Learn Swedish: Forskaren sa att de skulle publicera resultatet veckan därpå. - The researcher said that they would publish the result the following week.

This is the core of reported speech in the past tense. If the researcher originally said, "We will publish the results next week" (nästa vecka), we have to shift the time perspective when reporting it later. If we used nästa vecka now, it would mean the week after today. Veckan därpå means "the following week" relative to when the researcher actually spoke.

Why is the verb skulle publicera rather than ska publicera?

Because the main reporting verb sa (said) is in the past tense, the verbs in the reported speech usually take a step back in time. The original direct quote was likely "Vi ska publicera..." (We will publish...). In indirect past-tense speech, ska shifts to its past form, skulle (would).

How exactly does the word därpå work here?

Därpå is a compound of där (there) and på (on), literally meaning "thereupon" or "after that". It is the standard way to shift "next" into a past-tense narrative. You will frequently see it in set phrases like dagen därpå (the following day) and året därpå (the following year). Notice that the time word before it must be in the definite form (veckan, not en vecka).

Since forskaren is singular, who does de refer to here?