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Can I shorten the sentence like this?

1- This is Peter, a student who is researching nuclear physics at a university .

2- This is Peter, a student researching nuclear physics at a university.

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  • It's "ugly", but I'm not sure it would actually be ungrammatical even to sayThis is Peter, who is a student who is researching nuclear physics. Both instances of who is are entirely optional, and it makes no difference to the meaning whether you include them or not. Commented Mar 24, 2021 at 18:44

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Yes

A present participle, like researching, is just an adjective. Applying an adjective to a noun means the same as "(noun) who is (adjective)" or "(noun) that is (adjective)". For example, these mean the same thing:

This is my fat cat.

This is my cat who is fat.

The words "who is fat" in the second form are called a relative clause (because it makes a statement that relates to the original noun).

Probably the only reason this isn't obvious is because in English, adjectives normally precede the noun they modify, but when a participle takes an object, like nuclear physics at a university in your example, the participle normally follows the noun.

Something else you must know

When you word something with a relative clause, you need to be aware of whether you mean the clause restrictively or nonrestrictively. If I know that you know that I have two cats, only one of which is fat, then I mean "who is fat" restrictively: the purpose of the relative clause is to narrow down ("restrict") the meaning of "cat", i.e. to indicate which cat this is—the fat one, not the skinny one.

If I think you do not even know that I have a cat, then the relative clause makes a separate statement in addition to the statement in the main clause. This "nonrestrictive" meaning requires a comma:

This is my cat​, who is fat.

That means the same as this longer version, which puts each statement into a separate sentence:

This is my cat. My cat is fat.

In the form with an adjective before the noun ("This is my fat cat"), the language does not distinguish between the restrictive and nonrestrictive meanings; usually the restrictive meaning is understood. The relative clause with the comma is needed if you want to be absolutely sure to convey the nonrestrictive meaning. This is the only circumstance I can think of where you should not reduce a relative clause like the one in your example to a participle that directly modifies the noun.

Your example introduces Peter as a student with the indefinite article a. The comma that you already have, before "a student", makes that whole phrase or clause nonrestrictive in regard to Peter: it's telling you a second fact about Peter, namely that he is a student who is doing research, etc. It's restrictive in regard to "student". So, the form with the relative clause ("Peter, who is…") should not get its own comma (exactly as you have it).

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