Lundi 20 juin 2016
IRMA
The "Joint Seminar in Algebraic and Complex Geometry" is a research seminar, organized by the research groups in Basel, Freiburg, Nancy and Strasbourg. The seminar meets roughly twice per semester in Strasbourg, for a full day. There are about four talks per meeting, both by invited guests and by speakers from the organizing universities. We aim to leave ample room for discussions and for a friendly chat.
The talks are open for everyone. Contact one of the organizers if you are interested in attending the meeting. We have some (very limited) funds that might help to support travel for some junior participants.
The seminar will meet in Strasbourg, June 20th in the conference room of the institute.
Organizer : G. Pacienza (Strasbourg)
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Lundi 20 juin 2016
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10:30
Patrick Graf
Algebraic approximation of Kähler threefolds of Kodaira dimension zero
The classical Kodaira problem asks whether every compact Kähler manifold admits an algebraic approximation, i.e. a flat deformation containing projective fibres arbitrarily close to the central fibre. As shown by Voisin, this is false in general, although it may still be true for minimal Kähler spaces. I will explain a recent result of mine in this direction, namely that a compact Kähler threefold with canonical singularities and vanishing first Chern class admits an algebraic approximation. As a corollary, the fundamental group of any Kähler threefold is a quotient of an extension of fundamental groups of projective manifolds, up to subgroups of finite index. -
11:45
Carlo Gasbarri
Liouville's inequality for transcendental points on projective varieties.
Liouville inequality is a lower bound of the norm of an integral section of a line bundle on an algebraic point of a variety. It is an important tool in may proofs in diophantine geometry and in transcendence. On transcendental points an inequality as good as Liouville inequality cannot hold. We will describe similar inequalities which hold for "many" transcendental points. -
14:30
Philipp Habegger
Diophantine Approximations of Definable Sets and Applications
The celebrated Pila-Wilkie Counting Theorem gives a strong bound for the number of rational points of bounded height on a set that is definable in an o-minimal structure. I will explain the notation of an o-minimal structure and discuss a result that bounds the number of rational approximations of a definable set. As an application we investigate sums of roots of unity of small modulus. -
16:00
Olivier Benoist
Curve classes on real threefolds.
The integral Hodge conjecture is a statement that predicts, when it holds true, what cohomology classes with integral coefficients on a smooth projective complex variety are algebraic. In this talk, I will describe a variant of this statement for varieties defined over the field of real numbers. I will prove some positive results for curve classes on real threefolds, and explain applications of these results to questions specific to real algebraic geometry (algebraicity of cohomology classes of the real locus, and existence of curves of even genus).
This is joint work with Olivier Wittenberg.