An Asymptotic Version of the Prime Power Conjecture for Perfect Difference Sets - Sarah Peluse

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.

Introduction
Perfect difference sets
When do they exist
Numerical difficulty
General nonexistence
Perfect different sets
Results
Is the theorem independent
The original prime power conjecture
Large seed on sets
Do all are seen on cells
The proof
The problem
Multiplier theory
Man theorem
Subcase
Hardest case