Explore the intricacies of abelian surfaces with real multiplication in this advanced mathematics lecture. Delve into topics such as simple reduction, finite extension, and density zero as Yunqing Tang from Princeton University presents her research on exceptional splitting of reductions. Gain insights into special devices, compact divisors, intersection numbers, and the application of CUDA programming in this field. Examine the concepts of special and rational divisors, global intersection numbers, and the ARCA equity structure. This talk, part of the Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program, offers a deep dive into cutting-edge mathematical research for those with a strong background in algebraic geometry and number theory.