Sivan is a researcher of literature from Kerala in southwest India, mainly that which was connected between the 14th and 18th centuries in Sanskrit, Malayalam, and a language that combines them. In addition, she researches and teaches poetics, women in Indian literature, and translation.

Her research focuses on Indian literature, particularly texts composed in the region of Kerala in the southwestern part of the subcontinent between the fourteenth and seventeenth centuries CE. During this period, authors in Kerala began writing in a literary language known as Maṇipravāḷam (“Rubies and Corals”), which blends Malayalam, the local language, with Sanskrit, the classical language of India and the primary medium of literary, philosophical, scientific, and religious expression. Many of the earliest works in Maṇipravāḷam center on local female protagonists—most often dancers or courtesans—whom the poet describes and praises. She is among a small number of scholars worldwide who read and write about these works, whose study requires proficiency in both Sanskrit and Old Malayalam, a combination of skills that is now rare, even in Kerala itself. Her research explores the encounter between local and cosmopolitan cultures, multilingualism, vernacular poetics, and representations of women in Indian literature.

Following the completion of her doctoral studies at the Hebrew University of Jerusalem under the supervision of Professor David Shulman, she undertook a postdoctoral fellowship at the Harvard Society of Fellows. She later held a postdoctoral position at the Mandel Scholion Research Center at the Hebrew University. For her doctoral dissertation—whose revised version she is currently completing as a book manuscript—she was awarded the Polonsky Prize for Innovation and Creativity in the Humanities. She subsequently received the Pines Prize for Outstanding Early Career Research.