The study of central limit theorems in number theory goes back to the famous theorem of Erdős and Kac on the probability distribution of the prime omega function. This theorem has several generalizations and analogues for sequences arising out of arithmetic objects such as model families of curves over finite fields, modular cusp forms and regular graphs. The fundamental idea in many cases is to model the sequences as sums of ``seemingly" independent random variables. We will discuss some of these results with a focus on central limit type theorems in the theory of modular forms.

Bio: Kaneenika Sinha is an Associate Professor of Mathematics at IISER Pune. She studies questions at the intersection of number theory and probability, mainly in the context of modular forms, elliptic curves and regular graphs. She received her Ph.D. from Queen's University in Canada under the supervision of Professor M. Ram Murty.