Previous Special Year Seminar
$A^1$ curves on quasi-projective varieties
Qile Chen
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...
The jumping coefficients of non-Q-Gorenstein multiplier ideals
Patrick Graf
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...
On some questions about minimal log discrepancies
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...
A survey of motivic homotopy theory
Marc Levine
11:00am|Physics Library, Bloomberg Hall 201
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.
Automorphisms of smooth canonically polarised surfaces in characteristic 2
Nikolaos Tziolas
Let $X$ be a smooth canonically polarised surface defined over
an algebraically closed field of characteristic 2. In this talk I
will present some results about the geometry of $X$ in the case
when the automorphism scheme $\mathrm{Aut}(X)$ of $X$ is...
Projectivity of the moduli space of KSBA stable pairs and applications
Zsolt Patakfalvi
KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher
dimensional generalizations of (weighted) stable pointed curves. I
will present a joint work in progress with Sándor Kovács on proving
the projectivity of this moduli space, by showing...
The cohomology groups of Hilbert schemes and compactified Jacobians of planar curves
I will first discuss a relation between the cohomology groups
(with rational coefficients) of the compactified Jacobian and those
of the Hilbert schemes of a projective irreducible curve $C$ with
planar singularities, which extends the classical...
Proper base change for zero cycles
We study the restriction map to the closed fiber for the Chow
group of zero-cycles over a complete discrete valuation ring. It
turns out that, for proper families of varieties and for certain
finite coefficients, the restriction map is an...
Algebraic curves, tropical geometry, and moduli
Tropical geometry gives a new approach to understanding old
questions about algebraic curves and their moduli spaces,
synthesizing techniques that range from Berkovich spaces to
elementary combinatorics. I will discuss an outline of this
method...
Samuel Grushevsky
The Torelli map associates to a genus g curve its Jacobian - a
$g$-dimensional principally polarized abelian variety. It turns
out, by the works of Mumford and Namikawa in the 1970s (resp.
Alexeev and Brunyate in 2010s), that the Torelli map extends...
