This is the 3165th most frequent Turkish word.
düzenledikleri
"Organized (by them)" or "that they organized."
Here, 'düzenledikleri' is used as a past relative participle, indicating 'organized by' referring to the exhibition.
Öğrencilerin düzenledikleri sergi çok başarılı oldu.
The exhibition the students organized was very successful.
In this context, 'düzenledikleri' serves as the relative participle modifying 'conference', specifying the organizers.
Düzenledikleri konferansa birçok konuşmacı katıldı.
Many speakers participated in the conference they organized.
'Düzenledikleri' here identifies the specific activities with relation to 'being organized by them'.