Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

The first scientific colloquium of the "RTG 2965 - From Geometry to Numbers: Moduli, Hodge Theory, Rational Points", will be held in the HU-Berlin on November 22nd.

All the talks take place in Room 1.013 of Haus 1, Johann-von-Neumann-Haus (Rudower Ch. 25, 12489 Berlin).

The program consists of the following four lectures:

• 10:00-11:00 -- Jarod Alper (University of Washington): Tannaka Duality and GAGA Theorems in Algebraic Geometry.

Tannaka Duality refers to the reconstruction of a compact group from its representations, while Serre's GAGA theorem relates coherent sheaves on an algebraic variety to its analytification.  This talk will explore various incarnations of these two classical theorems in algebraic geometry with applications to moduli theory. 

• 11:30-12:30 -- Tim Browning (IST Austria): A motivic circle method.

The circle method has been a versatile tool in the study of rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to information about moduli spaces of rational curves on hypersurfaces. I will report on joint work with Margaret Bilu on implementing a circle method with an even more geometric flavour, where the computations take place in a suitable Grothendieck ring of varieties. We establish analogues for the key steps of the method, enabling us to approximate the classes of the above moduli spaces directly without recourse to point counting.

• 14:30-15:30 -- Soheyla Feyzbakhsh (Imperial College London): Relations of Kuznetsov components of a Gushel-Mukai variety and its hyperplane sections.

Let X be a very general Gushel–Mukai variety of dimension n>3, and let Y be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of X and Y. In this talk, I will show that the Bridgeland stability of objects is preserved under both of these functors and discuss some applications of this result. Joint work with Henfei Guo, Zhiyu Liu and Shizhuo Zhang.

• 16:00-17:00 -- Rahul Pandharipande (ETH Zürich): Geometry of the compactifications of the moduli of abelian varieties.

I will discuss recent results and conjectures concerning the structure of cycle classes on A_g and its toroidal compactifications. I will present joint work with Canning, Molcho, and Oprea on projections, a calculation of the Euler characteristic of A_g by Iribar López, and a new conjecture by Pixton about the Hodge class.