inhomogeneous systems\, i.e. w ith a density that depends on the position\,

or ientation or other internal degrees of freedom. It can be viewed as an

extension of the virial in version (developed for homogeneous systems) to

uncountably many species. The key technical tool i s a combinatorial identity for

a special type o f trees which allows us to implement the inversion step as well

as to prove its convergence. Appl ications include classical density functional

t heory\, Onsager'\;s functional for liquid cryst als\, hard spheres of different sizes

and shape s. Furthermore\, the method can be generalized in order to provide

convergence for other expansio ns commonly used in the liquid state theory.

Th e validity is always in the gas regime\, but with the new method we improve

the original radius o f convergence for the hard spheres as proved by Le bowitz

and Penrose and subsequent works. This i s joint work with Sabine Jansen and

Tobias Kuna .

LOCATION:Seminar Room 2\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR