Geometry of Strings and Gravity

弦理论和引力背景下的基础物理问题常常可以被重新表述为纯粹的几何问题，弦理论的真空空间，特别是超对称（BPS）物体的光谱。在真空模空间的某些“墙壁”上，BPS物体可以衰变为质量较小的BPS物体。这种穿墙现象有着极其丰富而神秘的数学结构。建议从不同的角度研究壁交叉，包括真空与高数量的超对称性，应用镜像对称性和弦对偶的工具。 了解BPS天体的光谱对于计算黑洞熵和拓扑弦理论有重要意义。 PI提出要发现新的几何不变量，这是必要的物理特性，这些字符串真空，并探讨最近定义的准本地质量，满足所有已知的一致性条件的影响。 这些项目解决了令人兴奋的问题，对理论物理，微分几何和代数几何有重要意义。 该提案的核心是培养博士后研究员和研究生，以进行前沿的跨学科研究，并有效地与物理和数学界进行互动。

Problems of fundamental physics in the context of string theory and gravity can often be rephrased purely as problems in geometry, the space of vacua of string theory and in particular the spectrum of supersymmetric (BPS) objects on them. On certain "walls" in the moduli space of vacua, a BPS object can decay to less massive BPS objects. Such a wallcrossing phenomenon has an extremely rich and mysterious mathematical structure. It is proposed to study wall-crossings from various points of views including vacua with high number of supersymmetries, applying tools of mirror symmetry and string dualities. Understanding the spectrum of BPS objects is important for calculating black hole entropy and topological string theory. The PI proposes to uncover new geometrical invariants which are necessary for physically characterizing these string vacua, and explore the implications of a recently defined quasi-local mass which satisfies all known consistency conditions. The projects address exciting questions that have important implications for theoretical physics, and for differential and algebraic geometry. Central to the proposal is the training of postdoctoral fellows and graduate students to conduct cutting edge cross-disciplinary research and to be effective in interacting with both the physics and mathematics communities.