2017-2019 Talbot Workshops

摘要奖：DMS 1623977，首席研究员：Haynes R.Miller该奖项为将于2017年、2018年和2019年举行的接下来三个塔尔博特研讨会提供支持。自2004年第一次会议以来，塔尔博特研讨会向代数拓扑学的年轻研究人员介绍了当代感兴趣的话题。这个一年一度的研讨会聚集了大约35名年轻参与者和一两名资深数学家，进行为期一周的静修；参与者大多是研究生，他们在导师的指导下通过交流讲座和讨论主题来了解本周的研究主题。研讨会非常成功，启发了许多学生未来的研究，并在参与者之间建立了许多合作。过去的Talbot研讨会关注同伦理论和周边领域的各种主题，从椭圆上同调(2004)和Fukaya范畴(2009)到非阿贝尔Hodge理论(2011)，以及最近(2016)，Hill-Hopkins-Ravenel解决长期存在的Kervaire不变问题(希尔和Ravenel作为导师)。2017年、2018年和2019年初步考虑的主题包括：三角范畴的稳定性条件、代数K-理论中的迹方法、保形场论、派生代数几何、应用拓扑学和Heegaard Floer理论。由于许多参与者是希望在一个有前途的研究领域开始的一年级或二年级研究生，讲座从基础开始，例如2016年研讨会中的模型类别介绍和等变同伦理论，并导致介绍与研讨会材料相关的开放问题。塔尔博特研讨会的网站是http://math.mit.edu/conferences/talbot/.

AbstractAward: DMS 1623977, Principal Investigator: Haynes R. MillerThis award provides support for the next three Talbot workshops to be held in 2017, 2018, and 2019. Since its initial meeting in 2004, the Talbot Workshop has introduced young researchers in algebraic topology to topics of contemporary interest. This annual workshop gathers about 35 young participants and one or two senior mathematicians for a week-long retreat; the participants, who are mostly graduate students, learn about the week's research topic by exchanging lectures and discussing the topic under the guidance of the mentors. The workshop has been extremely successful, inspiring the future research of many students and establishing numerous collaborations among the participants. The workshop's unique format, in which participants live and cook together in a rental house, helps to create and sustain the collaborative atmosphere.Past Talbot Workshops have focused on a wide variety of topics in homotopy theory and surrounding areas, from elliptic cohomology (2004) and Fukaya categories (2009) to non-abelian Hodge theory (2011) and, most recently (2016), the Hill-Hopkins-Ravenel solution of the longstanding Kervaire invariant problem (with Hill and Ravenel as mentors). The topics under preliminary consideration for 2017, 2018, and 2019 include: stability conditions on triangulated categories, trace methods in algebraic K-theory, conformal field theory, derived algebraic geometry, applied topology, and Heegaard Floer theory. As many of the participants are first- or second-year graduate students looking to get a start in a promising research area, the lectures begin with basics, such as an introduction to model categories and to equivariant homotopy theory in the 2016 workshop, and lead up to a presentation of open problems related to the workshop material. The web site for the Talbot workshops is http://math.mit.edu/conferences/talbot/.