Michael McQuillan (mathematician)

Michael Liam McQuillan is a Scottish mathematician studying algebraic geometry. As of 2019 he is Professor at the University of Rome Tor Vergata.

Michael Liam McQuillan
CitizenshipUnited Kingdom
EducationPh.D., Harvard University, 1992
Occupationmathematician

Career

Michael McQuillan received the doctorate in 1992 at Harvard University under Barry Mazur ("Division points on semi-Abelian varieties").[1][2]

In his dissertation he proved a twenty-year-old conjecture of Serge Lang about semi-Abelian varieties. He extended the theory developed by Paul Vojta, an analogy of the Nevanlinna theory, part of the value distribution theory of holomorphic functions, to diophantine geometry. He developed the method of dynamic diophantine approximation which he applied to transcendental algebraic geometry and therefore to varieties over the complex numbers, where methods of complex analysis can be used.

In particular he solved or made progress on several conjectures about the hyperbolicity of subvarieties of algebraic varieties. For example, he gave a new proof of a conjecture of André Bloch (1926) about holomorphic curves in closed subvarieties of Abelian varieties,[3] proved a conjecture of Shoshichi Kobayashi (about the Kobayashi-hyperbolicity of generic hypersurfaces of high degree in projective n-dimensional space) in the three-dimensional case[4] and achieved partial results on a conjecture of Mark Green and Phillip Griffiths (which states that a holomorphic curve on an algebraic surface of general type with cannot be Zariski-dense).[5]

From 1996 to 2001 he was a post-doctoral Research Fellow at All Souls College of the University of Oxford[6] and in 2009 was Professor at the University of Glasgow as well as Advanced Research Fellow of the British Engineering and Physical Sciences Research Council.

McQuillan's research interests are in algebraic geometry. He has also investigated algebraic differential equations on varieties and works on non-commutative Mori theory.

In 2000 he received the EMS Prize.[7] In 2001 he was awarded the Whitehead Prize of the London Mathematical Society for his work.[8] In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (Integrating ). In 2001 he received the Whittaker Prize.

As of 2019 he is Professor at the University of Rome Tor Vergata.

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References
  1. "Harvard Department of Mathematics PhD Dissertations Archival Listing". Harvard University. Archived from the original on 4 April 2019. Retrieved 17 July 2019.
  2. Michael McQuillan at the Mathematics Genealogy Project
  3. McQuillan, Michael Liam (1996). "A new proof of the Bloch conjecture". Journal of Algebraic Geometry. 5 (1): 107–117. MR 1358036. Bloch's proof was incomplete. Ochiai proved special cases. The first proof was by Mark Green, who presented a further proof with Phillip Griffiths in 1979.
  4. McQuillan, Michael Liam (1999). "Holomorphic curves on hyperplane sections of 3-folds". Geometric and Functional Analysis. 9 (2): 370–392. doi:10.1007/s000390050091. MR 1692470. At about the same time Jean-Pierre Demailly and J. El-Goul also achieved similar results.
  5. McQuillan, Michael Liam (1998). "Diophantine approximations and foliations". Publications Mathématiques de l'IHÉS. 87: 121–174. doi:10.1007/BF02698862. MR 1659270.
  6. "Dr Michael McQuillan". All Souls College.
  7. "Mathematics People (excerpt from Notices)" (PDF). American Mathematical Society. 2000.
  8. "Citation for Michael McQuillan (Laudatio for the Whitehead Prize)". London Mathematical Society. 2001-07-02. Archived from the original on 2004-08-22.
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