AG Seminar Spring 2018
Student No.:40
Time:Tue 15:30-16:30
Instructor:Eduard Looijenga, Fu Lei, Xu Quan, Pan Jinzhao  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-3-15
Ending Date:2018-6-7

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.





Speaker: Tian Zhiyu [Yangzhou Peking University]

Title: Asymptotic behaviour of space of rational curves

Abstract: I will discuss some conjectural description of asymptotic behaviours of the moduli space of rational curves as the degree goes to infinity, some consequences, and some evidences.


Speaker: Wu Yitao [Yangzhou University]

Title: P-adic period maps and local invariant cycle theorem

Abstract: In this talk, I'll first give a brief introduction to the p-adic period maps and comparison theorems, which play a central role in the p-adic Hodge theory. I'll then talk about some advanced topics based on the period maps—the p-adic local invariant cycle theorem.


Speaker: Shing-Tung Yau [Harvard University & Tsinghua university]

Title: Summary of Calabi-Yau Geometry

Abstract: In this talk, I will give a summary of Calabi-Yau geometry from its origin to development. Also, I will introduce most of important aspects of Calabi-Yau including BCOV theory and Gromov-Witten Invariant,Donaldson-Thomas invaraints, Moduli of Calabi-Yau manifold, K-stablity and so on. Meanwhile, I also explain the relations between these aspects and present status of these apsects.


Speaker: Yin Qizheng [BICMR,Peking University]

Title: Rational curves and special subvarieties in holomorphic symplectic varieties

Abstract: Holomorphic symplectic (a.k.a. hyper-Kähler) varieties form one of the three building blocks of varieties with trivial canonical bundle. We discuss the search of special subvarieties inside holomorphic symplectic varieties, together with applications to algebraic cycles, as well as an approach via rational curves. Many open questions will be presented. We also give concrete examples in the case of the Fano variety of lines in a cubic 4-fold.



Speaker: Raphael Achet [YMSC,Tsinghua university]

Title: The Picard groups of unipotent algebraic groups over an arbitrary field

Abstract: In this talk, firstly, we recall some basic results on the structure of unipotent algebraic groups over an arbitrary field. Then, we discuss the Picard group of the unipotent algebraic groups of dimension one.

Moreover, we define a "restricted" Picard functor and we show that if a unipotent algebraic group admits a regular completion then its "restricted" Picard functor is representable.

With this "restricted" Picard functor and geometric arguments we generalise a result of B. Totaro: if the Picard group of a unipotent group is nontrivial then it admits a nontrivial extension by the multiplicative group. Finally, if time permit, we will show that the Picard group of a unirational unipotent group is finite.



Speaker: Zongying [Shantou University]

Title: Equidimensionality and regularity

Abstract: The existence of an equidimensional morphism f admitting everywhere etale local sections, from a regular algebraic space X to a locally noetherian normal algebraic space S of residue characteristics zero with excellent local rings, implies that S is regular and f flat.




Speaker: Hu Zhenyu [National Taiwan University]

Title: Birational geometry in the LC category

Abstract:  In birational algebraic geometry we can quantify the type of singularities which occur: the most complex ones are the so-called \Log Canonical"(LC for short). There are milder ones, for example the \KLT" singularities.Most known results around MMP work in the KLT category, but not for the LC models. However, many important applications of MMP, such as higher dimensional moduli theory, require us to work with LC models. In this report I will talk about some of the developments in recent years focusing on extending techniques from KLT to LC, aiming at generalizing some techniques of Birkar -Cascini-Hacon-Mckernan(JAMS 2010).




Speaker: Xu Quan [YMSC, Tsinghua University]

Title: Syntomic cohomologies in syntomic regulator

Abstract: At the beginning, we will fast recall the analogue from complex regulators to p-adic regualtors. Then we investigate some kinds of syntomic cohomologies in syntomic regulator, inclduing my recent result on log rigid syntomic cohomology.If time permits, we also
talk about the relation between syntomic regulator and p-adic integrtion.



Speaker: Sun Shenghao [Tsinghua University]

Title: l-independence, perverse sheaves, and some related problems

Abstract: In the theory of etale cohomology, there is a type of problems called "independence of l". Basically, it asks whether any family of l-adic sheaves, though for varying primes l but which are compatible in some sense, remains compatible under any cohomological operation. One particular l-independence that we expect after the operation is applied is the domain of lissity, and this question has a variant w.r.t. the perverse t-structure. We will explain the relevant notions and state the theorem. Time permitting, we will also discuss some related questions in the end.