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I'm an academic researcher with a very good publication track record in computer science.

I'm considering the possibility of applying for a research position at a well known telecommunications company with a large research department. But I still would like to have the possibility of publishing theoretical work.

1) Are researchers in private companies usually allowed to publish theoretical work produced in cooperation with researchers outside the company?

2) Are researchers in private companies usually allowed to publish theoretical work produced inside the company?

Speaking as a researcher at a private for-profit company, who also publishes frequently, it all depends on the nature of the business model and the position.

Most people at companies do not publish, either because the company has no interest in publishing or because their particular job doesn't involve much of scientific interest. For companies that are involved in cutting edge work, however, scientific publishing can gain credibility and visibility for the organization just like it does for people at universities. This is the case for the company I work for, particularly given that many of our projects are federally funded research where the government is paying us in part to disseminate knowledge.

Nor is there any necessary conflict between protecting intellectual property and publishing. The three main strategies for protecting IP are copyright, patent, and trade secret. Of those, only trade secret is incompatible with publishing, and it is generally the most fragile and least used in any case.

The biggest obstacle to publishing in private industry is simply priority and time. Writing a manuscript is a lot of work, and if management doesn't see much benefit, they will likely want you to use those hours for things more directly connected to the bottom line. You might be able to publish out of hours, but that can be a more complex negotiation.

Bottom line: it really depends on the particular circumstances. The best way to know if you will be able to publish is to look at whether others in the group you are joining publish. If so, you probably can. If not, there are likely major obstacles, whether formal or merely pragmatic.

It is not possible to answer your question unless you specify the company name. Many companies are very active in research, and many companies are not. As you are not an employee yet, you cannot ask the HR, but you can search.

For example, if you search for "deep learning" in ACM, and click on institutions on the left menu, you can see there is Microsoft, IBM and Google there. ACM also keeps company profiles, so you know what topic they are interested in, for example this is profile of Google.

Someone (from Amazon) just told me that Amazon had nearly turned FLoC into a private Amazon event. The conferences at FloC are highly theoretical, and among the most prestigious in logic.

But actually, you don't need to ask this question, as in the companies that are active in research, the directors/principal engineers etc are often former professors, and we followers immediately know where big shots move :-)

Update: thanks @Anyon for pointing out that the company name was editted out. Yes, that company does publish, see its profile in ACM.

In general terms, if the publication is, in any way, related to the company's business it will probably be contractually forbidden unless specific permission is given for the paper.

Signing on with a company that depends on IP usually means that anything you produce is theirs, not yours. Read the contract to be sure. Some contracts try to bind you forever, even when you leave the company. The legality of these can be challenged and they may be illegal in some places.

However, if your other work is completely unrelated, then it is probably ok, but it needs to be "released" by whoever is responsible for IP control at the company.

On rare occasions (THE WOZ at HP, for example), a company will give permission to do something that would otherwise be prohibited, but normally because they lack sufficient insight to see the consequences. If they are happy enough to make an exception, make sure you have it in writing - signed and maybe notarized.