Indranil Biswas and Mahan Mj
27 January 2020 to 31 January 2020
Madhava Lecture Hall, ICTS Bangalore

Birational geometry is one of the current research trends in fields of Algebraic Geometry and Analytic Geometry. It came into prominence during mid-1980s, and has since seen a rise in research. The proposed lectures are on two topics of birational geometry.

Speaker : Yohan Brunebarbe
Title : Hyperbolicity and Fundamental groups.
Abstract : The course will focus on the interplay between the linear representations of the fundamental groups; the holomorphic (pluri) differentials and hyperbolicity of complex projective manifolds. It will also introduce the necessary tools and techniques of variational and mixed Hodge theories, to help prove that a local system of geometric origin on a 'special' manifold has a virtually abelian monodromy. The course will also explore on using non-abelian Hodge theory and harmonic maps to treat the general case.

Speaker : Frederic Campana
Title : Birational Geometry and Orbifold Pairs : Arithmetic and hyperbolic aspects.
Abstract : Birational geometry aims at deducing the qualitative structure of complex projective manifolds $X$ from the positivity/negativity properties of their canonical bundles $K_X$. The course will explain how to achieve this goal using the notion of 'special' manifolds, which generalise rational and elliptic curves. A manifold is indeed defined to be special if, for any p>0, no line subbundle of $\Omega^p_X$ has top Kodaira dimension $p$. The functorial 'core map' $c_X:X\to C_X$ then canonically splits any $X$ into its 'special' part (the fibres) and its `general type' part (the orbifold base). This spitting permits to give a simple (but still conjectural) description of the distribution of entire curves and rational points on any $X$.

program  ictsresin