All Outputs (5)

Machine learning detects terminal singularities (2023)
Conference Proceeding

Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have Q-factorial termi... Read More about Machine learning detects terminal singularities.

Toric Sarkisov Links of Toric Fano Varieties (2023)
Conference Proceeding

We explain a web of Sarkisov links that overlies the classification of Fano weighted projective spaces in dimensions 3 and 4, extending results of Prokhorov.

On the Fine Interior of Three-Dimensional Canonical Fano Polytopes (2022)
Conference Proceeding

The Fine interior ∆FI of a d-dimensional lattice polytope ∆ is a rational subpolytope of ∆ which is important for constructing minimal birational models of non-degenerate hypersurfaces defined by Laurent polynomials with Newton polytope ∆. This paper... Read More about On the Fine Interior of Three-Dimensional Canonical Fano Polytopes.

Interactions with Lattice Polytopes (2022)
Conference Proceeding

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symm... Read More about Interactions with Lattice Polytopes.

Mirror symmetry and Fano manifolds (2013)
Conference Proceeding

We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these ideas.