Gabi Danon's research deals mostly with the syntax of features and agreement; and with how the syntax of recursive nominal constructions interacts with their meaning.
His work on grammatical features looks at their role at the interfaces between syntax and other modules of grammar. This includes features such as definiteness, number, case and person, with a focus on apparent mismatches between the expected semantic content of these features and their distribution, as well as on their role in agreement and agreement mismatches. Specific research projects deal with the syntax and agreement patterns of quantified noun phrases, the use of non-agreeing subjects, and the distribution of definiteness features.
Other work focuses on constraints on genitive constructions in Modern Hebrew and other languages. Of particular interest are 'non-prototypical' genitive constructions that do not express relations like possession or kinship, especially in the context of a language that offers multiple genitive constructions.
Gabi Danon's current work uses corpora and experimental methods in addition to introspective acceptability judgments for studying grammatical phenomenon involving variation and/or gradience and the ways these relate to the underlying grammatical representations.
Here's a pretty (but) meaningless visualisation of keywords from some of Gabi Danon's published work: