International Conference on Galois Representations, Automorphic Forms and Shimura Varieties

这项提案是为了支持美国参加2011年6月20-23日在台湾新竹国家理论科学中心（NCTS）举行的“伽罗瓦表示、自同构形式和志村变种国际会议”。这次会议的目的是展示伽罗瓦表现的多面性及其相互联系。邀请的演讲者包括非同余模形式、函数域超越理论、p进Hodge理论、伽罗瓦表示的模性、自同构表示、l -函数和志村变数算法等方面的专家。本文将从理论和计算两个方面阐述伽罗瓦表示、志村变数的自同构形式和算法的最新进展及其应用。在本次会议之前，Henri Darmon将提供一个关于“代数循环和p进变形”的短期课程来为学生做准备。会议结束后将举行两个关于非同余模形式和算术几何的特别日活动，以促进对更多重点主题的进一步研究导向的讨论。会议期间的演讲幻灯片将在国家科学技术中心的网站上发布。在怀尔斯证明费马大定理之后，伽罗瓦表示的研究课题引起了极大的关注。怀尔斯的证明在数学的几个重要领域之间开辟了新的联系，从解析和组合数论到算术几何。会议的主题集中在这些主题之间的相互作用。希望通过此类活动促进国际合作，从而在这些研究领域之间建立更深入的联系。关于会议的更多信息可以在以下网站上找到：//math.cts.nthu.edu.tw/Mathematics/GRAFSV2011.htm

This proposal is to support US participants to "An international conference on Galois representations, automorphic forms and Shimura varieties" which will take place during June 20-23, 2011, at the National Center for Theoretical Sciences (NCTS), Hsinchu, Taiwan. The purpose of this conference is to showcase the multi-facets of Galois representations and their inter-connections. The invited speakers include experts working on noncongruence modular forms, transcendence theory over function fields, p-adic Hodge theory, modularity of Galois representations, automorphic representations, L-functions, and arithmetic of Shimura varieties. Recent advances in and applications of Galois representations, automorphic forms and arithmetic of Shimura varieties, from theoretical and computational aspects, will be addressed. Preceding this conference, Henri Darmon will offer a short course on "Algebraic cycles and p-adic deformations" to prepare the students. Two accompanying special day activities on noncongruence modular forms and arithmetic geometry will be held after the conference to facilitate further research oriented discussions on more focused subjects. The slides of talks during the conference will be posted on the website of NCTS.The research topics on Galois representations has generated a tremendous attention after Wiles' proof of Fermat's last theorem. Wiles' proof opened up new connections among several important areas of mathematics, from analytic and combinatorial number theory to arithmetic geometry. The topics of the conference focuses on the interaction among these topics. It is hoped that international collaborations will be fostered through this kind of activities leading to further and deeper connections among these research fields. More information about the conference can be found at the websitehttp://math.cts.nthu.edu.tw/Mathematics/GRAFSV2011.htm