This is the 4302nd most frequent Russian word.
архитектуре
The Russian word "архитектуре" means "architecture" in English (in the dative or prepositional case).
Here, 'архитектуре' is in the prepositional case, singular, indicating the topic being discussed, namely 'architecture'.
Говоря об архитектуре Санкт-Петербурга, нельзя не восхититься её величием.
Speaking about the architecture of Saint Petersburg, one cannot help but admire its grandeur.
In this instance, 'архитектуре' serves as part of the construction 'интересоваться чем?' which requires the prepositional case, referring to 'architecture'.
Студент интересуется архитектуре древнего Рима.
The student is interested in the architecture of ancient Rome.
The usage of 'архитектуре' in this sentence reflects its role in describing a subject related to architecture, using the prepositional case for the phrase ‘related to’.