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.
2017-11-23
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.