Interacting stochastic particle systems in continuum

In the talk will be presented an overview of recent developments in the theory of interacting particle systems (IPS). The case of lattice systems is well known and widely studied. Contrary to the lattice case, IPS in continuum are only at the beginning of considerations. Particular topics to be discussed are following:
- Spatial birth and death processes;
- Glauber dynamics in continuum: equilibrium case, spectral gap, invariant subspaces;
- Glauber dynamics in continuum: non-equilibrium case and related Bogoliubov hierarchy;
- Kawasaki dynamics in continuum and scaling limits;
- Contact models: probabilistic approach and a solution via Bogoliubov type hierarchy, contact models in random media.