Frontiers in Geometry Conference 2022

几何前沿会议将于2022年8月1日至12日在意大利的里雅斯特的阿卜杜勒·萨拉姆国际理论物理中心（ICTP）举行。 该会议为期两周（为期一周的研究生暑期学校，然后是为期一周的会议），由Paul Feehan（罗格斯大学），Lenhard Ng（杜克大学），Peter Ozsváth（普林斯顿大学），Yongbin Ruan（浙江大学）和Paul Seidel（麻省理工学院）共同组织。国际理论物理中心数学科代理科长Claudio阿雷佐是当地会议的共同组织者。该活动的科学主题包括低维和辛拓扑，纽结理论和规范理论的分析方面。暑期学校由五位杰出的早期职业数学家领导，会议有25位著名的数学家，都是顶尖的科学家。会议网站与暑期研究生班网站相链接，并将由国际理论物理中心开发和维护：http://indico.ictp.it/event/9706There一直在关注低维和辛拓扑学的最新进展，这是对Floer同调和Khovanov同调的不断深入理解所推动的。此外，有承诺的全新的不变量和方法，这产生了进步的分析方面的规范理论（新的紧凑性定理和高维规范理论方程）和伪全纯曲线。例如，有一个正在进行的努力，使用Kapustin-Witten方程提取琼斯多项式和Khovanov同调的更本质的几何定义，并最终，这些不变量的新推广。对其中任何一个主题的理解将丰富对所有主题的理解。拟议的会议将汇集来自世界各地的这些专题研究前沿的专家。会议预计将产生知识转移，新的合作和思想的交叉施肥，并进一步激励研究生和早期职业数学家。由于国际理论物理中心的地理位置集中在欧洲主要数学系，靠近良好的公共交通设施，而且国际理论物理中心也致力于接待发展中国家的数学家，参加者将有机会与一群杰出而多元化的数学领袖和后起之秀互动。该奖项反映了NSF的法定使命，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，被认为值得支持。

The Frontiers in Geometry Conference will take place during the period August 1-12, 2022, at the Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. The conference is a two-week activity (a one-week graduate summer school, followed by a one-week conference) that is co-organized by Paul Feehan (Rutgers University), Lenhard Ng (Duke University), Peter Ozsváth (Princeton University), Yongbin Ruan (Zhejiang University), and Paul Seidel (MIT). Claudio Arezzo, Acting Head of the Mathematics Section, ICTP, is the local meeting co-organizer. The scientific themes of the event include low-dimensional and symplectic topology, knot theory, and analytical aspects of gauge theory. The summer school is led by five eminent early-career mathematicians and the conference features twenty-five well-known mathematicians, all leading scientists. The conference website links to that of the graduate summer school and will be developed and maintained by ICTP: http://indico.ictp.it/event/9706There has been exciting recent progress in low-dimensional and symplectic topology, spurred by the growing understanding of Floer homologies and Khovanov homology. Moreover, there is promise of entirely new invariants and methods, which arise out of progress in the analytical aspects of gauge theory (new compactness theorems and higher-dimensional gauge-theoretic equations) and of pseudo-holomorphic curves. For example, there is an ongoing effort to use the Kapustin-Witten equations to extract a more intrinsically geometric definition of the Jones polynomial and Khovanov homology and, eventually, new generalizations of those invariants. Gains in the understanding of any one of these topics will enrich the understanding of all. The proposed meeting will bring together experts at the frontier of research in these topics from around the world. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and early-career mathematicians. Because of the location of ICTP within a geographic concentration of leading European mathematics departments and near good public transportation facilities and because of ICTP's commitment to hosting mathematicians from developing countries as well, the U.S.-based participants will have the opportunity to interact with a distinguished and diverse group of mathematical leaders and rising stars. The meeting will thus help to support, train and encourage the next generation of researchers and strengthen international connections among them.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.