BAGELS, Fall 2019

When/Where: Thursday 2:30 PM - 3:30 PM in LCB 121.


Date Speaker Title
August 29th Yen-An

Abstract: Multiplier ideal sheaf plays an important role in algebraic geometry. For the first half of the talk, I will introduce the multiplier ideal sheaf and some of its properties. Then, for the second half, I will show how to make use of the multiplier ideal sheaf to get a quadratic bound for Fujita's base point freeness conjecture.

September 5th You-Cheng

Abstract: In this talk, I will first recall the construction of normal cone and its properties. Then I will use it to define refined Gysin homomorphisms, which can be understood as the algebraic geometry version of cap product. As applications, I will talk about the ring structure on the Chow group of nonsingular variety and the construction of virtual fundamental class with a given moduli problem.

September 12th Seungsu

Abstract: In general, there is a counter example for Kawamata Viehweg vanishing theorem on positive characteristic. However, we still have the vanishing theorem for the globally F-regular varieties. In this talk, we will briefly discuss the proof of Kodaira vanishing in characteristic 0 and then will show the Kawamata Viehweg vanishing on globally F regular varieties.

September 19th Marin

Abstract: In this talk, I will explain how to construct a nef line bundle on a moduli space of Bridgeland-semistable objects. This line bundle varies with the stability condition, which can change the moduli space birationally. As an application, one can use the stability conditions on the plane to run the minimal model program for the Hilbert scheme of points.

September 26th Christian

Abstract: Geometric class field theory constructs abelian covers of algebraic curves (with prescribed ramification). The key idea is to construct sheaves on the Picard group of the curve. In this talk we will discuss geometric class field theory, what it has to do with class field theory, and generalizations where the Picard group is replaced with the moduli space of rank n vector bundles.

October 3rd Matteo

Abstract: The derived category D(X) of a smooth projective variety X carries a great deal of the geometric information of X. It is a natural question to ask whether this information is enough to recover X uniquely — this is true, for example, in the case of the category of coherent sheaves Coh(X). In this talk I will briefly introduce D(X) and then prove Bondal and Orlov’s Theorem, which answers the previous questions positively in the case of K_X being ample (or anti-ample). I will also give a couple of counterexamples in the case of K_X=0 (the so-called Fourier-Mukai partners).

October 10th Fall Break No talk
October 17th Ziwen

Abstract: The volume of a Fano manifold plays an important role in the study of Fano manifolds. One interesting question is to find upper bounds of the volumes for various classes of Fano manifolds. In this talk, I will consider Fano 3-folds first. By classification results of Fano 3-folds, we know that the volumes of Fano 3-folds are bounded by 64, which is the volume of the projective 3-space. I will also show how to compute explicitly upper bounds of the volumes for some particular classes of Fano 3-folds. This is not going to give any new upper bounds better than 64 for Fano 3-folds. However, similar questions become more interesting for higher dimensional Fano manifolds.

October 24th Qingyuan

Abstract: This is the abstract.

October 31th Lingyao

Abstract: This is the abstract.

November 7th Hanlin

Abstract: This is the abstract.

November 14th Jose

Abstract: This is the abstract.

November 21th Junpeng

Abstract: This is the abstract.

November 28th Thanksgiving No talk
December 5th Wei

Abstract: This is the abstract.

Past seminars

Spring 2019
Fall 2018
Spring 2018
Fall 2017
Spring 2017
Fall 2016
Spring 2016
Fall 2015