Algebraic Geometry Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
29 May 2018
15:45
Milena Hering
Abstract



Varieties admitting Frobenius splittings exhibit very nice properties.
For example, many nice properties of toric varieties can be deduced from
the fact that they are Frobenius split. Varieties admitting a diagonal
splitting exhibit even nicer properties. In this talk I will give an
overview over the consequences of the existence of such splittings and
then discuss criteria for toric varieties to be diagonally split.

  • Algebraic Geometry Seminar
12 June 2018
15:45
Abstract

I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality.  New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including  Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems.

  • Algebraic Geometry Seminar
4 July 2018
14:30
Paul Arne Østvær
Abstract

Motivic homotopy theory gives a way of viewing algebraic varieties and topological spaces as objects in the same category, where homotopies are parametrised  by the affine line.  In particular, there is a notion of $\mathbb A^1$ contractible varieties.  Affine spaces are $\mathbb A^1$ contractible by definition.  The Koras-Russell threefold KR defined by the equation $x + x^2y + z^2 + t^3 = 0$ in $\mathbb A^4$ is the first nontrivial example of an $\mathbb A^1$ contractible smooth affine variety.  We will discuss this example in some detail, and speculate on whether one can use motivic homotopy theory to distinguish between KR and $\mathbb A^3$.

  • Algebraic Geometry Seminar
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