Direct flights to Apatity. Apatity is a small town but it has the airport connected with Moscow (Domodedovo airport) and St.Petersburg. The flights are operated by Severstal-Avia, http://severstal-avia.ru/en). People living in Apatity use it extensively.
The flight from Moscow/St.Petersburg takes about 2.5/2 hours and costs about 130/110 USD one way; the return cost is twice of that.
The Apatity airport is about 30 minutes drive from the town, and there are mini-van taxis costing about 5-7 USD/person.
Using direct flights to/from Apatity should be good for people who wishes to stay for one or more days in Moscow or St.Petersburg before or after the meeting.
Arriving via Murmansk. For those coming straight to the meeting it might be more convenient to fly to Murmansk and then use ground transfer to Apatity.
Murmansk has more frequent connections with Moscow and St.Petersburg. You may be able to buy a connection ticket from your place to Murmansk if you use Aeroflot or its partner carriers (SkyTeam Alliance).
From Murmansk airport to Apatity: It is possible to go by a mini-van or usual taxi, which takes 2.5 to 3 hours and costs about 3500 to 4500 RUR (60 to 75 USD) per vehicle (from 1 up to 5-6 persons).
The organizers have made every effort to help in transportation from the airports.