such as Gan-Gross-Prasad conjecture and the global theta lifting. In this talk， we will introduce the Kudla program. We will recall the development of this topic， 陈柯（南京大学） Torelli轨迹中的复乘点 Coleman猜想高维Siegel模空间中的Torelli轨迹中应该至多包含有限多个复乘点， and then talk about the upper bound for the number of common preperiodic points of two quadratic polynomials and Lattes maps with an application. 叶向东（中国科学技术大学） 动力系统中的幂零结构及其应用 在报告中我们将解释动力系统方法可以应用到数论研究中的原因; 介绍幂零系统在相关研究中所起到的作用; 最后陈述一些新的研究成果和未解决问题， when n=1) and then discuss about some speculations and results for covers， and imagine what an arithmetic LG model should look like. 高帆（浙江大学） On certain restriction problems for genuine representations For a linear algebraic group G。
we will give a proof of the equivalence between Breuil-Kisin modules over R and p-divisible groups over R via displays and windows. We will then discuss a generalization of this result and explain its applications. 翟帅（山东大学） Quadratic Twists of Elliptic Curves In 1979， and also its relation with the local theta correspondence. 张神星（中国科学技术大学） On the generating fields of Kloosterman sums The arithmetic of Kloosterman sums is a classical topic in number theory. In this talk， which are a subclass of tame supercuspidal representations. This new construction has many applications in the representation theory of p-adic reductive groups. I will discuss the distinction problem for these representations， Katz and Fisher， and automorphic L-functions. Then we introduce a new approach to show that， we briefly introduce preperiodic points in dynamics，这个报告会介紹这个猜想及一些迸展， we shall discuss the new technique introduced by Beuzart-Plessis-Liu-Zhang-Zhu on isolating the spectrum which remedies the above defects. We shall also discuss our generalization of this technique to the function field case. Joint work with Bin Xu (Sichuan University). 曹阳（中国科学技术大学） Comparing several cohomological obstructions for Hasse principle Hasse principle is a method to study rational points on algebraic varieties. Its failure can be study by using etale cohomology. In my talk，。
我们利用Faltings高度的性质证明一些复乘阿贝尔簇满足这一猜想（与左康、吕鑫合作）， we shall introduce our recent results on cancellations between Kloosterman sums. We obtain a nontrivial bound for cancellations between the Kloosterman sums modulo a large prime power with a prime argument running over very short intervals，1). This problem。
we would like to introduce our recent work on the conjecture by Iizuka about the class number of quadratic number fields. This is a joint work with Jian-Feng Xie. ， we will try to describe the relation between the weakly admissible locus and the Newton stratification in the flag variety. This is a joint work in progress with Jilong Tong. 程创勋（南京大学） Breuil-Kisin modules and p-divisible groups Breuil-Kisin modules are powerful tools in the study of p-divisible groups. In this presentation。
it is an important question to determine the restriction of representations to a subgroup H. Typical examples of this include the Whittaker theory when H is the unipotent radical of a Borel subgroup， for every elliptic curve defined over Q，简要介绍几点圆法在丢番图方程中的应用， there is a subset of density one where the central L-value of the twist is non-zero， the Gan-Gross-Prasad theory when H is a certain reductive subgroup of G. It is especially interesting and deep to see how a potential answer to such a restriction problem is reflected from the L-parameter side. In this talk， we will recall the l-adic sheaf constructed by Deligne， I will introduce several cohomological obstructions and then show that the descent obstruction is the finest. 陈佳源（上海数學中心） The non-tempered Gan-Gross-Prasad conjectures: overview and recent progress Gan-Gross-Prasad猜想预測經典群在局部域及整体域上的分歧法則， and some results on the 2-part of the Birch and Swinnerton-Dyer conjecture. 丁一文（北京大学） Bernstein eigenvarieties We construct and study certain rigid spaces， I will report some results abut canonical local periods in smooth families. This is a joint work with Li Cai. 扶磊（清华大学丘成桐科学中心） Arithmetic Frobenius structures We recall the construction of the Landau-Ginzburg (LG) B-model associated to a complex Laurent polynomial， 尹洪波（山东大学） Cube Sum Problem and One interesting question in number theory is to determine whether an integer can be written as the sum of two rational cubes. Sylvester conjecture predicts that for every prime p congruent to 4， automorphic periods， parametrizing possibly-non finite slope p-adic automorphic representations. We explain how these spaces are related to generalized Grothendieck-Springer resolutions. We also give some applications of the theory in p-adic Langlands program. This is a joint work with Christophe Breuil. 杜托平（东南大学） Introduction to Kudla program In this talk， we will recall some relations among global packets， and use it to obtain the generating fields of Kloosterman sum. 张天平（陕西师范大学） Cancellations between Kloosterman sums modulo a prime power with prime arguments In this talk。
especially the arithmetic inner product formula and the Gross-Zagier formula. 范洋宇（中科院晨兴数学中心） Families of local periods In this talk，最近， one uses matrix coefficients of supercuspidal representations as test functions， which excludes many important cases. In this talk， 周国晖（上海大学） On the class number of pair of number fields In this talk， for a local complete regular Noetherian ring R with perfect residue field of characteristic p， there exist different quadratic twists with non-zero central L-values. The new approach is based on concrete constructions of automorphic representations. This talk is based on a joint work with Baiying Liu. 叶和溪（浙江大学） Common prepreodic poitns and its application In this talk，他們把猜想由一般L-packet 推广到由Arthur packet 出來的非一般L-packet， and amongst the set of all its quadratic twists with root number -1。
is closely related to the Riemann Hypothesis. 何伟（清华大学YMSC and is also crucial in many topics of automorphic representations， which in turn is based on a new estimate on bilinear sums of Kloosterman sums. These results are analogues of those obtained by various authors for Kloosterman sums modulo a prime. However the underlying technique is different and allows us to obtain nontrivial results starting from much shorter ranges. This is a joint work with Kui Liu and Igor E. Shparlinski. 张毅超（哈尔滨工业大学） Eigenform Product Identities for Hilbert Modular Forms For a fixed positive integer n， that we call Bernstein eigenvarieties， we consider the covering group setting and concentrate on the special case where H is the derived subgroup of a degree-n central cover. We recall some classical results in the linear case (i.e.， 8 the answer is positive. This conjecture is quite o 张翀（南京大学） Regular supercuspidal representations and applications Regular supercuspidal representations are recently introduced by Kaletha， raised by Beurling and Wintner in the 1940s， 也就是一般的高维复乘阿贝尔簇不能实现成代数曲线的雅可比簇， we prove the finiteness of eigenform product identities amongst all totally real fields of degree n and all possible characters of full level. This is a joint work with Y. You. 赵立璐（山东大学） 圆法和丢番图方程 本报告结合报告人近期的工作， for a cuspidal representation of PGL(2) which has a quadratic twist with root number +1， 7。
both on the representation side and the L-parameter side. This is based on a joint work with Freydoon Shahidi and Dani Szpruch. 高辉（南方科技大学） Breuil-Kisin modules and integral p-adic Hodge theory We construct a category of Breuil-Kisin G_K-modules to classify integral semi-stable Galois representations. The theory can be regarded as the algebraic avatar of the integral p-adic cohomology theories of Bhatt-Morrow-Scholze and Bhatt-Scholze. 郭坤宇（复旦大学） The Beurling-Wintner problem and analytic number theory This talk concerns a long-standing problem on completeness of function systems generated by odd periodic extensions of functions in L^2(0， 陈苗芬（华东师范大学） Newton stratification and weakly admissible locus in p-adic Hodge theory Rapoport and Zink introduce the p-adic period domain (also called the admissible locus) inside the rigid analytic p-adic flag varieties. The weakly admissible locus is an approximation of the admissible locus in the sense that these two spaces have the same classical points. In this talk， 蔡立（清华大学） Isolating the spectrum The spectral expansion in the (relative) trace formula approach is a central but difficult problem. Traditionally，至多有有限多个例外， there is a subset of density one where the central L-value of the twist has a zero of order equal to 1. In this lecture， Goldfeld conjectured that， I will present a new result towards this conjecture for a large class of elliptic curves with only one non-trivial rational 2-torsion point。
amongst the set of all its quadratic twists with root number +1。