Michael McQuillan

Michael Liam McQuillan is a British mathematician who studies algebraic geometry .

Life

McQuillan received his PhD from Harvard University in 1992 with Barry Mazur (Division Points on Semi-Abelian Varieties). He was from 1996 to 2001 research fellow at All Souls College of the University of Oxford and then a professor at the University of Glasgow and Advanced Research Fellow of the British EPSRC . Currently (2019) he is a professor at Tor Vergata University .

McQuillan deals with algebraic geometry. In his dissertation he proved a twenty year old conjecture by Serge Lang about semiabelian varieties. He developed the theory found by Paul Vojta (analogy of the Nevanlinna theory of the value distribution of the function theory in Diophantine geometry) and applied the method he developed of dynamic Diophantine approximation in transcendent algebraic geometry (i.e. for varieties over the complex numbers, where methods of complex analysis are applicable). In particular, he solved or made progress in some conjectures about the hyperbolicity of sub-varieties of algebraic varieties. For example, he gave a new proof of a conjecture by André Bloch (1926) about holomorphic curves in closed sub-varieties of Abelian varieties, proved a conjecture by Shōshichi Kobayashi (about the Kobayashi hyperbolicity of generic hypersurfaces of high degree in projective n-dimensional space) in the three-dimensional case and partial results obtained with a conjecture by Mark Green and Phillip Griffiths (which says that a holomorphic curve on an algebraic surface of general type can be non- Zariski - dense ) ${\displaystyle c_{1}^{2}>c_{2}}$

He also studied algebraic differential equations on varieties and works on non-commutative Mori theory .

In 2000 he received the EMS Prize . In 2001 he received the Whitehead Prize from the London Mathematical Society for his work . In 2002 he was invited speaker at the ICM in Beijing ( integrating ${\displaystyle \partial {\bar {\partial }}}$ ). In 2001 he received the Whittaker Prize .

Web links

• Homepage in Glasgow
• Laudation for the Whitehead Prize ( Memento from July 1, 2004 in the Internet Archive )
• Laudation for EMS Prize, Notices AMS 2000 (PDF file)

Individual evidence

1. ↑ Harvard Department of Mathematics PhD Dissertations Archival Listing . Harvard University. Retrieved July 17, 2019.
2. ^ McQuillan A new proof of the Bloch conjecture , Journal Algebraic Geometry, Vol. 5, 1996, p. 107. Bloch's proof was incomplete. Ochiai proved special cases. The first proof was from Mark Green, who gave another proof with Phillip Griffiths in 1979.
3. ↑ McQuillan Holomorphic curves on hyperplane sections of 3-folds , Gem.Funct.Analysis Vol. 9, 1999, p. 370. At about the same time, Jean-Pierre Demailly and J. El-Goul also achieved similar results
4. ↑ McQuillan Diophantine approximations and foliations , Pub.Math.IHES, Vol. 87, 1998, pp. 121-174.