Research interest

The mathematically exact model of (special) relativistic quantum mechanics.

What is the wave equation of the particles which are moving faster than light?
What quantities describe the particles (mass, spin, something else?) and what will be the wave equation of the particles which live on a 1+1 and 2+1 dimensional space-time and we consider the (special-)relativistic motion?
Consider the 1+1 and 2+1 dimensional space-time with classical (non-relativistic, or Galileian relativistic) symmetry. What quantities describe the particles (mass, spin, something else?) and what will be the wave equation of these particles?

Connection between information geometry and quantum mechanics.

The state space of a finite level quantum system can be endowed with Riemannian metric using monotone metrics. What kind of physical quantities correspond to the differential geometrycal invariants of this space?

The connection between time-travel and general relativity.

If time-travelling is possible in the Gödel-universe?
How one can make 'time-machine' using a Kerr-type rotating black-hole or a charged black-hole?
What can we say about causality if one can travel in time?

Noncommutative geometry and the K-theory of C^*-algebras.