Explore the intricacies of mod p Galois representations in this 30-minute conference talk presented by Suneel Kumar at the International Centre for Theoretical Sciences. Delve into the topic of local constancy within the context of rational points on modular curves, a key area of study in arithmetic geometry. Gain insights into the theoretical foundations and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. This talk is part of a broader program focusing on elliptic curves, modular forms, and modular curves, bringing together experts in arithmetic geometry to share cutting-edge research and foster future developments in the field.