Algebraic Geometry Seminar
Fall 2026
Regular Day: Tuesday
Regular Time: 3:30PM - 4:30PM
Regular Location: LCB 215
| Date | Speaker | Talk Information | Details |
|---|---|---|---|
|
August 25 |
—
|
|
|
|
September 1 |
Yuchen Liu
|
The notion of special valuations, i.e. finitely generated valuations inducing klt degenerations of Fano
varieties, plays an important role in the recent study of K-stability and moduli of Fano varieties. Given an affine
log Calabi-Yau variety $U$, we show that its special skeleton, namely the space of special valuations in the dual
complex of $U$, is independent of the choice of its Fano compactifications. Consequently, the special skeleton of
$U$ is invariant under the action of $\text{Aut}(U)$. As an example, when $U$ is the complement of a Markov cubic surface
in the affine three-space, we show that the action of three Vieta involutions on the special skeleton exhibits a
surprising connection with dynamics on the hyperbolic plane.
|
|
|
September 15 |
Sridhar Venkatesh
|
For a complex algebraic variety X embedded inside a smooth variety Y, the local cohomology sheaves of X in Y carry additional structure of a (mixed) Hodge module. In the hypersurface and the
local complete intersection (lci) case, this has been widely leveraged to prove various results about higher Du Bois and higher rational singularities, among other things. We investigate these local
cohomology sheaves when X is a toric variety (which is typically non-lci) and prove various results about them. A few applications include showing that the local cohomological dimension of a toric
variety is NOT a combinatorial invariant, and some new results about the singular cohomology of toric varieties. This is based on joint work with Hyunsuk Kim.
|
|
|
September 22 |
Jonathon Fleck
|
The Hilbert schemes classifying the closed subschemes of projective
space with a fixed Hilbert polynomial are normally thought of as static
objects via Grothendieck's construction. Moreover, for projective spaces of
dimensions three or more they have been shown to satisfy a Murphy's Law of
arbitrarily bad behavior. The Hilbert schemes are known, however, to be
linearly connected via Borel-fixed ideals by a Theorem of Hartshorne. In
this talk, we use Borel-fixed ideals to realize the Hilbert schemes as
moduli spaces of Bridgeland-stable objects and use that to study variational
properties.
|
|
|
September 29 |
Fabio Bernasconi
|
Coming soon
|
|
|
October 6 |
Daniel Apsley
|
Coming soon
|
|
|
October 20 |
Ying Wang
|
Coming soon
|
|
|
October 27 |
Dano Kim
|
Coming soon
|
|
|
November 3 |
Roi Docampo
|
Coming soon.
|
|
|
November 10 |
Franco Rota
|
Coming soon
|
|
|
December 1 |
Anh Duc Vo
|
Coming soon
|
|
|
December 8 |
Wanchun Shen
|
Coming soon
|