Speaker: Kang Zuo (Mainz University)
Time: Friday, 20.Sep.2019, 14:3016:00
Place: Room 402, Mathematical Building
Abstract: In this talk I shall present an arithmetic Simpson correspondence between rank2 logarithmic periodic Higgs bundles and motivic local systems on hyperbolic affine curves via $p$ to $\ell$ companions conjectured by Deligne and solved by Abe and Drinfeld’s work on Langlands correspondence over function fields. This is a joint work with Raju Krishnamoorthy and Jinbang Yang.

Speaker: Hao Sun (Shanghai Normal University)
Time: Friday, 20.Sep.2019, 16:0017:00
Place: Room 402, Mathematical Building
Abstract: In this talk, I will introduce the recent progress of Bogomolov's inequality in positive characteristic and Bogomolov type inequalities for threefolds. The related applications will be discussed.

Speaker: Ke Chen (Nanjing University)
Time: Monday, 23.Sep.2019, 13:3014:30
Place: Room 401, Mathematical Building
Abstract: Coleman and Oort conjectured that when the genus g is large enough, every Shimura subvariety in the Siegel modular variety A_g should not be contained generically in the open Torelli locus T_g. We prove this for Shimura subvarieties of unitary type satisfying certain numerical conditions. This is a joint work with K. Zuo and X. Lu.

Speaker: Sichen Li (East China Normal University and National University of Singapore)
Time: Friday, 11.Oct.2019， 13:0014:00
Place: Room 402, Mathematical Building
Abstract: Let $X$ be a projective variety of dimension $n\ge1$ over an algebraically closed field of arbitrary characteristic. We prove a FujikiLieberman type theorem on the structure of the automorphism group of $X$. Let $G$ be a group of zero entropy automorphisms of $X$ and $G_0$ the set of elements in $G$ which are isotopic to the identity. We show that after replacing $G$ by a suitable finiteindex subgroup, $G/G_0$ is a unipotent group of the derived length at most $n1$. This result was first proved by Dinh, Oguiso and Zhang for compact K\"ahler manifolds.

Speaker: Zhi Qi (Zhejiang University)
Time: Friday, 18.Oct.2019, 13:
3014:
30
Place: Room 402, Mathematical Building
Abstract: In this talk, I will first introduce the thesis of Akshay Venkatesh on Beyond Endoscopy for $\mathrm{Sym}^2$ $L$functions on $\mathrm{GL}_2$ over $\mathbb{Q}$ or a totally real field. The idea follows a suggestion of Peter Sarnak on using the Kuznetsov relative trace formula instead of the ArthurSelberg trace formula for the Beyond Endoscopy problem. I will then discuss how to generalize Venkatesh's work from totally real to arbitrary number fields. The main supplement is an integral formula for the Fourier transform of Bessel functions over $\mathbb{C}$.

Speaker: Chuangxun Cheng (Nanjing University)
Time: Friday, 18.Oct.2019, 14:4015:40
Place: Room 402, Mathematical Building
Abstract: Serre remarked that his modularity conjecture could be viewed as part of a mod p Langlands philosophy. Indeed the weak conjecture can be viewed as asserting the existence of a global mod p Langlands correspondence for GL2/Q, and the strong conjecture can be viewed as a localglobal compatibility statement. In this talk, I will explain a precise interpretation of this remark provided by Emerton and its generalization to totally real fields proposed by BuzzardDiamondJarvis.

Speaker: Jie Liu (Morningside Center of Mathematics Chinese Academy of Sciences)
Time: Friday, 1.Nov.2019, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: Let $H$ be an ample line bundle over an $n$dimensional projective manifold $X$. Fujita's conjecture says that $K_X+mH$ is basepoint free for $m\geq n+1$ and $K_X+mH$ is very ample for $m\geq n+2$. On the other hand, Demailly introduced the socalled Seshadri constant to measure the positivity of $H$ locally at a point. In this talk, I will consider the case where $X$ is a Fano manifold and $H$ is the fundamental line bundle of $X$. I will explain how the existence of good ladders can be applied to the study of Fujita conjecture and the Seshadri constants in this situation. In particular, some applications to Fano manifolds with large index will be presented.

Speaker: Yifei Chen (Chinese Academy of Sciences)
Time: Friday, 1.Nov.2019, 14:4015:40
Place: Room 402, Mathematical Building
Abstract: In this talk, we will discuss the following problem:
For a fixed positive integer n and a fixed positive real number $\epsilon$, let $X_{a1a2...an} \to A^n$ be
the weighted blowup at the origin with the weight $(a1, a2, ..., an)$, where $a1, a2, ..., an$ are coprime positive integers such that $a1 \leq a2 \leq ... \leq an$. If the log pair $(X_{a1a2...an},0)$ is $\epsilon$lc, is $a1$ bounded? Precisely, for a fixed positive real number $\epsilon$, is there a positive integer $M$ depending only on $n$ and $\epsiln$, such that if $(X_{a1a2...an},0)$ is $\epsilon$lc, then $a_1 \leq M$.

Speaker: Yunfeng Jiang (ShanghaiTech University and University of Kansas)
Time: Friday, 15.Nov.2019, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: For a real four manifold, the Sduality conjecture of
VafaWitten (1994) predicts that the Stransformation sends the gauge group
SU(r)invariants counting instantons to the Langlands dual gauge group
SU(r)/Z_rinvariants; and both of the invariants satisfy modularity
properties. The SU(r)VafaWitten invariants have been constructed by
TanakaThomas using the moduli space of semistable Higgs bundle or sheaves
on a smooth projective surface. In this talk I will present the idea of
using moduli space of twisted sheaves and twisted Higgs sheaves on a
projective surface to define the Langlands dual gauge group
SU(r)/Z_rVafaWitten invariants, and prove the Sduality conjecture of
VafaWitten for projective plane in rank two and K3 surfaces in prime ranks.

Speaker: Xinyi Fang (East China Normal University)
Time: Friday, 22.Nov.2019, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: We study vector bundles on flag varieties over algebraic closed field k. In the first part, we suppose G=Gk(d,n) (d≤n−d) to be the Grassmannian manifold parameterizing linear subspaces of dimension d in k^n, where k is an algebraic closed field of characteristic p>0. Let E be a uniform vector bundle on G of rank r≤d. We show that E is a direct sum of line bundles unless it is a twist of either the pull back of the universal bundle Hd or its dual under the mth absolute Frobenius morphism, where(m≥0). In the second part, splitting properties of vector bundles on general flag varieties over characteristic 0 are considered.

Speaker: Mulin Li (Hunan University)
Time: Friday, 22.Nov.2019, 14:4015:40
Place: Room 402, Mathematical Building
Abstract: Virtual residue was first introduced by Chang and Li to interpret the correlations of the LandauGinzburg model. It is a generalization of the classical Grothendieck residue. We will discuss about the basic properties of the virtual residue, and the applications of it in algebraic geometry such as the CayleyBacharach theorems with excess vanishing.

Speaker: Zhiyuan Li (Fudan University)
Time: Friday, 13.Dec.2019, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: In this talk, I will give a survey on the study of minimal model program on moduli space of K3 surfaces. More precisely, I will discuss the relation between various compactifications of moduli of K3 surfaces via Briational Geometry. Those compactifications come from GIT, arithmetic and singularity theory.

Speaker: Jinxing Xu (University of Science and Technology of China)
Time: Friday, 13.Dec.2019, 14:4015:40
Place: Room 402, Mathematical Building
Abstract: The cyclic triple cover of the three dimensional complex projective space branched along six hyperplanes in general position is a CalabiYau threefold. By varying the hyperplane arrangements, we get a complete family of CalabiYau threefolds. I will show the global Torelli theorem holds for this CalabiYau family. The main ingredients of the proof are DeligneMostow's results on branched cyclic covers of the projective line and a monodromy group computation. This is a joint work with Mao Sheng.

Speaker: Zhi Jiang (Fudan University)
Time: Friday, 27.Dec.2019, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: We will explain some decomposition theorems of pushforwards of pluricanonical bundles to abelian varieties due to ChenJiang, PareschiPopaSchnell, and LombardiPopaSchnell. Then we will explain how to extend these results to singular spaces. Finally, we shall give some geometric applications of these results.

Speaker: Chuanhao Wei (Stony Brook University)
Time: Friday, 10.Jan.2020, 13:3014:30
Place: Room 402, Mathematical Building
Abstract: In this talk, I will introduce the hyperbolicity part of the Shafarevich Conjecture, which claims that a family of smooth curves of g>1 over C^* must be isotrivial, and its generalizations. In particular, I'll show our recent result, which shows that the logKodaira dimension of the base space of a family of smooth projective varieties is no less than the family's variation.
