UC Riverside Algebraic Geometry Seminar

Date	Speaker	Title	Abstract
(*) Tuesday, January 10, 2017 Start: 2:10 PM Location: Surge 268	Everyone UC Riverside	Organizational Meeting	Organizational Meeting
(*) Tuesday, January 17, 2017 Start: 2:10 PM Location: Surge 268	Kari Vilonen Northwestern University	Cartan theorems over a discrete valuation base	I will discuss Cartan theorems for Stein manifolds over a discrete valuation base. Although such situations are commonly considered in algebraic geometry we could not find any prior work in this direction in the context of analytic geometry. Nuclearity, a notion introduced by Groethendieck, plays an important role in our theory. This is joint work with Jari Taskinen.
Thursday, January 26, 2017 Start: 1:10 PM Location: Surge 268	Carl Mautner UC Riverside	Symplectic resolutions and hypertoric varieties	This talk will survey some basic definitions and results surrounding symplectic structures in algebraic geometry. After these generalities, we will restrict our attention to a class of symplectic varieties called hypertoric varieties and discuss some of their salient features.
Thursday, February 2, 2017 Start: 1:10 PM Location: Surge 268	Cristian Martinez UC Santa Barbara	Bogomolov-Gieseker Inequalities and Stability Conditions.	Given a Chern character v and an ample class H on a smooth projective complex surface, there is a distinguished open set of stability conditions so that the only semistable objects of type v are coherent sheaves that are Gieseker semistable with respect to H. Moving away from this chamber to its boundary corresponds to a contraction of the Gieseker moduli. This, for instance, accounts for all smooth MMPs on surfaces. One of the key ingredients in the construction of stability conditions on surfaces is the Bogomolov-Gieseker inequality on the Chern character of a semistable sheaf. On some threefolds a generalized inequality is satisfied by a class of "semistable" complexes, allowing for the construction of stability conditions. In this talk I will explore some of the ideas above and show a class of stable complexes violating the generalized Bogomolov-Gieseker inequality on blow-ups of smooth threefolds.
Thursday, February 16, 2017 Start: 1:10 PM Location: Surge 268	Wenhao Ou UCLA	Fano varieties where all pseudoeffective divisors are also numerically effective	We recall that a divisor in a smooth projective variety is said to be numerically effective (or nef) if it meets each curve with non negative intersection number, and is called pseudoeffective if it is the limit of effective Q-divisor classes. Both of these properties are ways in which a divisor can be in some sense “positive”. A nef divisor is always pseudoeffective, but the converse is not true in general. A Fano varity is a special variety whose anti-canonical divisor is ample. From the Cone Theorem, it turns out that the geometry of a Fano variety is closely related to its nef divisors. In this talk, we will consider Fano varieties such that all pseudoeffective divisors are nef. Wisniewski shows that the Picard number of such a variety is at most equal to its dimension. Druel classifies these varieties when these two numbers are equal. We classify the case when the Picard number is equal to the dimension minus 1.
Thursday, February 23, 2017 Start: 1:10 PM Location: Surge 268	Burt Totaro UCLA	Hodge theory of classifying spaces	The goal of this talk is to create a correspondence between the representation theory of algebraic groups and the topology of Lie groups. The idea is to study the Hodge theory of the classifying space of a reductive group over a field of characteristic p, the case of characteristic 0 being well known. The approach yields new calculations in representation theory, motivated by topology.
Thursday, March 2, 2017 Start: 1:10 PM Location: Surge 268	Stefano Vidussi UC Riverside	Kodaira fibrations and surface group extensions	In this talk I will discuss some constraints on surface group-by-surface group extensions to be fundamental groups of Kodaira fibrations.
Thursday, March 9, 2017 Start: 1:10 PM Location: Surge 268	Christopher Lyons California State University, Fullerton	Applications of some double covers of a class of surfaces of general type	We will focus on complex algebraic surfaces with invariants p_g=q=1 and K^2=2, an interesting class of surfaces of general type first classified in the late 1970s by Bombieri-Catanese and Horikawa. Inspired by work of Ishida, we describe how to obtain polynomial equations for unramified double covers of these surfaces. These more accessible double covers allow one to obtain results about the original surfaces themselves. First we will discuss how one may obtain (via zeta functions) an explicit surface with p_g=q=1, K^2=2 having minimal Picard number. This result and others then contribute towards proofs about the larger family of surfaces with these invariants, such as a big monodromy theorem and the Tate Conjecture in characteristic zero. This is joint work with Paul Lewis.
Thursday, March 16, 2017 Start: 1:10 PM Location: Surge 268	Humberto Diaz UC Riverside	Algebraic Cycles mod n. Episode II.	In this talk, I will give an overview of the group of algebraic cycles on a smooth projective variety and some infinitude results for this group. I will also report on work in progress for a new case of infinitude with mod n coefficients.