Workshop: Structures on Free Resolutions

该奖项支持参加一个研讨会式的数学会议，题为自由决议的结构，并于2017年10月26日至28日在德克萨斯州拉伯克的德克萨斯理工大学举行。它将汇集成熟的和早期的职业研究人员，就密切相关的主题发表演讲并参加讲习班活动，目的是营造一个有利于合作和讨论的环境。本次研讨会的主题是交换代数的丰富领域及其快速变化的景观的代表。预计约有45名与会者，其中包括9名特邀发言人。特别鼓励妇女和代表性不足的少数群体成员参与。本次研讨会将有助于交换和同调代数领域提供了一个焦点，最近已经看到了很多进展：结构上的自由决议。本次研讨会的主题将包括通用自由决议，线性，Boij-Söderberg理论，泰特决议，检测Koszul和Golod属性，庞加莱系列的合理性，Betti数的增长和结构，以及syzygies的研究，这代表了广泛的方法来研究自由决议的结构。可以预期，本次会议将通过确定重要的主题和问题，以及开始与这些主题相关的新对话和合作，为该领域的未来研究奠定基础。

This award supports participation in a workshop-style mathematics conference entitled Structures on Free Resolutions and taking place at Texas Tech University in Lubbock, TX, from October 26-28, 2017. It will bring together established and early-career researchers to give lectures and participate in workshop activities on closely related topics, with a goal of fostering an environment conducive to collaboration and discussion. The topics to be included in this workshop are representative of the rich area of commutative algebra and its quickly changing landscape. About 45 participants are expected, which includes 9 invited speakers. Participation by women and members of underrepresented minorities is particularly encouraged. This workshop will contribute to the fields of commutative and homological algebra by providing a focus for a topic that has seen a lot of progress recently: structures on free resolutions. Topics represented at this workshop will include generic free resolutions, linearity, Boij-Söderberg theory, Tate resolutions, detection of Koszul and Golod properties, rationality of Poincaré series, growth and structure of Betti numbers, and studies of syzygies, which represent a wide range of approaches to studying structures on free resolutions. One can expect that this meeting will set the ground work for future research in this area by identifying important motifs and questions as well as starting new conversations and collaborations related to these topics.