Here are the Evolving Stars field research tasks:
Catch 3 Eevee reward - 20 Eevee Candy
Spin 10 PokéStops or Gyms reward - 1 King’s Rock or 1 Dragon Scale
Spin 15 PokéStops or Gyms reward - 1 Sinnoh Stone
Spin 20 PokéStops or Gyms reward - 1 Unova Stone
Evolve 1 Pokémon reward - 500 Stardust
Evolve 3 Pokémon reward - 2000 Stardust
Power up Pokémon 5 times reward - 25 Venusaur, Charizard, Blastoise, Steelix, Kangaskhan or Aerodactyl Mega Energy
Power up Pokémon 7 times reward - 25 Gyarados or Altaria Mega Energy
Meanwhile, the following Pokémon will be appearing more frequently in the wild throughout the Evolving Stars event:
Litwick
Kakuna
Pidgeotto
Poliwhirl
Kadabra
Haunter
Rhyhorn
Seadra
Scyther
Eevee
Swinub
Ralts
Duskull
Tynamo
Litwick
Helioptile
Finally, from Thursday, 6th October until Thursday, 13th October, you can partake in the Evolution Cup