What could be a good word for "a group of intellectuals" or "a group of smart learners"? Any suggestions of related terms also invited.
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 ...
In England I would probably use the word boffins.
Our crack team of boffins laboured through the night decoding enemy transmissions.
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.
literati [ˌlɪtəˈrɑːtiː]: literary or scholarly people
You might be interested in the word "salon", which was used to refer to a gathering of intellectuals in 17th and 18th century France.
Maybe circle, as in Vienna Circle. Depending on the specific nature of those groups, you can call them "philosophical circles", "scientific circles" etc or, more generally, "intellectual circles". But, in general, the historically relevant groups were named after the name of the city in which they were held (eg. Vienna, Bloomsbury) or after their leading figures, as in Kraft Circle.
If I'm correctly understanding your question, I'd think that "forum" would work nicely.
A meeting or medium where ideas and views on a particular issue can be exchanged.
An Internet message board.
This doesn't quite convey the part "...on topics of their specializations/interests.", at least not to me. You could prepend "interest" for the added meaning.
After a hard day of work, people of all sorts gather at the local watering hole to hold an interest forum.
Of course, the fact that forum has predominantly come to refer to an internet forum may be a stumbling block to understanding its meaning, although the concept is the same.
A group of people who socialize with one another is a society.
If the site is specifically about academia, the word school might work, as it can denote people who study together (as in "boarding school"), study the same subject ("Duke University School of Nursing"), or are like-minded (school of thought).
What about brains trust (depending on where you are). It's exactly what you say—a group or team or crew of brainiacs, perhaps tasked with achieving some goal, developing a new strategy, or whatever the case may be.
"Let's put the brains trust on that problem, while we continue to unload the trucks..."
It's not really negative, or rude; it's more grudgingly admiring. And I think it's probably USA enough to get you through.
Note: IMO the only other suggestion here that works and actually describes a tasked group, as the OP asks, is Fumble's think-tank.
You might look for material related to the Algonquin Round Table, perhaps the most famous American intellectual/witty group, from the 1920s in New York City.
They referred to themselves as the Vicious Circle, but a Round Table might be allusive enough for your purposes, depending on the context and your audience.
One of the problems here is that OP is trying to force an association between "intellectuals" and "smart learners".
Many individuals and groups have one of those attributes but not the other; they're not therefore a natural pairing. For example, intelligensia correlates strongly with "intellectuals", but hardly at all with "smart learners"; in most usages, the intelligensia are an elite class wrapped up in their own artistic/social/political prejudices, uninterested in learning about anything beyond that microcosm.
Possibilities, depending on various other attributes of the group/attitudes of the speaker, might be...
There are of course a whole host of more or less derogatory terms for people and groups of people who are intellectually-minded and/or intellectually sharp, but I'm assuming OP doesn't want that (coterie and clique above steer well into that territory - as do all the others, depending on your stance).