Given a variety $Y$ with a rectangular Lefschetz decomposition
of its derived category, I will discuss an interesting relation
between the derived categories of a cyclic cover of $Y$ and its
branch divisor. As examples, I will describe the cases of...
Let $R$ be a regular semi-local domain, containing a field. Let
$G$ be a reductive group scheme over $R$. We prove that a principal
$G$-bundle over $R$ is trivial, if it is trivial over the fraction
field of $R$. If the regular semi-local domain $R$...
I will try to tell the story of the projective line minus three
points from the point of view of periods, and if time permits,
discuss some open problems.
This is joint work with G .Garkusha. Using the machinery of
framed sheaves developed by Voevodsky, a triangulated category of
framed motives is introduced and studied. To any smooth algebraic
variety $X$, the framed motive $M_{fr}(X)$ is associated...
Starting from an example in which the Hitchin correspondence can
be written down explicitly, we look at what might be said relating
the incidence complex of the boundary of the character variety, and
the Hitchin map.
I will try to tell the story of the projective line minus three
points from the point of view of periods, and if time permits,
discuss some open problems.
In this talk, I will present the recent joint work with Yi Zhu
on $A^1$-connectedness for quasi-projective varieties. The theory
of $A^1$-connectedness for quasi-projective varieties is an
analogue of rationally connectedness for projective...
De Fernex and Hacon associated a multiplier ideal sheaf to a
pair $(X, \mathfrak a^c)$ consisting of a normal variety and a
closed subscheme, which generalizes the usual notion where the
canonical divisor $K_X$ is assumed to be Q-Cartier. I will...
The minimal log discrepancy is a measure of singularities of
pairs. While akin to the log canonical threshold, it turns out to
be much more difficult to study, with many questions still open. I
will discuss a question about the boundedness of...
We discuss developments in motivic homotopy theory over the last
ten years, including structural aspects, the role of Postnikov
towers, oriented theories and quadratic forms.
