Prof. Dr. Mihai Paun – Freiburg Institute for Advanced Studies

Prof. Dr. Mihai Paun

University of Illinois in Chicago
Mathematics

External Senior Fellow (Marie S. Curie FCFP)
June – July 2016
May – August 2017

E-Mail: mpaun@uic.edu

Last Update: 31.08.2017

Curriculum Vitae

I obtained my PhD from Universit´e Joseph Fourier, Grenoble, in January 1998 under the supervision of Jean-Pierre Demailly. Currently I am “Several Complex Variables Professor” at KIAS, Seoul. 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 (hopefully…) positively complement the existent techniques in algebraic geometry.

My current research interests are spinning around three main themes, as follows.

Estimates for the Monge-Ampere operator and applications to algebraic geometry
L2 metrics on direct images of relative canonical bundles.
Analytic version of Steenbrink vanishing theorem.

Selected Publications

A numerical criterion for the Kahler cone of the compact Kahler manifolds, joint with J.{P. Demailly, Annals of Math., 159, 2004.
Siu’s invariance of plurigenera: a one{tower proof, preprint 2005, in J. Differential Geom. 76 (2007), no. 3, 485493.
Relative critical exponents, non-vanishing and metrics with minimal singularities. Invent. Math. 187 (2012), no. 1, 195258.
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, 203259.
Kodaira dimension of algebraic ber spaces over abelian varieties, joint with Junyan Cao, arXiv:1504.01095, accepted for publication Invent. Math. 2016.

FRIAS Project

Monge-Ampere equations and Kodaira dimension of algebraic fiber spaces

In the program of classification of algebraic varieties the Kodaira dimension is a birational invariant playing a dominant role. A crucial subadditivity property of this invariant was formulated by S. Iitaka long time ago. The main questions we intend to treat during our research visit at FRIAS are gravitating around this theme. We expect that the theory of Monge-Ampere equations combined with the algebraic geometry techniques developed over the last three decades will lead to new and interesting results in the direction of Iitaka conjecture.