Conference: Tech Topology Summer School 2023

技术拓扑暑期学校，将于2023年7月24日至28日，在技术的格鲁吉亚研究所是两年一度的暑期学校的第二部分。2023年暑期学校将专注于低维拓扑中的一个基本猜想，称为L空间猜想，它涉及该领域内的三个非常不同的领域。将有小型课程介绍这些领域，辅之以研究讲座。学生和博士后研究人员将有机会进行五分钟的照明讲座，向广大观众宣传他们的工作。也将有问题会议，学生可以得到帮助，在讲座和其他活动中提出的材料，旨在激发兴趣和刺激参与者之间的合作。暑期学校预计将提供大量的早期职业数学家的数学工具，开始为这一令人兴奋的现代研究领域作出贡献。技术拓扑暑期学校将与卡梅隆戈登（德克萨斯大学奥斯汀分校）的演讲开幕L-空间猜想的状态，概述了过去几年的主要进展。L空间猜想假定了三个不同但相关的主题之间的关系，这将是亚当·克莱（马尼托巴大学）、欧文·戴（斯坦福大学）和雷切尔·罗伯茨（圣路易斯华盛顿大学）教授的迷你课程的重点。这些主题是：Heegaard Floer同源性，基本群体的有序性，以及绷紧的叶理。迷你课程将由Nathan Dunfield（伊利诺伊大学香槟分校），Jonathan Hanselman（普林斯顿大学），Tao Li（波士顿学院）和Hannah Turner（格鲁吉亚理工学院）的研究讲座补充。问题讨论会将在下午举行。数学的价值在于讲座和谈话，以及在谈话之间发生的讨论，导致新的合作和指导关系。更多信息可以在暑期学校网站www.example.com上找到https://sites.gatech.edu/ttss23/This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

The Tech Topology Summer School, to be held July 24-28, 2023, at the Georgia Institute of Technology is the second installment of a biennial summer school. The 2023 summer school will focus on a fundamental conjecture in low-dimensional topology, called the L-space conjecture, that relates three very different areas within this field. There will be mini-courses introducing these areas, complemented by research talks. Students and postdoctoral researchers will have an opportunity to give five-minute lighting talks to advertise their work to a large audience. There will also be problem sessions where students can get help with material presented in the lectures and other activities geared to stimulate interest and spur collaboration among the participants. The summer school is expected to provide a large group of early career mathematicians with mathematical tools to start contributing to this exciting area of modern research.The Tech Topology Summer School will open with a talk by Cameron Gordon (University of Texas, Austin) on the state of the L-space conjecture, outlining major progress of the past several years. The L-space conjecture posits a relationship between three distinct yet related topics, which will be the focus of the mini-courses taught by Adam Clay (University of Manitoba), Irving Dai (Stanford University), and Rachel Roberts (Washington University in St. Louis). These topics are: Heegaard Floer homology, orderability of fundamental groups, and taut foliations. The mini-courses will be complemented by research talks by Nathan Dunfield (University of Illinois at Urbana-Champaign), Jonathan Hanselman (Princeton University), Tao Li (Boston College), and Hannah Turner (Georgia Institute of Technology). Problem sessions will be held in the afternoons. The mathematical value lies both in the lectures and talks as well as in the discussions that take place between the talks, leading to new collaborations and mentoring relationships. More information can be found at the summer school website https://sites.gatech.edu/ttss23/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.