Simple word related to "a group of intellectuals" or "a group of smart learners"

Intelligentsia. A word of Russian origin (интеллигенция,intelligyentsia), imported into English in 1905, according to the Online Etymology Dictionary . It might be a little outmoded now.

Of course you might invent words like punditorat ...

I can suggest nerds or eggheads (some might consider this impolite though).

@Georges Elencwajg has given a good choice in intelligentsia which has the synonyms clerisy and literati.

clerisy: men of learning as a class or collectively; the intelligentsia or literati.

and

literati [ˌlɪtəˈrɑːtiː]: literary or scholarly people

In England I would probably use the word boffins.

Our crack team of boffins laboured through the night decoding enemy transmissions.

Collective nouns?

• Pomposity of professors
• A pretension of intellects

From AllSorts:

• A spell of wizards
• An arrogance of intellectuals