Toric Variety

Toric varieties are geometric shapes defined by polynomial equations, possessing a special symmetry that simplifies their study. Current research focuses on classifying these varieties, particularly those with specific properties like terminal singularities, using machine learning techniques such as neural networks and dimensionality reduction methods like PCA and t-SNE. This work aims to improve our understanding of the structure and properties of toric varieties, with applications in areas like theoretical physics (e.g., string theory and gauge theories) and optimization problems (e.g., linear programming). The application of machine learning is revealing previously unknown patterns and potentially accelerating theoretical discoveries in algebraic geometry.