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 symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

Inhalt

Gennadiy Averkov, Di erence between families of weakly and strongly maximal integral lattice-free polytopes.- Victor Batyrev, Alexander Kasprzyk, and Karin Schaller, On the Fine interior of three-dimensional canonical Fano polytopes.- Mónica Blanco, Lattice distances in 3-dimensional quantum jumps.- Amanda Cameron, Rodica Dinu, Mateusz Michalek, and Tim Seynnaeve, Flag matroids: algebra and geometry.- Daniel Cavey and Edwin Kutas, Classi cation of minimal polygons with speci ed singularity content.- Tom Coates, Alessio Corti, and Genival da Silva Jr, On the topology of Fano smoothings.- Sandra Di Rocco and Anders Lundman, Computing Seshadri constants on smooth toric surfaces.- Akihiro Higashitani, The characterisation problem of Ehrhart polynomials of lattice polytopes.- Johannes Hofscheier, The ring of conditions for horospherical homogeneous spaces.- Katharina Jochemko, Linear recursions for integer point transforms.- Valentina Kiritchenko and Maria Padalko, Schubert calculus on Newton-Okounkov polytopes.- Bach Le Tran, An Eisenbud-Goto-type upper bound for the Castelnuovo-Mumford regularity of fake weighted projective spaces.- Milena Pabiniak, Toric degenerations in symplectic geometry.- Andrea Petracci, On deformations of toric Fano varieties Thomas Prince, Polygons of nite mutation type.- Hendrik Süß, Orbit spaces of maximal torus actions on oriented Grassmannians of planes .- Akiyoshi Tsuchiya, The re exive dimension of (0, 1)-polytopes