Vadim Kuznetsov. Informal Biography by Eyes of His First Adviser

The paper is dedicated to the memory of prominent theoretical physicist and mathematician Dr. Vadim Kuznetsov who worked, in particular, in the fields of the nonlinear dynamics, separation of variables, integrability theory, special functions. It includes his short research biography, an account of the start of his research career and the list of publications.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Some Spacetimes with Higher Rank Killing-Stackel Tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime

Cops vs. Gambler

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop moves from vertex to adjacent vertex with the goal of minimizing expected capture time. Players move simultaneously. We show that when the gambler's distribution is known, the expected capture time (with best play) on any connected $n$-vertex graph is exactly $n$. We also give bounds on the (generally greater) expected capture time when the gambler's distribution is unknown to the cop.Comment: 6 pages, 0 figure