Virginia Topology Conference 2018

该奖项为2018年弗吉尼亚拓扑会议提供部分支持，该会议将于2018年12月12日至14日在弗吉尼亚大学校园内举行。会议将汇集来自各个职业阶段的数学家。 科学家，会议将提供一个及时的论坛之间的互动研究小组在四维拓扑谁接近类似的研究问题，使用不同的工具集，并刺激学习，数学发展，以及这些群体之间的合作。为了促进专业发展，会议包括为研究生预留的发言时间，这将被安排，以便最大限度地提高高级数学家或其他可能有旅行限制的人的出席率，从而确保初级演讲者的最广泛接触。会议活动的安排将尽可能增加处于不同职业阶段和情况的研究人员之间的互动机会。组织者还将尽一切努力鼓励妇女和代表性不足的群体的成员参加。 规范理论在四维光滑流形的研究中占据主导地位已有近35年的历史，但四维流形拓扑中仍有许多问题没有得到规范理论的解决。在过去的几年中，出现了某些建设性的技术，用于研究光滑四维拓扑中的问题，以三分的形式;三分理论吸引了拓扑学家的极大兴趣，并包含了以类似于Akbulut和Kirby在20世纪70年代的处理演算的方式揭示四维流形的新结构或性质的潜力。这次会议的中心目标是汇集研究人员在规范理论和三分之间的潜在联系的各个方面，希望刺激该领域的中心问题的进一步进展：这些问题包括三分和规范理论不变量的四维流形和曲面之间的关系，链接的广义性质R猜想，以及Andrews-Curtis猜想。发言者名单包括规范理论，三，四流形拓扑和Heegaard Floer不变量的专家，以及三分理论的发展和应用的先驱。会议网站可以在www.example.com上找到http://www.faculty.virginia.edu/tmark/VTC2018/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知识价值和更广泛的影响审查标准进行评估来支持。

This award provides partial support for the 2018 Virginia Topology Conference, which will be held December 12-14, 2018, on the campus of the University of Virginia. The conference will bring together a collection of mathematicians from all career stages. Scientifically, the conference will provide a timely forum for interaction between groups of researchers in four-dimensional topology who approach similar research questions using different sets of tools, and stimulate learning, mathematical development, and collaboration between these groups. To promote professional development, the conference includes speaking slots set aside for graduate students, which will be scheduled so as to maximize attendance by senior mathematicians or others who may have travel constraints, thereby ensuring the broadest exposure for the junior speakers. Conference activities will be scheduled so as to maximize opportunities for interactions between researchers at different career stages and situations. The organizers will also make every effort to encourage participation by women and members of underrepresented groups. Gauge theory has played a dominant role in the study of smooth four-dimensional manifolds for nearly thirty-five years, but there are many questions in four-manifold topology that have not been resolved by gauge-theoretic methods. In the last few years certain constructive techniques have emerged for the study of problems in smooth four-dimensional topology, in the form of trisections; the theory of trisections is attracting considerable interest among topologists and contains the potential to uncover new structure or properties of four-manifolds in a manner similar to the handle calculus due to Akbulut and Kirby in the 1970s. The central goal of this conference is to bring together researchers on various sides of the potential connection between gauge theory and trisections, with the hope of stimulating further progress on central problems in the field: these include the relationship between trisections and gauge-theoretic invariants of four-manifolds and surfaces they contain, the generalized Property R conjecture for links, and the Andrews-Curtis conjecture. The list of speakers includes experts in gauge theory, three- and four-manifold topology, and Heegaard Floer invariants, as well as pioneers in the development and application of trisection theory. The conference web site can be found at http://www.faculty.virginia.edu/tmark/VTC2018/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.