GAeL XXIV

The 24th edition of GAeL will take place in Nesin Mathematics Village (Turkey) from 13 June to 17 June 2016. There will be three minicourses, selected contributed talks by participants and poster sessions. Here is the preliminary programm for the minicourses.

David Cox (Amherst College)

Title: Toric Varieties

Abstract (draft):
Lecture I: Review of Toric Geometry
Lecture II: The Toric Minimal Model Program
Lecture III: Reflexive Polytopes and Mirror Symmetry
Lecture IV: Multigraded Commutative Algebra and Geometric Modeling
(more information)

Christian Liedtke (TU München)

Title: Models of Curves, Abelian varieties, and K3 surfaces

Abstract (draft): Given a smooth and proper variety over the field of fractions of a local and complete discrete valuation ring R, is it possible to find “good” models of this variety over R? For some classes of varieties, we have satisfactory answers: namely, minimal models for curves, Néron models for Abelian varieties, and Kulikov models for K3 surfaces. A necessary (and sometimes even sufficient) condition for having a smooth model (a.k.a. good reduction) is an unramified Galois-action on cohomology (a.k.a. trivial monodromy in the complex setting over a disk). I will introduce and discuss these models, state and prove some results, and proceed to some more recent questions and developments. If time permits, I will give applications to reduction modulo finite characteristic, degenerations of families, and compactifications of moduli spaces.

Timothy Logvinenko (Cardiff University)

Title: DG-categories with a view towards algebraic geometry

Abstract (draft): The main aim of this lecture course is to explain some DG-categorical techniques for working with the derived category of coherent sheaves on an algebraic variety. These provide an extra layer of precision and overcome many of the standard shortcomings.
We gain natural constructions for e.g. functorial cones, convolutions of a complex of sheaves or gluing two categories along a functor.
To this end, I will begin with an introduction to the necessary abstract machinery, starting from basic principles. The notion of a DG-category and DG-modules over it. Basic properties of DG-modules: h-projective, perfect, acyclic. Derived category of a DG-category. Bimodules. Twisted complexes. Pre-triangulated categories. DG-enhancements. Homotopy category of DG-categories and quasi-functors.
I will then talk about the applications of these to algebraic geometry.


Sponsors

GAeL XXIV is made possible by the generous support of: