Computational Representation Theory in Number Theory

该奖项提供了部分参与者支持研讨会“数论中的计算表示理论”举行2015年7月27日至31日在俄勒冈州州立大学科瓦利斯，俄勒冈州。 本次研讨会将促进当前与表示论相关的计算数论研究的产生和传播。 特别是，它将促进高级和初级研究人员之间的研究合作。 讲习班还将通过L函数和模块化形式数据库（LMFDB）（网址：http://www.lmfdb.org/）传播结果，解决获取这些领域最新计算数据的需要。 本网站为数学界提供数据，这些数据是现代数论界感兴趣的数学对象的严格计算的结果，并为对数论感兴趣的学生和研究人员发挥教育作用。本次研讨会的主题是表示类型之间的联系，特别是伽罗瓦表示，以及数论中其他感兴趣的对象，包括L函数和椭圆曲线，重点是计算。该研讨会包括讲座阿廷表示，积分表示，模p伽罗瓦表示，和L-进表示。 该研讨会旨在推进计算表示理论的研究，特别是伽罗瓦表示及其在数论中的应用。 该讲习班还将促进这些领域的专家和初级研究人员之间的合作。研讨会将采用典型的会议和研讨会的混合形式。 上午将致力于邀请研究会谈，下午将致力于小组工作。 在下午的会议上，小组将研究问题，生成计算数据，或通过L函数和模块化形式数据库（LMFDB）向公众展示计算工作。更多细节可以在http://people.oregonstate.edu/~swisherh/CRTNTconference/index.html上找到。

This award provides partial participant support for the workshop "Computational Representation Theory in Number Theory" held July 27-31, 2015 at Oregon State University in Corvallis, Oregon. This workshop will promote the generation and dissemination of current research in computational number theory related to representation theory. In particular, it will foster research collaboration between senior and junior researchers. The workshop will also address the need for access to recent computational data in these areas by disseminating results through the L-functions and Modular Forms Database (LMFDB), located at http://www.lmfdb.org/. This website serves the mathematical community by providing data that is the result of rigorous computations of mathematical objects of interest in the modern number theory community, as well as by playing an educational role for students and researchers interested in number theory.The theme of this workshop is the connection between types of representations, particularly Galois representations, and other objects of interest in number theory, including L-functions and elliptic curves, with a focus on computation. The workshop includes lectures on Artin representations, integral representations, mod p Galois representations, and l-adic representations. The workshop is intended to advance research in computational representation theory, particularly Galois representations and their applications to number theory. This workshop will also foster collaboration between experts and junior researchers in these areas. The workshop will be a hybrid of typical conference and workshop formats. The mornings will be dedicated to invited research talks and the afternoons will be dedicated to work in small groups. During the afternoon sessions groups will work on research questions, generating computational data, or presenting computational work to the public through the L-functions and Modular Forms Database (LMFDB). More details can be found at http://people.oregonstate.edu/~swisherh/CRTNTconference/index.html.