### Yunping Jiang The City University of New York

Oscillating Property, MMA and MMLS Flows CUNY Graduate Center, 365 5th Ave, the Science Center, 4th Floor.Recently, Sarnak's conjecture attracts many people who work in number theory and dynamical systems. In this talk, I will talk about my recent work with Fan on oscillating sequences and MMA and MMLS flows in the frame of this conjecture. This work confirms Sarnak's conjecture for a large class of zero entropy flows. Furthermore, I will talk about my work on higher order oscillating sequences and affine distal flows on the \(d\)-torus. A consequence of this is that Sarnak's conjecture is held for all zero entropy affine flows on the $2$-torus and all affine distal flows on the $d$-torus for all $d>2$. It is known that the Möbius function is an example of a higher order oscillating sequence. I will also talk about my recent work with Akiyama on the discovery of a different kind of a higher order oscillating sequence.