Professor Mihai Păun
I obtained my PhD from Université Joseph Fourier, Grenoble, in January 1998 under the supervision of Jean-Pierre Demailly. My primary research interests lie in the field of complex algebraic and differential geometry. The main research directions I have followed so far share many common points with problems arising from algebraic geometry. However, the methods that I am currently using in my research are mostly analytic, which positively complement the existent techniques in algebraic geometry.
My current research interests focus around these themes:
- Estimates for the Monge-Ampère operator and applications to algebraic geometry
- L2 metrics on direct images of relative canonical bundles.
Further papers can be found on the arXiv
- A numerical criterion for the Kähler cone of a compact Kähler manifolds, joint with J.-P. Demailly, in Annals of Math., 159, 2004. (journal)
- Siu's invariance of plurigenera: a one-tower proof, preprint 2005, in J. Differential Geom. 76 (2007), no. 3, 485-493. (journal)
- Relative critical exponents, non-vanishing and metrics with minimal singularities, in Invent. Math. 187 (2012), no. 1, 195-258. (journal)
- Extension theorems, non-vanishing and the existence of good minimal models, joint with Demailly, Jean-Pierre et Hacon, Christopher D., in Acta Math. 210 (2013), no. 2, 203-259. (journal)
- Kodaira dimension of algebraic fiber spaces over abelian varieties, joint with Junyan Cao, in Invent. Math. 207, 345-387 (2017). (journal)