sciences (; ÖAW) is a legal entity under the special protection of the Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every fi ...

in 2006. In 2012 he became an inaugural

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of AMS fellows
retrieved 2013-11-03.

Selected publications

;Research papers *. *. *. ;Survey articles *. Updated as "Valuations and dissections" (by McMullen alone) in ''Handbook of convex geometry'' (1993), . ;Books *. *.

References

{{DEFAULTSORT:McMullen, Peter 1942 births Living people 20th-century British mathematicians 21st-century British mathematicians Alumni of Trinity College, Cambridge Western Washington University faculty Academics of University College London Fellows of the American Mathematical Society Members of the Austrian Academy of Sciences British geometers