Lectures on the Calabi-Yau Landscape

Understand

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.