Program
AG Seminar Winter 2017
Student No.:40
Time:Thursday 15:30-16:30, 2017.11.9-2018.1.25
Instructor:Eduard Looijenga, Fu Lei, Xu Quan, Pan Jinzhao  
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Bldg.
Starting Date:2017-11-9
Ending Date:2018-1-25

Welcome to the AG seminar in YMSC, Tsinghua University. We will continue the AG seminar this semester.
We will invite the newly faculties and post-docs, also visitors to give a talk so that we can have more knowlege to each other and academic communication.

 

2017-12-21

Time: Thursday 15:30-16:30, 2017-12-21
Place: Conference room 3,  Floor 2, Jin Chun Yuan West Building
Speaker: Wang Zhenjian [YMSC,Tsinghua University]

Title: On homogeneous polynomials determined by their Jacobian ideals

Abstract: The Jacobian ideal is an important algebraic object that can be constructed from a homogeneous polynomial. In this talk, we shall discuss which homogeneous polynomials can be re-constructed (up to a multiplicative constant) from their Jacobian ideals.

  

 

2017-12-14

Time: Thursday 15:30-16:30, 2017-12-14
Place: Conference room 3,  Floor 2, Jin Chun Yuan West Building
Speaker: Pan Xuanyu [Amss, Chinese academy of Sciences]

Title: 1-Cycles on Fano manifolds

Abstract: In this talk, I will give a survey on the 1-cycles on Fano manifolds. It is well known that Fano manifolds have many rational curves, in particular, they are rationally connected. The geometry of Fano manifolds is governed by rational curves. So the cycles on Fano manifolds should be understood from their rational curves. Under this observation, I will also talk about a recent joint work with Cristian Minoccheri on 1-cycles on higher Fano manifolds.

 

2017-11-30

Time: Thursday 15:30-16:30, 2017-11-30
Place: Conference room 3,  Floor 2, Jin Chun Yuan West building
Speaker: Wen Hao, Tsinghua University

Title: Counting Multiplicities in a Hypersurface over a Number Field
Abstract: In this talk, I will consider a multiplicity-counting problem, concerning rational points (moreover, algebraic points) of a bounded height in a projective hypersurface over a number field. Using techniques of intersection theory, I will give an upper bound for the sum of the multiplicity of these points, with respect to a fixed counting function, in terms of the degree of the hypersurface, the dimension of the singular locus and the upper bound of height.
  

 

2017-11-23

Time: Thursday 15:30-16:30, 2017-11-23
Place: Conference room 3,  Floor 2, Jin Chun Yuan West building
Speaker: Zuo Huaiqing, YMSC, Tsinghua University
Title: New derivation Lie algebras and non-existence of negative weight derivations of isolated singularities
Abstract: Let $R$ be a positively graded Artinian algebra. A long-standing conjecture in algebraic geometry, and rational homotopy theory is the non-existence of negative weight derivations on $R$.  On the one hand, Aleksandrov conjectured that there is no negative weight derivation when $R$ is a complete intersection algebra.  On the other hand, Wahl conjectured that non-existence of negative weight derivations is still true for  positive dimensional positively graded $R$. In this talk, we shall first introduce new derivation Lie algebras of isolated singularities and some results related to these new Lie algebras. Also our recent progresses on the above conjectures will be presented.

 

2017-11-16

Time: Thursday 15:30-16:30, 2017-11-16
Place: Conference room 3,  Floor 2, Jin Chun Yuan West building
Speaker: Hui Chunyin, YMSC, Tsinghua University
Title:On the semi-simplicity of geometric Monodromy action in \mathbb{F}_{l} coefficients.
Abstract: Let X/\mathbb{F}_{q} be a smooth separated geometrically connected variety and f: Y \to X a smooth projective morphism. Let t be a geometry point of X and w \in mathb{Z}_{>0}. A celebrated result of Deligne states the geometric etale fundamental group II:=\pi_{1}^{et}(X_{\bar{\mathbb{F}_{q}}}, t) is semi-simple on H^{w}(Y_{t}, \mathbb{Q}_{l}) for all prime l not dividing q. By comparing the invariant dimensions of sufficiently many l-adic and mod l represntation arising from H^{l}(Y_{t}, \mathbb{Q}_{l}) and H^{w}(Y_{t}, F_{l}) respectively, we prove  II is semi-simple on H^{w}(Y_{t}, \mathbb{F}_{l}) for all sufficiently large l, generalizing Deligne's result. This is a joint work with Anna Cadoret and Akio Tamagawa.

 

2017-11-09
Time: Thursday 15:30-16:30, 2017-11-09
Place: Conference Room 3, Floor 2, Jin Chun Yuan West Building
Speaker: Li Duo, YMSC  Tsinghua University
Title: Simple birational maps
Abstract: We study K-equivalent birational maps which are resolved by a single blowup.  Examples of such maps include standard flops and twisted Mukai flops. We give a criterion for such maps to be a standard flop or a twisted Mukai flop. As an application, we classify all such birational maps up to dimension 5.

 

2017-11-30

Time: Thursday 15:30-16:30, 2017-11-30
Place: Conference room 3,  Floor 2, Jin Chun Yuan West building
Speaker: Wen Hao, Tsinghua University
Title: Counting Multiplicities in a Hypersurface over a Number Field

Abstract: In this talk, I will consider a multiplicity-counting problem, concerning rational points (moreover, algebraic points) of a bounded height in a projective hypersurface over a number field. Using techniques of intersection theory, I will give an upper bound for the sum of the multiplicity of these points, with respect to a fixed counting function, in terms of the degree of the hypersurface, the dimension of the singular locus and the upper bound of height.