A complete classification of unimodular valuations on the set of lattice polygons with values
in the spaces of polynomials and formal power series, respectively, is established. The …

We classify translatively exponential and GL (2, Z) covariant valuations on lattice polygons
valued at measurable real functions. A typical example of such valuations is induced by the …

We generalize RP Stanley's celebrated theorem that the h⁎-polynomial of the Ehrhart series
of a rational polytope has nonnegative coefficients and is monotone under containment of …

The h*-polynomial captures the enumeration of lattice points in dilates of rational polytopes.
For various classes of polytopes, there are many potential properties of this polynomial …

This thesis addresses classical lattice point problems in discrete and convex geometry.
Integer points in convex bodies are the central objects of our studies. In the second chapter …

An overview of tensor valuations on lattice polytopes is provided composed of two
contributions that began the development of the theory of these valuations; a …

The term of Ehrhart tensor polynomials is a natural popularization of the Ehrhart polynomial
of lattice polytopes which is a much more used in different applications. As our fundamental …