Explore an in-depth lecture on perfect difference sets and their connection to the prime power conjecture. Delve into the mathematical intricacies of when these sets exist, the numerical challenges they present, and the general nonexistence theorems. Examine the speaker's results, including an asymptotic version of the prime power conjecture, and follow the proof's progression through various subcases. Gain insights into multiplier theory and its application to this problem. Suitable for advanced mathematics students and researchers interested in number theory and combinatorics.