Computational Representation Theory in Number Theory

该奖项为2015年7月27日至31日在俄勒冈州科瓦利斯的俄勒冈州立大学举行的“数论中的计算表示理论”研讨会提供部分参与者支持。本次研讨会将促进与表示理论相关的计算数论当前研究的产生和传播。特别是，它将促进高级和初级研究员之间的研究合作。讲习班还将通过设在http://www.lmfdb.org/的l -函数和模数形式数据库传播结果，解决获取这些领域最新计算数据的需要。该网站为数学界提供数据，这些数据是对现代数论界感兴趣的数学对象进行严格计算的结果，同时也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，特别是伽罗瓦表示，与数论中其他感兴趣的对象之间的联系，包括l函数和椭圆曲线，重点是计算。工作坊包括阿廷表示法、积分表示法、模伽罗瓦表示法和l进表示法的讲座。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。该研讨会还将促进这些领域的专家和初级研究人员之间的合作。讲习班将是典型会议和讲习班形式的混合体。上午将专门用于受邀的研究讲座，下午将致力于小组工作。在下午的会议期间，小组将研究问题，生成计算数据，或通过l -函数和模块化表格数据库（LMFDB）向公众展示计算工作。更多详细信息请访问http://people.oregonstate.edu/~swisherh/CRTNTconference/index.html。

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.