Conference: Richmond Geometry Meeting: Geometric Topology and Moduli

该奖项支持将于2024年8月9日至11日在弗吉尼亚州里士满的弗吉尼亚联邦大学举办的里士满几何会议：几何拓扑和模量。该会议旨在联合低维拓扑和代数几何领域的专家，跨越不同的职业阶段和隶属关系。除了由国际知名专家提供的讲座外，还将通过展示早期职业研究人员贡献的海报会议和职业和指导小组来促进垂直整合的参与。会议将探讨低维拓扑、代数几何和数学物理的交叉。这种跨学科探索的根源可以追溯到20世纪80年代末Witten的开创性工作以及chen - simons理论中Jones多项式的出现。从那时起，由于几代数学家和物理学家的共同努力，结理论、模空间和弦理论之间的深刻联系出现了。值得注意的发展包括Heegaard Floer同调和Fukaya曲面范畴之间的深刻联系，Khovanov同调揭示的复杂相互作用，以及Gromov-Witten和Donaldson-Thomas理论的对应关系。曲线模空间的研究，如Heegaard flower同调，在许多发展中起着关键的作用。前三届里士满几何会议，包括虚拟和面对面的聚会，展示了一波在结理论、代数几何和弦理论方面的合作进展。诸如编织品种、Khovanov同伦、链接晶格同调和家庭中的GW/DT对应等主题已被探索，揭示了相互依赖突破的联系。该奖项支持第四届里士满几何会议，为传播这一动态研究领域的最新发现提供了重要平台。欲了解更多信息，请访问里士满几何会议网站：https://math.vcu.edu/rgmThis奖项反映了NSF的法定使命，并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。

This award supports the Richmond Geometry Meeting: Geometric Topology and Moduli scheduled for August 9-11, 2024, hosted at Virginia Commonwealth University in Richmond, VA. The conference is designed to unite experts in low-dimensional topology and algebraic geometry, spanning diverse career stages and affiliations. Beyond lectures delivered by internationally recognized experts, vertically integrated participation will be fostered by a poster session showcasing the contributions of early-career researchers and a Career and Mentorship Panel. The conference will investigate the intersection of low-dimensional topology, algebraic geometry, and mathematical physics. The roots of this interdisciplinary exploration trace back to Witten's groundbreaking work in the late 1980s and the emergence of the Jones polynomial in Chern-Simons theory. Since then, a landscape of profound connections between knot theory, moduli spaces, and string theory has emerged, due to the collective efforts of generations of mathematicians and physicists. Noteworthy developments include the deep ties between Heegaard Floer homology and the Fukaya category of surfaces, the intricate interplay revealed by Khovanov homology, and the correspondence of Gromov-Witten and Donaldson-Thomas theories. The study of moduli spaces of curves, as exemplified in Heegaard Floer homology, has played a pivotal role in several developments. The preceding three editions of the Richmond Geometry Meeting, encompassing both virtual and in-person gatherings, have showcased a wave of collaborative advancements in knot theory, algebraic geometry, and string theory. Topics such as braid varieties, Khovanov homotopy, link lattice homology, and the GW/DT correspondence in families have been explored, unveiling a nexus of interdependent breakthroughs. This award supports the fourth edition of the Richmond Geometry Meeting, providing a vital platform for the dissemination of the latest findings in this dynamic realm of research. For more information, please visit the Richmond Geometry Meeting website: https://math.vcu.edu/rgmThis 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.