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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.
List of contents
G. Averkov, Difference between families of weakly and strongly maximal integral lattice-free polytopes.- V. Batyrev, A. Kasprzyk, and K. Schaller, On the Fine interior of three-dimensional canonical Fano polytopes.- M. Blanco, Lattice distances in 3-dimensional quantum jumps.- A. Cameron, R. Dinu, M. Michalek, and T. Seynnaeve, Flag matroids: algebra and geometry.- D. Cavey and E. Kutas, Classification of minimal polygons with specified singularity content.- T. Coates, A. Corti, and Genival da Silva Jr, On the topology of Fano smoothings.- S. Di Rocco and A. Lundman, Computing Seshadri constants on smooth toric surfaces.- A. Higashitani, The characterisation problem of Ehrhart polynomials of lattice polytopes.- J. Hofscheier, The ring of conditions for horospherical homogeneous spaces.- K. Jochemko, Linear recursions for integer point transforms.- V. Kiritchenko and M. 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.- M. Pabiniak, Toric degenerations in symplectic geometry.- A. Petracci, On deformations of toric Fano varieties.- T. Prince, Polygons of finite mutation type.- Hendrik Süß, Orbit spaces of maximal torus actions on oriented Grassmannians of planes.- A. Tsuchiya, The re exive dimension of (0, 1)-polytopes.-
