Colloquium: Tuesday June 18, 2024. Speaker: Tamar Ziegler (HUJI). Title: “Sign patterns of the Mobius function”.
Time: Tuesday, 18.06.24 at 14:00-15:00
Location: Room 614, Science and Education Building, University of Haifa.
Zoom link: https://us02web.zoom.us/j/88665951849?pwd=Tjg5UlRjKzE2ZHN1NkNXWmp5R1V1dz09
Meeting ID: 886 6595 1849
Passcode: Contact Sefi Ladkani
Abstract:
The Mobius function is one of the most important arithmetic functions. There is a vague yet well known principle regarding its randomness properties called the “Mobius randomness law”. It basically states that the Mobius function should be orthogonal to any “structured” sequence. P. Sarnak suggested a far reaching conjecture as a possible formalization of this principle. He conjectured that “structured sequences” should correspond to sequences arising from deterministic dynamical systems. I will describe progress in recent years towards these conjectures building on major advances in ergodic theory, additive combinatorics, and analytic number theory.
