The birational geometry of Calabi-Yau threefolds is intricate even with many advances in modern higher-dimensional geometry. In the first half of the talk, we report the joint work with Atsushi Ito (Okayama) and Sz-Sheng Wang (Academia Sinica at Taiwan), in which we describe explicitly the birational geometry of a class of Calabi-Yau threefolds. These examples are related to Reid’s fantasy and the Morrison-Kawamata cone conjecture. (Journal of Pure and Applied Algebra (2022), DOI: https://doi.org/10.1016/j.jpaa.2021.106841; Journal of Geometry and Physics (2024), DOI:10.1016/j.geomphys.2023.105053)
Simulating molecular ground states on quantum computers holds immense potential for advancing quantum chemistry. However, the complexity of the question increases with the size of the molecule, limiting its feasibility. To address this challenge, we propose the Subspace Restriction Scheme (SRS) and test a novel subspace, the Multiplicity Hund subspace (MHS), which is inspired by Hund’s rule and molecular multiplicity. It has less ground-state energy difference in the tested 15 molecules than other known QC methods. (Chiang-L. Molecular Ground State Simulation by Subspace Restriction and Hund's Rule. arXiv:2404.03268)