Workshop: Structures on Free Resolutions

该奖项支持参加于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的题为自由决议结构的研讨会式数学会议。它将把已有的和职业生涯早期的研究人员聚集在一起，就密切相关的主题讲课和参加讲习班活动，目的是营造一个有利于合作和讨论的环境。本研讨会将包括的主题代表了交换代数的丰富领域及其迅速变化的格局。预计将有约45人参加，其中包括9名受邀演讲者。特别鼓励妇女和代表人数不足的少数群体成员参与。这个研讨会将通过提供一个最近取得了很大进展的主题的焦点：自由分解的结构，来为交换代数和同调代数领域做出贡献。参加这次研讨会的主题将包括一般自由分辨率、线性、BOIJ-Söderberg理论、Tate分辨率、Koszul和Golod性质的检测、Poincaré级数的有理性、Betti数的增长和结构以及合子的研究，这些都代表了研究自由分辨率结构的广泛方法。可以预期，这次会议将确定重要的主题和问题，并开始与这些主题有关的新的对话和合作，从而为今后在这一领域的研究奠定基础。

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.