Congruences of Mock Theta Functions

Ramanujan's theta functions form the backbone of much of his work on q-series and continue to be important objects in modern number theory. These functions satisfy numerous identities and appear naturally in Partition Theory as well. Another of Ramanujan's remarkable discoveries is the theory of mock theta functions, which he introduced in his final letter to Hardy in 1920. In this talk, we will see how the mock theta functions differ from theta functions and explore them in more details from an arithmetic lens. The coefficients of the mock theta functions carry their arithmetic hearts, and studying them leads to new congruences, identities, and structural insights. We will see certain congruence properties of some mock theta functions and their proofs.