Machine Learning the Landscape - Lecture 1

Dive into the first lecture of the Machine Learning the Landscape series, delivered by Yang-Hui He at the Kavli Asian Winter School on Strings, Particles and Cosmology. Explore fundamental concepts in mathematics and string theory, including Riemann surfaces, cohomology, Calabi-Yau manifolds, and string phenomenology. Learn about heterotic compactification, special holonomy, and topological properties of Calabi-Yau manifolds. Discover explicit examples of these complex geometric structures and their applications in theoretical physics. Engage with cutting-edge topics such as cyclic manifolds, triadophilia, and Complete Intersection Calabi-Yau (CICY) 3-folds. Conclude with a Q&A session to deepen your understanding of these advanced concepts in high-energy theory and mathematical physics.

Start
Machine- Learning the Landscape Lecture 1
PLAN
Further Reading
A Classic Problem in Mathematics
Classical Results for Riemann Surface
Some Rudiments & Nomenclature
Cohomology
Calabi-Yau
String Phenomenology
Heterotic Compactification
Mille Viae ducunt hominies Romam
Covariant Constant Spinor
Summary
Special Holonomy
Some Topological Properties I
Some Topological Properties II
Explicit Examples of Calabi-Yau Manifolds
As Projective Varieties
Mille Viae ducunt hominies Romam
Cyclic Manifolds
Triadophilia: A 40-year search
Complete Intersection Calabi-Yau CICY 3-folds
Part I
Q&A