Previous Special Year Seminar
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...
On the homology and the tree of $SL_2$ over polynomial rings, and reflexive sheaves of rank 2 on projective spaces II
11:00am|Physics Library, Bloomberg Hall 201
We will first quickly recall basic facts on the tree of SL_2
over a field K with a discrete valuation v, following Serre's book.
We will then generalize the geometric interpretation given in that
book for curves to a higher dimensional situation...
Exceptional collections and the Néron-Severi lattice for surfaces
Moduli of degree 4 K3 surfaces revisited
For low degree K3 surfaces there are several way of constructing
and compactifying the moduli space (via period maps, via GIT, or
via KSBA). In the case of degree 2 K3 surface, the relationship
between various compactifications is well understood by...
On the homology and the tree of $SL_2$ over polynomial rings, and reflexive sheaves of rank 2 on projective spaces I
11:00am|Physics Library, Bloomberg Hall 201
We will first quickly recall basic facts on the tree of SL_2
over a field K with a discrete valuation v, following Serre's book.
We will then generalize the geometric interpretation given in that
book for curves to a higher dimensional situation...
Toric chordality and applications
Karim Adiprasito
Inspired by the elementary notion of graph chordality, we
introduce the notion of toric chordality, which naturally gives a
tool to to study the geometry and combinatorics of cohomology
classes of toric varieties and the weight algebras of
polytopes...
A birational model of the Cartwright-Steger surface
Igor Dolgachev
A Cartwright-Steger surface is a complex ball quotient by a
certain arithmetic cocompact group associated to the cyclotomic
field $Q(e^{2\pi i/12})$, its numerical invariants are with $c_1^2
= 3c_2 = 9, p_g = q = 1$. It is a cyclic degree 3 cover of...
On descending cohomology geometrically
Sebastian Casalaina-Martin
In this talk I will present some joint work with Jeff Achter
concerning the problem of determining when the cohomology of a
smooth projective variety over the rational numbers can be modeled
by an abelian variety. The primary motivation is a problem...