Applied Mathematics.
Dynamical Systems, Classical Mechanics.

The science of Dynamical Systems is the study of systems that evolve according to some underlying principle. A large number of mathematical techniques are involved; often ordinary or partial differential equations (when the system changes smoothly). Classical Mechanics is the study of mechanical systems that are governed by Newton's, Lagrange's, Hamilton's, or Einstein's equations of motion (as opposed to, e.g., quantum mechanical equations of motion). The field is important, active, and has evolved considerably in the last 40 years.

In preparation:
Tip of the Iceberg (with M.Deryabin), on the stability and dynamics of icebergs.

Recent papers:
High-dimensional bowling (with M. Deryabin), on high dimensional balls rolling on high dimensional hyperplanes. Regular and Chaotic Dynamics 8, 319, (2003).

On integrability of a heavy rigid body sinking in an ideal fluid. (with M.Deriabine) - ZAMP 54, 1 (2003)

Exponentially Long Equilibration time for a 1-D Classical Gas, J. Stat. Mech, 11. 343 (1999). (with G. Benettin, University of Padova).

Finite Metric Spaces, Global Analysis, Differential Geometry.

Among the mathematical tools used in the study of dynamical systems are the subjects of Differential Geometry, and, more generally, Global Analysis. They are also beautiful and profound mathematical disciplines in their own right. Recently I have explored, with S. Markvorsen and others, the connecetions between the linear algebra of metric matrices (the metric information in a finite metric space) and the geometry of the (potentially) imbedding space. Which geometric properties of the space reveal themselves as matrix properties of generic metric matrices? Only one thing is clear: the final word. has not yet been spoken.

In preparation:
De novo generation of molecular structures using optimization to select graphs on a given lattice. with R. Bywater, T. Poulsen and P. Røgen .

Recent papers:
Hyperbolic Spaces Are of Strictly Negative Type (with S. Markvorsen and S. Kokkendorff. Proc. Am. Math. Soc. 130, 175 , (2000).

Finite Metric Spaces of Strictly Negative Type, Linear Algebra and Its Applications 4, 456 (1998). (with P.Lisonek, S. Markvorsen and C. Thomassen).