ERC ALKAGE: description of the project

The purpose of the ALKAGE project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, J.-P. Demailly has developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let us mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. The first goal of the project will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of the project is the analysis of the structure of projective or compact Kähler manifolds. The ultimate goal would be a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...), to higher dimensions. The general plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, it should be possible to go much further and to enhance the national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the ERC grant will be used to create even stronger interactions.





Several PhD grants and PostDoc positions will be supported by the ALKAGE program during the period 2015-2020. The PhD grants have a duration of 3 years, and PostDoc positions are normally for one year, renewable once. Applicants are expected to work in the general area of the program. They should send a CV, a letter of motivation and all usual documents (passport or ID document, diploms, recommendation letters) to

There is still one PostDoc position to be filled during the academic year 2016-2017. The deadline for applications is set on March 31, 2016.




ALKAGE workshop, May 17-20, 2016 at Institut Fourier

A one week workshop will be organized from May 17 to May 20 at Institut Fourier. The general themes covered include: vanishing theorems, structure of algebraic varieties, Kähler geometry, special, metrics, entire functions, holomorphic foliations.





Young-Jun Choi hired as Post-Doc on February 1, 2016

Dr Young-Jun Choi, a former student of Professor Kang-Tae Kim and a former researcher at KIAS in Seoul, has joined Institut Fourier as a PostDoc supported by the ERC ALKAGE on February 1, 2016. His recent work is concerned with Kähler geometry, especially the study of variations of pseudoconvex domains via Kähler-Einstein metrics, and the semipositivity of fiberwise Ricci flat Kähler metrics on Calabi-Yau fibrations.





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