T-duality and K-theory: Unity of condensed matter and string theory

这个项目旨在以K理论和T对偶性为指导主题，揭示弦论和凝聚态物理学前沿的最新发现背后的深层数学结构。受弦理论的启发，将发展T-对偶技术和几何傅里叶-穆凯变换来研究物质的拓扑相。同样，拓扑材料激发了对实扭曲K-理论和T-对偶的详细研究，这些理论也适用于方向折弦理论。预期的结果包括对拓扑材料理论及其与弦理论的联系有更深入的理解，以及广泛应用于物理科学的动机良好的数学。这一理解为新的技术应用铺平了道路。

This project aims to uncover deep mathematical structures which underlie recent discoveries at the forefront of string theory and condensed matter physics, using K-theory and T-duality as guiding themes. Inspired by string theory, T-duality techniques and geometric Fourier-Mukai transforms will be developed to study topological phases of matter. Similarly, topological materials motivate the detailed study of real twisted K-theory and T-duality, which are then applicable to orientifold string theories. Anticipated outcomes include a deeper understanding of the theory of topological materials and its connection to string theory, and well-motivated mathematics widely applicable to the physical sciences. This understanding paves the way for novel technological applications.