Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China

• Dongho Byeon (Seoul University)
  • Title: Elliptic curves of rank 1 satisfying the 3-part of the Birch and Swinnerton-Dyer conjecture
  • Abstract: Let E be an elliptic curve over Q of conductor N and K be an imaginary quadratic field, where all prime divisors of N are split. If the analytic rank of E over K is equal to 1, then the Gross and Zagier formula for the value of the derivative of the L-function of E over K, when combined with the Birch and Swinnerton-Dyer conjecture, gives a conjectural formula for the order of the Shafarevich-Tate group of E over K. In this talk, we show that there are infinitely many elliptic curves E such that for a positive proportion of imaginary quadratic fields K, the 3-part of the conjectural formula is true.



• Dohoon Choi (Korea Aerospace University)
  • Title: Non-vanishing of central values of modular L-functions mod $\ell$
  • Abstract: In this talk, considering the non-existence of newform having a reducible Galois representation, we study the algebraic parts of the central critical values of these twisted L-series modulo primes $\ell$. As an application, we consider, under the assumption of BSD conjecture, the non-vanishing for the orders of the Tate-Shafarevich groups of elliptic curves mod $\ell$.



• John H. Coates (Cambridge University)
  • Title: The non-commutative main conjecture for modular forms of weight > 2
  • Abstract: TBA



• Tuan Ngo Dac (Université Paris 13)
  • Title: On compactifications of moduli spaces of shtukas
  • Abstract: The Langlands correspondence over function fields for GL(n) was proved by Drinfeld and Lafforgue via the study of moduli spaces of shtukas for GL(n). In this talk, we discuss the problem of compactifying moduli spaces for a general reductive group G (split over a finite field). This is a joint work with Y. Varshavsky.



• Sanoli Gun (IMSC, Chennai)
  • Title: On a conjecture of Chowla and Milnor
  • Abstract: In this talk, we discuss about a conjecture of Chowla and Milnor about non-vanishing of $L$-functions at integers $k >1$ of periodic arithmetic functions. We also discuss its relation to multiple zeta values and polylogarithms.



• Tamotsu Ikeda (Kyoto Unviersity)
  • Title: Stabilization of the trace formule for the covering groups of SL2 and its application to the theory of Kohneu plus space
  • Abstract: TBA



• Naoki Imai (RIMS, Kyoto)
  • Title: Dimensions of moduli spaces of finite flat models
  • Abstract: A finite flat model is a finite flat group scheme over the ring of integers of a p-adic field with a fixed generic fiber. In this talk, we discuss a moduli space of finite flat models. Especially, we give a dimensional bound of the moduli spaces using a ramification index of a p-adic field.



• Junmyeong Jang (KIAS)
  • Title: The ordinarity of an isotrivial elliptic fibration
  • Abstract: In this talk, we will see a criterion of the ordinarity for isotrivial elliptic surfaces over a field of positive characterisitc in terms of the generic fiber and a suitable covering of the base. Using this, we will prove the ordinary reduction theorem for some isotrivial elliptic surfaces defined over a number field.



• Dihua Jiang (University of Minnesota)
  • Title: Automorphic Descents and Stable Arthur Packets
  • Abstract: It is a report of my recent work with David Ginzburg and David Soudry on construction of relations among different stable Arthur packets via the automorphic descent method.



• Shinichi Kobayashi (Tohoku University)
  • Title: The p-adic Gross-Zagier formula for elliptic curves at supersingular primes
  • Abstract: The p-adic Gross-Zagier formula for elliptic curves is a formula relating the derivative of the p-adic L-function of elliptic curves with the p-adic height of Heegner points. The formula is proved by B. Perrin-Riou in 1980's if p is a good ordinary prime and recently by the speaker if p is a good supersingular prime. In this talk, we explain the proof and an application for the full Birch and Swinnerton-Dyer conjecture.



• Masato Kurihara (Keio University)
  • Title: Euler systems of Gauss sum type
  • Abstract: I will talk on the Euler systems and Kolyvagin systems of Gauss sum type and their applications.



• Xiaoqing Li (SUNY & Buffalo University)
  • Title: The L^2 restriction of a GL(3) Maass form to GL(2)
  • Abstract: In this talk, we sill study the L^2 restriction problem of a GL(3) Maass form to GL(2). By Parseval's formula, the problem becomes bounding averages of different families of GL(3)xGL(2) L-functions. Assuming the Lindel of hypothesis for these GL(3)xGL(2) L-functions as we usually do, one can achieve a sharp bound in terms of the analytic conductor of the varying GL(3) Maass form. However, we will give an unconditional proof of this sharp bound for selfdual GL(3) Maass forms. For nonselfdual GL(3) Maass forms, our bounds depend on the bounds of the first Fourier coefficients of the GL(3) Maass forms. This is a joint work with Matt Young.



• Yoichi Mieda (Kyushu University)
  • Title: Lefschetz trace formula and l-adic cohomology of the Rapoport-Zink spaces for GSp(4)
  • Abstract: Rapoport-Zink spaces are certain moduli spaces of quasi-isogenies of p-divisible groups with additional structures and can be regarded as local analogues of Shimura varieties. Kottwitz' conjecture predicts that their l-adic cohomology partially realize the local Langlands correspondence and the local Jacquet-Langlands correspondence for rather general reductive groups. In this talk, we will investigate the l-adic cohomology of the Rapoport-Zink space for GSp(4) by using Lefschetz trace formula for open adic spaces, and give a partial result on the conjecture of Kottwitz.



• Ramdorai Sujatha (TIFR, India)
  • Title: Iwasawa theory for Hida deformations
  • Abstract: We shall talk about some recent results proved on the Iwasawa theory of the Selmer and fine Selmer group for Hida deformations.



• Yichao Tian (AMSS & Princeton University)
  • Title: Classicality of overconvergent Hilbert modular forms in the quadratic inert case
  • Abstract: A famous theorem of Coleman says that an overconvergent p-adic elliptic modular form of small slope is classical. Now let F be a quadratic real field, and p be a rational prime that is inert in F. In this talk, I will explain that an overconvergent p-adic Hilbert modular form for F of integer weights (k_1,k_2) and slope < min{k_1, k_2}-2 is actually classical.



• Jing Yu (Taiwan University)
  • Title: On Transcendence theory for Drinfeld modules
  • Abstract: Drinfeld modules and its generalizations play an important role mathematics in the last 4 decades. We will report on the aspect of Drinfeld module theory relating to transcendence theory of positive characteristic, in particular recent progress on algebraic independence of periods which go much further than, e.g. the classical theory of elliptic curves. This throws new lights on classical open problems. The method of proof is based on realizing a version of Grothendieck's program of motives, so-called t-motives. We will also talk about algebraic independence of values of Drinfeld modular forms at algebraic points, and formulate still open questions in the positive characteristic world.



• Xinyi Yuan (Columbia University)
  • Title: Derivative of the triple product L-function
  • Abstract: In this talk, I will introduce a Gross--Zagier type formula relating the central derivative of the triple product L-function and the Beilinson--Bloch height of the Gross--Schoen diagonal cycle. I will focus on a description using representation theory parallel to Ichino's central value formula. It is a joint work with Shou-wu Zhang and Wei Zhang.



• Shouwu Zhang (Columbia University)
• Title: Gross-Zagier formula without newforms
• Abstract: In this talk, I will explain a Gross-Zagier formula for abelian varieties parametrized by Shimura curves without using newform theory.



• Weizhe Zheng (Columbia University)
• Title: Mod $\ell$ cohomology algebra of quotient stacks
• Abstract: Let $G$ be a compact Lie group acting on a topological space $X$. Quillen's theory of equivariant cohomology algebra relates the ring structure of $H^*_G(X,\mathbf{F}_\ell)$ to the elementary abelian $\ell$-subgroups of $X$ and the connected components of the fixed point sets under these subgroups. In this talk, we give an algebraic analogue of Quillen's theory, with coefficients. We will also discuss finiteness and localization in the algebraic setting. This is a joint work with Luc Illusie.