Here is a short summary of the article. I personally find some of the examples unnatural and therefore cannot support the hypothesis of this paper.
There are two constructions of pronoun "что" with an adjective, which may be illustrated by examples "что нового" (adjective in genitive) and "что новое" (adjective in nominative\accusative). They both mean the same ("something new"). They can be used in questions, in relative clauses, in subordinate sentences with "if" and with some demonstrative particles.
The question that this work is trying to answer is "In what cases which of the two constructions should be used?".
The main hypothesis of the paper is that "что новое" is employed more often with indefinite and demonstrative "что", while "что нового" is more frequently employed with "что" when it is used to form a question or a relative clause. Examples:
1 A question: Что нового/новое произошло? (нового is preferred)
2 A relative: единственное, что нового/новое произошло (нового is preferred)
3 A demonstrative: вот что новое/нового произошло (новое is preferred)
Semantically, any adjective may be used in these constructions. When it is used with adjectives "такой" and "свой", the genitive case is seen more often.
Syntactic position and the type of the predicate have strong influence on the type of construction that can be used.
If the construction is used as a subject of an active action, nominative case is preferred (4). If the verb denotes a state or is passive, both nominative and genitive are allowed. (5 and 6)
4 Так что же хорошее может порадовать, дать надежду нам, людям старшего поколения (...)?
5 Что такого случилось, что я должен уйти?
6 Что своего вы привнесли в сюжет романа?
Pronoun may or may not be placed together with the adjective (Что у тебя нового? vs. Что нового у тебя?). When adjective and noun are placed together, the probability of nominative case is higher (about 25 percent) than when they are placed separately (10 percent). The statistics is collected for 4 constructions, see section 4 of the article for examples.
Finally, in construction with conjunction "если" (see 7), the probability of nominative case is higher than in other constructions (about 48 percent when placed together, about 90 percent when placed apart). Example:
7 Так что если что новое узнал - пиши, звони, кидай на E-mail.
In these constructions "что новое" actually means "something new" and can be changed into "что-то новое".
"Чего нового" is a colloquial variant, it is used with genitive more often, but nominative cases exist, too.
The tendency of using the adjective in the nominative\accusative case together with pronoun "что" in case if they are put together is a sign that here pronoun "что" is an indefinite pronoun (I didn't get why this conclusion is made, but I guess it has something to do with the fact that using nominative\accusative case looks like agreement, and the use of genitive looks like government).