Thema der Dissertation:
Fine Polyhedral Adjunction, Weighted Ehrhart Theory, and Tensor Network Varieties Thema der Disputation:
On the Classification of Degree 1 Lattice Polytopes
Fine Polyhedral Adjunction, Weighted Ehrhart Theory, and Tensor Network Varieties Thema der Disputation:
On the Classification of Degree 1 Lattice Polytopes
Abstract: The notion of degree of a lattice polytope as a measure of how soon interior lattice points appear in its dilations, arising from its Ehrhart Series, is one that has been involved in the classification of lattice polytopes. A previous classification of lattice polygons, namely in the two-dimensional case, without interior lattice points is due independently to Arkinstall, Khovanskii, Koelman and Schicho. In this talk we present the more general classification due to Batyrev and Nill (2006), which completely classifies all lattice polytopes of degree at most 1 in any dimension. The main result of this classification shows that every lattice polytope of degree at most 1 has the structure of either a lattice pyramid over twice the standard triangle, namely, is an exceptional simplex, or is a so-called Lawrence prism. We introduce the concepts necessary from Ehrhart Theory in order to define the notion of degree of a lattice polytope and define the exceptional simplex and Lawrence prism as our central objects of study. We then present the main ingredients in this classification, through which we recognize the rigidity in the polytope structure that the condition on the degree imposes on a lattice polytope and its combinatorics.
Zeit & Ort
23.10.2025 | 16:00
Seminarraum 019
(Fachbereich Mathematik und Informatik, Arnimallee 3, 14195 Berlin)
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