Titlebook: Interactions with Lattice Polytopes; Magdeburg, Germany, Alexander M. Kasprzyk,Benjamin Nill Conference proceedings 2022 Springer Nature S

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Computing Seshadri Constants on Smooth Toric Surfaces,shadri constant at the general point can often be determined in terms of easily computable invariants of the surfaces at hand. When the core of the associated polygon is a point we show that the surface can be constructed via consecutive equivariant blow-ups of either . or ..

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The Characterisation Problem of Ehrhart Polynomials of Lattice Polytopes,, we survey the results on this problem including recent developments. We discuss the characterisation of Ehrhart polynomials in several particular cases: small dimensions; small volumes; palindromic; small degrees. We also suggest some possible further questions.

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,Toric Degenerations in Symplectic Geometry,tic structure into this process, providing a very useful tool for solving certain problems in symplectic geometry. Below we present two applications of this method: questions about the Gromov width, and cohomological rigidity problems.

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,Difference Between Families of Weakly and Strongly Maximal Integral Lattice-Free Polytopes,t . holds for . and, for each ., . is a proper subfamily of .. We derive a super-exponential lower bound on the number of polytopes in . (with standard identification of integral polytopes up to affine unimodular transformations).

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,Flag Matroids: Algebra and Geometry,omial. In this review we describe all these constructions in detail, and moreover we generalise some of them to polymatroids. More precisely, we study the class of flag matroids and their relations to flag varieties. In this way, we obtain an analogue of the Tutte polynomial for flag matroids.

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On the Topology of Fano Smoothings,he topology of the general fiber from combinatorial data on .. This provides evidence for the Corti–Hacking–Petracci conjectures, and verifies that their construction is compatible with expectations from Mirror Symmetry.

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,The Reflexive Dimension of (0, 1)-Polytopes,tue of the algebraic technique on Gröbner bases and a linear algebraic technique, many families of reflexive polytopes arising from several classes of (0, 1)-polytopes are presented, and we see that the (0, 1)-polytopes are unimodularly equivalent to facets of some reflexive polytopes.

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,The Ring of Conditions for Horospherical Homogeneous Spaces,una–Vust theory of spherical embeddings and explain the complete combinatorial description of horospherical varieties (an important subfamily of spherical varieties). We conclude with the definition of the ring of conditions of spherical homogeneous spaces and give an explicit description for the horospherical case.

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Conference proceedings 2022in 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 geomet

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