Let $\mathbf{G}$ be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map $F:\mathbf{G}→\mathbf{G}$ and $\mathbf{G}:=\mathbf{G}^F$, such that the root system ...

We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the $p$-adic integers $\mathbb{Z}_p$. To this end, we associate to such a Lie algebra a ternary quadratic form over ...

The current article arose from a lecture1 given by the author in October 2005 on the work of R. Hamilton and G. Perelman on Ricci-flow and explains central analytical ingredients in geometric parabolic evolution equations ...

Much as non-Newtonian fluids exhibit secondary flows in elliptic pipes, rarefied gases exhibit secondary heat flows between elliptical cylinders. The phenomenon may be called non-Fourierian, because it is not covered by ...

In this paper we present a method to obtain resolutions of symplectic orbifolds arising as quotients of pre-symplectic semi-free S1-actions. This includes, in particular, all orbifolds arising from symplectic reduction of ...

This lecture is of very introductory nature. The goal will be to describe specific concrete questions, and to use them as a tool to convey some general ideas. Let me therefore skip the general introduction and immediately ...

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial ...

In this paper we introduce the notion of a gemetric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter ...

A finite test set for an integer maximation problem enables us to verify whether a feasible point atains the global maximum. We establish in this paper several general results that apply to integer maximization problems ...

In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil’s staircases) supported on limit sets of finitely generated conformal iterated ...