All Outputs (7)

On the maximum dual volume of a canonical Fano polytope (2022)
Journal Article
Balletti, G., Kasprzyk, A. M., & Nill, B. (2022). On the maximum dual volume of a canonical Fano polytope. Forum of Mathematics, Sigma, 10, Article e109. https://doi.org/10.1017/fms.2022.93

We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved... Read More about On the maximum dual volume of a canonical Fano polytope.

Recent Developments in Algebraic Geometry: To Miles Reid for his 70th Birthday (2022)
Book
Abban, H., Brown, G., Kasprzyk, A., & Mori, S. (Eds.). (2022). Recent Developments in Algebraic Geometry: To Miles Reid for his 70th Birthday. Cambridge University Press (CUP)

On the Fine Interior of Three-Dimensional Canonical Fano Polytopes (2022)
Conference Proceeding
Batyrev, V., Kasprzyk, A., & Schaller, K. (2022). On the Fine Interior of Three-Dimensional Canonical Fano Polytopes. In Interactions with Lattice Polytopes (11-47). https://doi.org/10.1007/978-3-030-98327-7_2

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
(2022). Interactions with Lattice Polytopes. In A. M. Kasprzyk, & B. Nill (Eds.), Interactions with Lattice Polytopes. https://doi.org/10.1007/978-3-030-98327-7

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.

Databases of quantum periods for Fano manifolds (2022)
Journal Article
Coates, T., & Kasprzyk, A. M. (2022). Databases of quantum periods for Fano manifolds. Scientific Data, 9, Article 163. https://doi.org/10.1038/s41597-022-01232-6

Fano manifolds are basic building blocks in geometry - they are, in a precise sense, atomic pieces of shapes. The classification of Fano manifolds is therefore an important problem in geometry, which has been open since the 1930s. One can think of th... Read More about Databases of quantum periods for Fano manifolds.

Laurent polynomials in Mirror Symmetry: why and how? (2022)
Journal Article
Kasprzyk, A., & Przyjalkowski, V. (2022). Laurent polynomials in Mirror Symmetry: why and how?. Proyecciones Journal of Mathematics, 41(2), 481-515. https://doi.org/10.22199/issn.0717-6279-5279

We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau-Ginzburg models for Fano varieties; how to apply them to cl... Read More about Laurent polynomials in Mirror Symmetry: why and how?.

Hilbert series, machine learning, and applications to physics (2022)
Journal Article
Bao, J., He, Y., Hirst, E., Hofscheier, J., Kasprzyk, A., & Majumder, S. (2022). Hilbert series, machine learning, and applications to physics. Physics Letters B, 827, Article 136966. https://doi.org/10.1016/j.physletb.2022.136966

We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstei... Read More about Hilbert series, machine learning, and applications to physics.