Demetrius

Schedule

Demetrius spends his mornings at home in the Carpenter's Shop, in the kitchen and at the microscope in his laboratory. On an ordinary spring day he goes outside in the afternoon, first by his garage and then to the cliff southeast of the house; in summer he spends the day at the fountain west of the Community Center, and in fall he takes notes by the northern end of the lake. His evenings end in the kitchen and by the bookshelf in his bedroom.

On Fridays he goes to the Stardrop Saloon and dances with his wife Robin. On rainy days he stays home with his notes and spends a short while behind the Carpenter's Shop counter. His clinic check-up is on Summer 25, and he goes to the Desert Festival in spring and the Night Market on Winter 16.

Source: Stardew Valley Wiki: Demetrius (Schedule)

Gifts

• Loves: Bean Hotpot, Ice Cream, Rice Pudding, Strawberry; also all universal loves.
• Likes: Dinosaur Egg, Purple Mushroom; also all universal likes; most eggs; most fruit.
• Hates: Holly; also all universal hates.

You can give him up to two gifts a week, plus one on his birthday (Summer 19), when a gift counts eight times.

Source: Stardew Valley Wiki: Demetrius (Gifts)

Heart events

• Any friendship level: He may mail you a specimen from his field studies (a Nautilus Shell, Rainbow Shell, Amethyst or Bream), more often as your friendship grows.
• Three hearts: He mails you the Fried Mushroom recipe as thanks for taking an interest in his work.
• Six hearts (his house, with Robin there): He and Robin are arguing over whether tomatoes are a fruit, and he asks you to settle it; siding with him raises his friendship with you, and saying vegetable lowers it.
• Seven hearts: He mails you the Autumn's Bounty recipe.

Source: Stardew Valley Wiki: Demetrius (Heart events)