Title: Refined open intersection numbers and the Kontsevich-Penner matrix model,
Abstract: A study of the intersection theory on the moduli space of Riemann surfaces
with boundary was recently initiated in a work of R. Pandharipande, J. P.
Solomon and the third author, where they introduced open intersection numbers
in genus 0. Their construction was later generalized to all genera by J. P.
Solomon and the third author. In this paper we consider a refinement of the
open intersection numbers by distinguishing contributions from surfaces with
different numbers of boundary components, and we calculate all these numbers.
We then construct a matrix model for the generating series of the refined open
intersection numbers and conjecture that it is equivalent to the
Kontsevich-Penner matrix model. An evidence for the conjecture is presented.
Another refinement of the open intersection numbers, which describes the
distribution of the boundary marked points on the boundary components, is also
discussed.