A workshop on murmurations was held at Brown University’s Institute for Computational and Experimental Research in Mathematics (ICERM) in August 2023. During the workshop, Nina Zubrilina, a student of Sarnak, presented her research on murmuration patterns in modular forms and proved that this type of murmuration follows an explicit formula she discovered. Other researchers have since proven the existence of different types of murmurations in modular forms and objects called Dirichlet characters. The discovery of murmurations was attributed to a significant dose of luck and the inexperience of one of the researchers, Pozdnyakov.
Key takeaways:
- Andrew Sutherland, a research scientist at MIT, used data from over a billion elliptic curves to study the robustness of murmurations, a phenomenon observed in elliptic curves and more general L-functions.
- Nina Zubrilina, a student of Sarnak, presented her research on murmuration patterns in modular forms and provided an explicit formula for this type of murmuration, which Sarnak called the 'Zubrilina murmuration density formula'.
- Other researchers have since proven the existence of different types of murmurations in modular forms and in objects called Dirichlet characters that are closely related to L-functions.
- The discovery of murmurations was partly due to luck and the inexperience of Pozdnyakov, who did not normalize the data, making the oscillations very big and visible.