Seminar of Advance Topics in Algebra and Geometry

报告人 Speaker:Xun Lin
组织者 Organizer:郑志伟
时间 Time:March 22-June 30, Wednesday, 1:30-3:05 pm
地点 Venue:Jinchunyuan West Building, Second Floor, Conference Room 3

Upcoming talk:

Title: Griffiths residue theorem and Landau-Ginzburg models

Speaker: Xun Lin (just graduated from YMSC, postdoc in MPIM)

Time: June 21 (Wed) 1:30-3:05 pm

Place: Jinchunyuan West Building, Floor 2, Conference room 3



A Griffiths’s classical theorem shows the primitive cohomology of a hypersurface is isomorphic to certain homogeneous pieces of the Jacobian algebra. I will review a new proof of Griffiths’s theorem using Orlov’s results of sigma-model/Landau-Ginzburg correspondence and the HKR isomorphism. The reference is “A category of Kernels for equivariant factorizations and its implications for Hodge theory” by Ballard, Favero, and Katzarkov.

Past talks:

Title: On Serrano conjecture
Speaker: Yuting Liu (YMSC, Phd Candidate)

Time: May 24 (Wed) 1:30-3:05 pm

Place: Jinchunyuan West Building, Floor 2, Conference Room 3


Strict nefness of divisors is a kind of positivity between nefness and ampleness. In general, strictly nef divisors may not be ample. However, People expect it to be true for (anti)canonical divisors or on Calabi-Yau varieties. F.Serrano proposed a weaker version of the famous Fujita conjecture with respect to strictly nef divisors. The conjecture implies all the expectation above. In this talk, I will firstly discuss the relationship between Serrano conjecture and other famous conjectures and then report recent progress on Serrano conjecture by Haidong Liu.

Title: Moduli of curves of genus 6 and K-stability

Speaker: Junyan Zhao (University of Illinois Chicago, Phd Candidate)

Time: May 17 (Wed), 1:30-3:05 pm

Place: Jinchunyuan West Building, Floor 2, Conference Room 3


A general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X_5 as a divisor of class -2K_{X_5}. This embedding is unique up to the action of the symmetric group S_5. Taking a double cover of X_5 branched along C yields a K3 surface Y. Thus the K-moduli spaces of the pair (X_5, cC) can be studied via wall-crossing and by relating them to the Hassett-Keel program for C and the HKL program for Y.  On the other hand, X_5 can be embedded in P^1 \times P^2 as a divisor of class O(1,2), under which -2K_X is linearly equivalent to O_X(2,2). One can study the VGIT-moduli spaces in this setting.  In this talk, I will compare these four types of compactified moduli spaces and their different birational models given by wall-crossing.

Title: A new proof of Torelli for cubic fourfolds.

Speaker:Xun Lin (林汛,YMSC博士生)

Time: April 19 (Wed.), 1:30-3:05 pm

Place: Jinchunyuan West Building, Floor 2, Conference Room 3


I will report a new proof of the global Torelli theorem for cubic fourfolds in a paper, Hochschild cohomology versus the Jacobian ring and the Torelli theorem for cubic fourfolds. Firstly, I will talk about how to recover the Jocobian ring of cubic fourfolds using categorical data, namely the K3 category of the cubic fourfolds. Then, we can recover the cubic fourfolds using a global version of Mather-Yau reconstruction for hypersurfaces. This is remarked as a categorical Torelli theorem for cubic fourfolds. Secondly, using derived Torelli for K3 surfaces and the categorical Torelli theorems for cubic fourfolds, we can prove the global Torelli theorems for cubic fourfolds. This new poof is closer in spirit to Donagi’s generic Torelli theorems for hypersurfaces.

Title: Recent developments on the irrationality of $p$-adic zeta values

Speaker:Li Lai (赖力,清华数学系博士生)

Time: April 12 (Wed.) 1:30-3:05 pm

Place: Jinchunyuan West Building, Floor 2, Conference Room 3


In this talk, we will discuss some recent developments and open problems on the irrationality of special values of the $p$-adic zeta function $zeta_p(\cdot)$. For example, we will show that at least one of the four $2$-adic zeta values $\zeta_2(7),\zeta_2(9),\zeta_2(11),\zeta_2(13)$ is irrational. The proof only involves elementary number theory, complex analysis, and $p$-adic analysis at the undergraduate level.

Talk 2:

Title: Gromov-Witten invariants of elliptic curves and configuration space integrals

Speaker: Jie Zhou

Time: March 29, 1:30-3:05 pm


Generating series of enumerative invariants are often suprisingly connected to period integrals. In this lecture I will explain two ways of establishing relations between Gromov-Witten invariants of elliptic curves and configuration space integrals. One is representation-theoretic based on works of Bloch-Okounkov and Okoukov-Pandharipande, the other is geometric via mirror symmetry. I will mainly focus on the 2nd one, in which regularization of divergent configuration space integrals plays an essential role.

Talk 1:

Title: Allcock's Monstrous Proposal

Speaker: Zhiwei Zheng

Time: March 22, 1:30-3:05 pm  


Daniel Allcock conjectured a relation between the orbifold fundamental group of a natural quotient of the 13-dimensional complex hyperbolic ball  and the monster simple group. If the conjecture is true, Allcock suggested to find an algebra-geometric way to explain the relation. These conjectures are mysterous. On one hand, the 13-dimensional ball is the largest one ever known admitting an action of a complex hyperbolic reflection group. And we do not find a modular meaning for this ball quotient. On the other hand, the monster simple group is the largest sporadic simple group, connecting to the famous moonshine phenomenon. In this talk, we are going to discuss the paper "A Monstrous Proposal" by Allcock.