# Michael McQuillan (mathematician)

Michael Liam McQuillan is a Scottish mathematician studying algebraic geometry.

McQuillan received the doctorate in 1993 at Harvard University under Barry Mazur ("Division points on semi-Abelian varieties"). Later he was at All Souls College of the University of Oxford 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. As of 2013 he is Professor at the University of Rome Tor Vergata.

McQuillan's research interests are in algebraic geometry. 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) and applied the method of dynamic diophantine approximation which he developed in the process, to transcendental algebraic geometry (and therefore for 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,[1] 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[2] 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).[3]

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

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

## References

1. ^ McQuillan, Michael Liam (1996). "A new proof of the Bloch conjecture". J. Algebraic Geom. 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.
2. ^ McQuillan, Michael Liam (1999). "Holomorphic curves on hyperplane sections of 3-folds". Geom. Funct. Anal. 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.
3. ^ McQuillan, Michael Liam (1998). "Diophantine approximations and foliations". Inst. Hautes Études Sci. Publ. Math. 87: 121–174. MR 1659270.