论文标题
卡拉比豪景观的讲座
Lectures on the Calabi-Yau Landscape
论文作者
论文摘要
在这些讲义中，我们调查了Calabi-yau三倍的景观，并使用机器学习来探索它。我们从景观的紧凑部分开始，尤其集中在完整的交点Calabi-yau品种（CICYS）和椭圆纤维上。非紧密的calabi-yau歧管体现在II型超弦理论中，它们作为震颤的表示形式出现，用于描述批量熟悉的四个维度中的规格理论。最后，考虑到大量的Calabi-Yau数据，还讨论了是否可以应用机器学习以及如何应用于代数几何和弦乐景观。这些笔记针对对数学和物理学感兴趣的初学者，并基于第二名作者在2019年PIMS夏季学校在萨斯喀彻温大学高能物理学的代数几何学上的讲座。
In these lecture notes, we survey the landscape of Calabi-Yau threefolds, and the use of machine learning to explore it. We begin with the compact portion of the landscape, focusing in particular on complete intersection Calabi-Yau varieties (CICYs) and elliptic fibrations. Non-compact Calabi-Yau manifolds are manifest in Type II superstring theories, they arise as representation varieties of quivers, used to describe gauge theories in the bulk familiar four dimensions. Finally, given the huge amount of Calabi-Yau data, whether and how machine learning can be applied to algebraic geometry and string landscape is also discussed. These notes are directed to the beginning graduate student interested in mathematics and in physics, and are based on lectures given by the 2nd author at the 2019 PIMS Summer School on Algebraic Geometry in High-Energy Physics at the University of Saskatchewan.
