I have a travertine stone sink, which has small pits in the side wall and base near the plug hole. We are finding that although regularly cleaned mould can form in these pits. Is there a way of coating the sink with a thin layer of clear resin that will fill in these pits and stop the mould from forming.

I'll give it a shot. If you have mold growing in the pits nothing is going to stick to it. Also the soap and grease is also going to keep anything from bonding. As inpractical as it sounds I think only sand blasting the pits with a hobby sand blaster gun would give you the etched surface you would need to apply a clear epoxy. Once cleaned you could apply the epoxy in a number of coats to build it up. (you must apply each aditional coat when the previous coat has reached a near tack free state as in the skinning process described on this site. Now sand flush and polish.

Hope this helps.

Fred