This is the 7850th most frequent Russian word.
калининском
"Калининском" is the prepositional case of "Калининский," meaning "Kalinin" as an adjective, often referring to something named after Mikhail Kalinin, such as a district or location.
In this sentence, 'калининском' refers to a geographic area, specifically a district named Kalininsky. It's an adjective form agreeing with a masculine singular noun 'районе.'
Я живу в Калининском районе.
I live in the Kalininsky district.
Here, 'калининском' describes the name of the park, serving as an adjective to specify its designation. It agrees with 'парке,' a masculine singular noun in prepositional case.
В Калининском парке много деревьев.
In Kalininsky Park, there are many trees.
In this instance, 'калининском' is used as part of the proper name of the university, describing its affiliation or attributes. It modifies 'университете,' a masculine singular noun in prepositional case.