会议日程

会议日程

签到:5月23日16:00-20:00 上海五角场大学路美壹酒店或 5月24日8:00-9:00光华楼东主楼1801

5月24日	5月25日
郗平 9:00-10:00	张通 8:30-9:30
茶歇 10:00-10:30	茶歇 9:30-10:00
肖正 10:30-11:30	曹阳 10:00-11:00
	骆文斌 11:00-12:00
午餐
许大昕 14:00-15:00	赵世豪 14:00-15:00
茶歇 15:00-15:30
易少云 15:30-16:30	张鼎新 15:30-16:30
杨丽萍 16:40-17:40
晚宴 18:15

报告题目和摘要

报告人：曹阳题目：Weak approximation for symmetric products and the fibration method 摘要：In the study of the Hasse principle and weak approximation for rational points on rationally connected varieties, the fibration method is a commonly used method, and the general case of this method depends on the Harpaz-Wittenberg conjecture. In this talk, we will discuss an unconditional fibration method for the large symmetric powers of rationally connected varieties.
报告人：骆文斌题目：Geometric Bogomolov conjecture for semi-abelian varieties 摘要：The geometric Bogomolov conjecture, originally formulated for abelian varieties over function fields, suggests that for a closed subvariety, its points of arbitrarily small canonical heights are Zariski dense if and only if it is special. This was a long-standing conjecture until the proof of Xie-Yuan. We generalize and prove the conjecture for semi-abelian varieties. A new phenomenon is that a special subvariety may not have a Zariski dense set of points of height 0. This is a joint work with Jiawei Yu.
报告人：郗平题目：The Brun--Titchmarsh theorem revisited 摘要： I will continue my talk at Fudan last year. We consider the distribution of primes $p\leq x$ in a large arithmetic progression $p\equiv a\bmod q$. The problem can be of different difficulties when $q$ is of different sizes compared to $x$. The classical Brun--Titchmarsh theorem gives an upper bound for the number of such primes. In this talk, we explain how to improve the classical work of Iwaniec on Brun--Titchmarsh theorem when $q$ is very close to $\sqrt{x},$ which is invalid in my talk of last year.
报告人：肖正题目：Hyperbolicity of $n+1$ Components and Non-Archimedean Curves 摘要： The celebrated Green-Griffiths-Lang conjecture predicts that if $X$ is a complex projective algebraic variety of general type, then every entire curve in $X$ is algebraically degenerate. Along this line, we prove a generalization of second main theorem in Nevanlinna theory. As applications, we obtain the hyperbolicity complement of $n+1$ components; for non-Archimedean entire curves, we prove the hyperbolicity complement of fewer components, with mild conditions. joint with Julie T.Y. Wang.
报告人：许大昕题目：Frobenius structure on theta connections and epipelagic Langlands parameters 摘要：In this talk, we first review the local monodromy at infinity of the Bessel F-isocrystals following Dwork, Sperber. Then we explain a generalization of this story for theta connections. Theta connections are certain rigid connections over $P^1$ minus two points, related to epipelagic representations under the geometric Langlands correspondence. As an application, we verify a conjecture of Reeder--Yu on the epipelagic Langlands parameters under some technical conditions. The talk is based on my joint work with Xinwen Zhu and a work in progress with Lingfei Yi.
报告人：杨丽萍题目：Unit roots of the unit root $L$-functions 摘要：Adolphson and Sperber expressed the unique unit root of the toric exponential sums in terms of the $A$-hypergeometric functions. For the unit root $L$-function of a family of toric exponential sums, Haessig and Sperber conjectured its unit root behaves similarly to the classical case studied by Adolphson and Sperber. Under a lower deformation hypothesis, Haessig and Sperber proved this conjecture is true. We will show that Haessig and Sperber's conjecture is true in general. This is a joint work with Zhang Hao.
报告人：易少云题目： On adelic Siegel Eisenstein series of degree 2 摘要： In this talk, we will discuss the classical Siegel Eisenstein series of weight $k$ and degree 2 within an adelic framework, mainly applying the method known as "Hecke summation". In the process, we recover the classical Fourier expansion of the Siegel Eisenstein series from an adelic point of view. One of our goals is to determine the automorphic representations associated to these Siegel Eisenstein series, particularly for the case of weight $k=2$, where the underlying global representation is highly reducible. We will begin by introducing the necessary background and motivation for this work. Next, we will review recent results in the study of classical and adelic Eisenstein series for GL(2) (the degree 1 case), which may be viewed as a toy example. Finally, we will present an overview of our ongoing work on the Siegel Eisenstein series of degree 2. These are joint works with Manami Roy and Ralf Schmidt.
报告人：张鼎新题目：Cohomological divisibility of exponential sums 摘要：40 odd years ago, Adolphson and Sperber demonstrated that the q-divisibility of complete exponential sums over F_q can be bounded by a specific combinatorial quantity using Dwork theory. While their result is p-adic in nature, the "independence of ℓ" conjecture suggests that the Frobenius eigenvalues of the ℓ-adic Artin-Schreier cohomology associated with these exponential sums should exhibit identical divisibility properties for every prime ℓ not dividing q. In this talk, I will present recent work in progress toward proving this divisibility for Frobenius eigenvalues.
报告人：张通题目：Slope inequality for threefolds fibred over curves 摘要： In the 1980s, Cornalba-Harris and Xiao established the optimal slope inequality for surfaces fibred over curves. The Arakelovian version for arithmetic surfaces was later obtained by Bost. Based on Xiao's method, various slope inequalities for threefolds fibred over curves were obtained, but it is not clear whether they are optimal. In this talk, I will introduce a recent joint work in progress with Y. Hu, proving some optimal lower bounds of the slope for threefolds fibred over curves.
报告人：赵世豪题目：Heights of Partial CM-Types and the Andre-Oort Conjecture 摘要：In the past twenty years, Pila and Zannier introduced a new method to prove unlikely intersection problems by utilizing tools from o-minimality and functional transcendence. Tsimerman used height bounds on the height of CM-types along with the Pila-Zannier method to prove the Andre-Oort Conjecture for the moduli space of abelian varieties. Recently, they have defined the height of a partial CM-type and proved height bounds on it to prove the full Andre-Oort Conjecture. We will discuss our work which gives a new proof of this height bound, as well as some results on how this relates to the Colmez Conjecture.

午餐及晚餐

会议期间5月24-25日的所有餐食安排在邯郸校区旦苑食堂。24-25日凭餐券在食堂二层使用（除楼清真窗口）。餐券仅可在一个窗口使用，不设找零

晚宴信息

仅限参会老师和博后参加