Angus Macintyre
Angus MacIntyre | |
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![]() Angus Macintyre in 2009 | |
Born | Angus John MacIntyre 1941 (age 82–83) |
Alma mater |
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Awards |
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Scientific career | |
Institutions | Queen Mary University of London University of Edinburgh University of Oxford Yale University |
Thesis | Classifying Pairs of Real-Closed Fields (1968) |
Doctoral advisor | Dana Scott[2] |
Doctoral students | Zoé Chatzidakis[2] Peter Winkler[2] |
Website | maths |
Angus John Macintyre
Education
After undergraduate study at the University of Cambridge, he completed his PhD at Stanford University under the supervision of Dana Scott in 1968.[2]
Career and research
From 1973 to 1985, he was Professor of Mathematics at
Macintyre is known for many important results. These include classification of aleph-one categorical theories of groups and fields in 1971, which was very influential in the development of geometric stability theory.[citation needed] In 1976, he proved a result on quantifier elimination for p-adic fields from which a theory of semi-algebraic and subanalytic geometry for p-adic fields follows (in analogy with that for the real field) as shown by Jan Denef and Lou van den Dries and others. This quantifier elimination theorem was used by Jan Denef in 1984 to prove a conjecture of Jean-Pierre Serre on rationality of various p-adic Poincaré series, and subsequently these methods have been applied to prove rationality of a wide range of generating functions in group theory (e.g. subgroup growth) and number theory by various authors, notably Dan Segal and Marcus du Sautoy. Macintyre worked with Zoé Chatzidakis and Lou van den Dries on definable sets over finite fields generalising the estimates of Serge Lang and André Weil to definable sets and revisiting the work of James Ax on the logic of finite and pseudofinite fields. He initiated and proved results on the model theory of difference fields and of Frobenius automorphisms, where he proved extensions of Ax's work to this setting (including model-companions and decidability). Independently Ehud Hrushovski has proved model-theoretic results on Frobenius automorphisms. Macintyre developed a first-order model theory for intersection theory and showed connections to Alexander Grothendieck's standard conjectures on algebraic cycles.
Macintyre has proved many results on the model theory of real and complex exponentiation. With
Macintyre and Jamshid Derakhshan have developed a model theory for the
The adele ring was introduced by
Jamshid Derakhshan and Angus Macintyre solved in 2023 affirmatively a problem of
Macintyre and Marek Karpinski have proved several results on VC-dimension, which has had applications to theoretical computer science and neural networks.
Awards and honours
He was elected a Fellow of the Royal Society in 1993.[1] In 2003, he was awarded the Pólya Prize by the London Mathematical Society. From 2009 to 2011, he was President of the London Mathematical Society (LMS).
References
- ^ a b c Anon (1993). "Professor Angus MacIntyre FRS". London: Royal Society. Archived from the original on 17 November 2015. One or more of the preceding sentences incorporates text from the royalsociety.org website where:
"All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License." --"Royal Society Terms, conditions and policies". Archived from the original on 25 September 2015. Retrieved 9 March 2016.
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: CS1 maint: bot: original URL status unknown (link) - ^ a b c d Angus Macintyre at the Mathematics Genealogy Project
- ^ Anon (2016). "Professor A Macintyre FRS". Queen Mary University of London. Archived from the original on 4 March 2016.