We consider two lifts of the parabolic quantum Bruhat graph, one into the Bruhat order in the affine Weyl group and the other into a level-zero weight poset first considered by Littelmann. The lift into the affine Weyl ...

We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript ...

Ordering of operators is purely combinatorial task involving a number of commutators shuffling components of operator expression to desired form. Here we show how it can be illustrated by simple urn models in which normal ...

The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization ...

The workshop brought together researchers from geometry, nonlinear functional analysis, calculus of variations, partial differential equations, and stochastics around a common topic: systems whose evolution is driven by ...

Variational principles for evolutionary systems take advantage of the rich toolbox provided by the theory of the calculus of variations. Such principles are available for Hamiltonian systems in classical mechanics, gradient ...

Given partitions $\alpha, \beta, \gamma$, the short exact sequences $0 \rightarrow N_\alpha \rightarrow N_\beta \rightarrow N_\gamma \rightarrow 0$ of nilpotent linear operators of Jordan types $\alpha, \beta, \gamma$, ...

Originating in diverse branches of mathematics, from polytope algebra and toric varieties to the theory of stressed graphs, virtual polytopes represent a natural algebraic generalization of convex polytopes. Introduced as ...