Michael McQuillan (mathematician)

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 ${\displaystyle c_{1}^{2}>c_{2}}$ 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 ${\displaystyle \partial {\bar {\partial }}}$). In 2001 he received the Whittaker Prize.

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