UC Riverside Algebraic Geometry Seminar

UC Riverside Algebraic Geometry Seminar


The UC Riverside Algebraic Geometry Seminar meets on Thursdays from 2:10pm to 3:00pm in Surge 268. For more information you may contact Ziv Ran (ziv.ran@ucr.edu) or Jose Gonzalez (jose.gonzalez@ucr.edu). Please find our schedule below. For information about reimbursements for our visitors click here.



Winter 2018

Date Speaker Title Abstract
Thursday, April 12, 2018
Start: 2:10 PM
Location: Surge 268
Humberto Diaz
UC Riverside
Group cohomology and the integral Hodge conjecture. Atiyah and Hirzebruch gave the first counterexamples to the integral Hodge conjecture. They produced torsion cohomology classes which are not represented by algebraic cycles. In this talk, I will give an introduction to the technique of group cohomology and show how it can be used to produce these counterexamples.
Thursday, April 19, 2018
Start: 2:10 PM
Location: Surge 282
Zhixian Zhu
UC Riverside
Multiplier ideals learning seminar: Plurigenera under ètale coverings. We will recall the definition and properties of the asymptotic multiplier ideals associated to a big divisor. In particular, we will state and prove Kollar's theorem on plurigenera under ètale coverings.
Thursday, April 26, 2018
Start: 2:10 PM
Location: Surge 282
Lei Song
UC Riverside
Asymptotic multiplier ideals: applications. I will talk about two applications of asymptotic multiplier ideals. One is a multiplicative formula for plurigenera under finite ètale coverings, and the other is a comparison theorem for symbolic powers of ideals.
Thursday, May 3, 2018
Start: 2:10 PM
Location: Surge 282
Ziv Ran
UC Riverside
Deformation invariance of plurigenera: preliminaries. A theorem of Siu, settling a long-standing conjecture, states that when a smooth projective variety moves in a family, the plurigenera are constant. We will discuss some preliminaries to the proof, beginning with the definition of various base loci associated to a divisor and continuing with a reduction of the invariance theorem to an extension theorem stating that under suitable conditions the map restricting sections of a line bundle on a divisor is surjective.
Thursday, May 10, 2018
Start: 2:10 PM
Location: Surge 282
Jose Gonzalez
UC Riverside
Deformation invariance of plurigenera and extension theorems. A theorem of Siu, settling a long-standing conjecture, states that when a smooth projective variety moves in a family, the plurigenera are constant. We have reduced its proof to showing an extension theorem stating that under suitable conditions the map restricting sections of a line bundle to a divisor is surjective. In this talk we will work toward the proof of this extension theorem.
Thursday, May 17, 2018
Start: 2:10 PM
Location: Surge 282
Zhixian Zhu
UC Riverside
Siu's extension theorem. In the previous seminar meetings we have reduced the proof of the invariance of plurigenera to an extension theorem. In this talk, we will finish the proof of the extension theorem. We start with an inclusion result between asymptotic multiplier ideals and asymptotic restricted multiplier ideals. Then we will combine it with the lemmas proved last week to show the extension theorem.
Thursday, May 24, 2018
Start: 2:10 PM
Location: Surge 282
Mike Pierce
UC Riverside
Examining the proof of the Ax-Grothendieck Theorem. The Ax-Grothendieck Theorem states that for a variety X over an algebraically closed field, an injective morphism from X to X must also be bijective. While this result itself is pretty nifty, it's the method of proof that really deserves some attention. So in this talk I'll prove the Ax-Grothendieck theorem, and then discuss some theorems from model theory, like compactness and the Lefschetz principle, that cleanly encapsulate the ideas that appear in the proof. Then if time permits, I'll talk about ultrafilters and ultraproducts, since these are important in the proofs of the model-theoretic results.
Thursday, May 31, 2018
Start: 2:10 PM
Location: Surge 282
Jason Lo
Cal State Northridge
Autoequivalences and moduli spaces on threefolds. Autoequivalences of the derived category of coherent sheaves are known to induce morphisms among moduli spaces of geometric objects, and relations among the invariants counting them. In this talk, I will explain how autoequivalences on a threefold can be used to construct morphisms between moduli spaces of stable pairs and certain quot schemes, as well as higher-rank analogues of such results.
Thursday, June 7, 2018
Start: 2:10 PM
Location: Surge 282
Ethan Kowalenko
UC Riverside
Computations with Perverse Sheaves. Intersection homology is a theory which extends Poincaré duality from smooth manifolds to stratifiable spaces. This extended duality is proved in the language of derived categories of "constructible" sheaves. The goal of this talk is NOT to rigorously define any of the words I just said. Instead, I would like to focus on two examples: the algebraic group GL3(C) acting on its flag variety and the toric variety V(xy-zw) inside C4. The first example is related to the theory behind the Kazhdan-Lusztig polynomials in representation theory, while the second is an example that I use often in my research. Through these examples, I wish to illustrate how perverse sheaves can be computed.