#### 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, one uses matrix coefficients of supercuspidal representations as test functions, which excludes many important cases. In this talk, 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, 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。最近，他們把猜想由一般L-packet 推广到由Arthur packet 出來的非一般L-packet。这个报告会介紹这个猜想及一些迸展。

#### 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， 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，至多有有限多个例外。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）。

#### 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, 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, for a local complete regular Noetherian ring R with perfect residue field of characteristic p, 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, Goldfeld conjectured that, for every elliptic curve defined over Q, amongst the set of all its quadratic twists with root number +1, there is a subset of density one where the central L-value of the twist is non-zero, and amongst the set of all its quadratic twists with root number -1, 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, 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, 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, that we call Bernstein eigenvarieties, 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 introduce the Kudla program. We will recall the development of this topic, 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, 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, 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, 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, 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 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., when n=1) and then discuss about some speculations and results for covers, 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(0,1). This problem, raised by Beurling and Wintner in the 1940s, is closely related to the Riemann Hypothesis.

#### 何伟（清华大学YMSC & BIMSA）

Theta lifting and quadratic twist L-values

Given a Diophantine Equation, one would like to study its analytic invariants to get some information on arithmetic. In this talk, we first review Tunnell’s theorem on congruent elliptic curves, which gives conjectural answer for the congruent number problem. Then we will talk about how to generalize Tunnell’s theorem to quadratic twist family of any newform with positive even weight.

#### 胡永泉（中科院晨兴数学中心）

On a generalization of Colmez’s functor

In 2005, Colmez defined an exact functor from the category of finite length admissible smooth representations of GL_2(Q_p) over a field of characteristic p to the category of finite length continuous representations of the absolute Galois group of Q_p. This functor has played a crucial role in the p-adic Langlands program for GL_2(Q_p). In this talk, I will review the construction of Colmez’s functor and a generalization due to Breuil. I will discuss the exactness and finiteness of this (generalized) functor. This is a joint work with Breuil, Herzig, Morra and Schraen.

#### 胡勇（南方科技大学）

On Suslin's conjecture about Rost kernels of division algebras

Let $F$ be a field, $\ell$ be a prime and $D$ be a central division $F$-algebra of $\ell$-power degree. By the Rost kernel of $D$ we mean the subgroup of $F^*$ consisting of elements $\lambda$ such that the cohomology class $(D)\cup (\lambda)\in H^3(F,\,\mathbb{Q}_{\ell}/\mathbb{Z}_{\ell}(2))$ vanishes. In general, this subgroup contains the Suslin group, which we define to be the group generated by $i$-th powers of reduced norms from $D^{\otimes i},\,\forall i\ge 1$. In 1985, Suslin conjectured that the Rost kernel and the Suslin group always coincide. In this talk we will discuss some new cases of his conjecture, for complete discrete valuation fields. This is based on a joint work with Zhengyao Wu.

#### 黄炳荣（山东大学）

On the Rankin-Selberg problem

In this talk, I will introduce a method to solve the Rankin-Selberg problem on the second moment of Fourier coefficients of a GL(2) automorphic form. This improves the classical result of Rankin and Selberg (in 1939/1940).

#### Rafael von Kanel（IAS Tsinghua University）

Integral points on coarse Hilbert moduli schemes

We present explicit height bounds for integral points on coarse Hilbert moduli schemes. To illustrate the main result, we discuss various explicit examples. We also explain the strategy of proof which combines the method of Faltings (Arakelov, Parsin, Szpiro) with modularity. This is joint work with Arno Kret.

#### 李加宁（中国科学技术大学）

几类数域的类群计算和应用

我将报告关于纯三次、四次数域的类群精确计算的新结果和猜想, 以及在岩泽理论、Gross曲线的算术上的应用。

#### 李永雄（清华大学）

Some results on Satge curve

Let p be an odd prime which is congruent to 2(or 5) modulo 9, the elliptic curve x^3+y^3=2p(or 2p^2) is called Satge curve in literature. In this talk, we will talk about some results about the Birch and Swinnerton-Dyer conjecture for Satge curve.

#### 梁永祺（中国科学技术大学）

某些Chatelet曲面丛的算术研究

我们关心某些曲线上的Chatelet曲面丛的算术性质。我们将介绍Lagrange插值在这类纤维丛的算术性质的研究中的应用： Hasse原则和弱逼近性质的Brauer-Manin障碍在基域扩张下的行为。

#### 林明辉（华中师范大学）

On characteristics elements in noncommutative Iwasawa theory

Let E be an elliptic curve with either good ordinary or split multiplicative reduction at each prime above p. We begin reviewing characteristics elements of Coates et al attached to the Selmer group of E over a p-adic Lie extension. We then discribe how these elements are related to the Selmer ranks in the intermediate subextension of the p-adic Lie extension.

#### 刘东文（浙江大学）

Period relations for Rankin-Selberg L-functions

In this talk we explain the proof of the period relations of critical Rankin-Selberg L-values for regular algebraic automorphic representations of GL(n)*GL(n-1). Joint work with Prof. Jian-Shu Li and Prof. Binyong Sun.

#### 刘一峰（浙江大学数学高等研究院）

Recent advances in Beilinson-Bloch conjecture

In this talk, we will survey recent advances toward the Beilinson-Bloch conjecture, which generalizes the BS-D conjecture to higher dimensions. In particular, we will introduce the arithmetic inner product formula, which is a higher dimensional analogue of the Gross-Zagier formula. The talk is based on joint work with Chao Li.

#### 刘余（清华大学丘成桐数学中心）

On a compactification of moduli space of Shtukas

Yun-Zhang prove the higher Gross-Zagier formula for GL_2 over function fields, using the moduli stack of Shtukas for GL_2. We discuss a compactification of this stack, aimed to study their conjecture on the middle dimension cohomology of the stack.

#### 吕广世（山东大学）

Cancellation in Additively Twisted Sums on GL(m)

In this talk, we shall introduce our series of work concerning cancellation in the sum of additively twisted coefficients of automorphic L-function on GL(m). We prove cancellation in these twisted sums for all automorphic L-function on GL(m) (m>3), uniformly in the additive character. Previously this is only known for m=2, 3. The proof of this series of work relies on the generalized Bourgain-Sarnak-Ziegler criterion, the method of Montgomery and Vaughan, the sieve method, and the theory of automorphic L-functions. We shall also state some relevant results about cancellation in algebraic twisted sums on GL(m).

#### 莫仲鹏（苏州大学）

橢圆曲线的 L 函数的特殊值与 Gross-Zagier 公式

作为椭圆曲线的 Birch and Swinnerton-Dyer 猜想的一个推论 ，是椭圆曲线的 L 函数的特殊值，当适当地被除以周期之后，是一个有理数的平方。在这个报告里，我们会讲述，在一系列的情形，这可以从一般的 Gross-Zagier 公式所推出。

#### 齐治（浙江大学）

Beyond the Weyl barrier for GL(2) exponential sums

In this talk, I will introduce the Bessel delta-method and two new variants of the van der Corput method in 2 dimensions, and I will explain how to go beyond the Weyl barrier 3/2=1.5 for GL(2) exponential sums up to 1.63651.... This is joint work wit

#### 孙智伟（南京大学）

The 11 unknowns theorem and its applications

The 11 unknowns theorem due to the speaker states that a general polynomial equation in 11 unknowns over the integers is uncidable. We focus on this theorem and its various applications.

#### 王浩然（清华大学）

On the mod p cohomology for GL_2 - the nonsemisimple case

I will report a joint work with Yongquan Hu, in which we study the mod p cohomology of Shimura curves from the point of mod p local Langlands correspondence, when the local Galois representation at v|p is non-semisimple and sufficiently generic.

#### 魏达盛（中科院数学与系统科学研究院）

Rational points on fibration with few non-split fibers

Let f: X \to P^1 be a dominant map whose generic fibre is rationally connected. Assume that the Brauer-Manin obstruction controls Hasse principle and weak approximation for rational points on all (or most) smooth fibers. A natural question is whether the same holds for the whole space X. With some assumptions, we will try to answer this question and give some applications. This is a joint work with Harpaz and Wittenberg.

#### 郗平（西安交通大学）

Lang--Trotter conjecture for CM elliptic curves

For any elliptic curve $E$ over $\mathbf{Q}$ and any non-zero integer $r$, the Lang--Trotter conjecture has predicted the asymptotic behaviours of the number of good primes $p\leqslant x$, denoted by $\pi_{E,r}(x)$, such that the Frobenius trace of $E$ at $p$ is equal to the given integer $r$. Quite recently, we are able to prove an estimate for $\pi_{E,r}(x)$ which confirms the upper bound part of the conjecture for CM elliptic curves. Moreover, intimate connections of this conjecture and Hardy--Littlewood conjecture can also be established to characterize the shape of the Lang--Trotter constant in $\pi_{E,r}(x)$. This is based on the joint work with Daqing Wan (in progress).

#### 肖梁（北京大学）

模形式p进斜率的若干问题

Gouvea和Mazur在上世纪八九十年代对模形式p进斜率的进行了开创性的深入研究，并借助数值计算提出了很多令人惊讶且深刻的猜想。之后Coleman和Mazur引入了p进特征曲线的概念更好地刻画了p进模形式的形变，并给出研究模形式p进斜率的几何框架。这次报告将综合介绍在模形式斜率方向的一些最新进展并试图解释p进斜率的研究和p进朗兰兹纲领的联系。

#### 熊玮（湖南大学）

Siegel Eisenstein级数的一些性质

Siegel Eisenstein级数是一类重要的Eisenstein级数，特别是它们出现在Siegel-Weil公式中。对数域上的Siegel Eisenstein级数已经有了很多研究。为了研究函数域上的Siegel-Weil公式，需要了解函数域上的Siegel Eisenstein级数的一些性质，比如其极点和留数。我们将对此简单介绍下。

#### 徐斌（清华大学）

Functoriality of endoscopic transfer for general symplectic and even orthogonal groups

Langlands’ functoriality conjecture reveals a deep connection of automorphic representations among different reductive groups. Most known cases of functoriality fit into the theory of endoscopy, which concerns a group G and its endoscopic groups. We study the endoscopic theory for G being a quasisplit general symplectic or even orthogonal group over a number field, and prove the functoriality of endoscopic transfer for tempered automorphic representations of these groups under some technical assumption.

#### 许宾（四川大学）

Concrete constructions of automorphic representations and central values of L-functions

The central values of L-functions play an important role in number theory and automorphic representation theory. For example, it is important for the study of elliptic curves; and is also crucial in many topics of automorphic representations, such as Gan-Gross-Prasad conjecture and the global theta lifting. In this talk, we will recall some relations among global packets, automorphic periods, and automorphic L-functions. Then we introduce a new approach to show that, for a cuspidal representation of PGL(2) which has a quadratic twist with root number +1, 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, we briefly introduce preperiodic points in dynamics, 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。

#### 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, 7, 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, 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, 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, we will recall the l-adic sheaf constructed by Deligne, Katz and Fisher, 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, 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, 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, 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，简要介绍几点圆法在丢番图方程中的应用。

#### 周国晖（上海大学）

On the class number of pair of number fields

In this talk, 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.