来源：赵永强 发布时间：2018-01-03 作者： 阅读数：2734次
Title：Basics on Modular Forms
Abstract：We plan to introduce some basics and theorems on the theory of modular forms. Our discussion will focus on the most studied elliptic modular forms and talk about their definition, construction and Hecke theory. We shall also see modular forms of different kinds and mention a special bridge between them: theta lifting. We make no attempt to present a complete and detailed theory but do hope a rough picture will suffice after piecing together the basics and theorems.
Title：Vinogradov's Mean Value Theorem via Efficient Congruencing
Abstract：Since 2011, Wooley has published a series of articles concerning Vinogradov's mean value theorem, using his "efficient congruencing" method. After over six years of perfection, he accomplished the proof of the so called main conjecture. In this talk, we introduce basic ideas of efficient congruencing. We also introduce some applications of Vinogradov's mean value theorem in additive number theory.
Title：Title: Lefschetz trace formula in Arakelov geometry
Abstract：This is a friendly introduction to Arakelov geometry. We take arithmetic Lefschetz trace formula as an example to show how classic results in scheme theoretic algebraic geometry were generalized to higher-dimensional Arakelov geometry, and why these generalizations are beneficial to the study of arithmetic problems.
Title：Square-free values of polynomials
Abstract：It is conjectured that any irreducible polynomial which satisfies the obvious congruence conditions should assume infinitely many square-free values. Unfortunately, this has been established only for polynomials of degree at most 3. Nobody knows how to show that any single quartic irreducible polynomial takes infinitely many square-free values. In this talk, we will give an introduction to this problem and discuss the so called “determinant method” used to attack this problem.