# NYC Dynamics Seminar at CUNY & Yeshiva University

NYC Dynamics Seminar at CUNY & Yeshiva University is a research level seminar with a broad agenda aimed at research mathematicians and graduate students whose interests include various aspects of the modern theory of dynamical systems and related topics in analysis, geometry, number theory and possibly other subjects. Its aim is to supplement more specialized seminars in the NYC area and provide a meeting place and a venue for discussions for mathematicians associated with various universities and colleges in the NYC metropolitan area working or interested in dynamical systems. The seminar will primarily feature speakers from outside the area specially invited for this purpose as well as mathematicians visiting various NYC universities. Core financial support for the seminar is provided by the Center for Mathematical Sciences at Yeshiva University. Support from other institutions who contribute to funding visits of seminar speakers will be acknowledged.

Organizers:
* Rodrigo Treviño is in Australia for the semester.
Locations:
• Yeshiva University, 215 Lexington Ave, Room 506. The entrance to the building is on the southeast corner of 33rd St and Lexington Ave.
• CUNY Graduate Center, 365 5th Ave. Rooms will likely vary from talk to talk.

Both locations require participants to present some form of identification to the security to be signed in.

Meeting Times: We plan to meet at 5pm roughly every other Wednesday, with some talks at the CUNY Graduate Center and some talks at Yeshiva University. The typical lecture time will be 1 hour, followed by a short period for questions or discussions.

## Talks from Spring 2017:

### Wednesday, February 8thYunping JiangThe 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.

### Wednesday, February 15thLiviana PalmisanoUniversity of Bristol

On circle maps with a flat interval and Cherry flows Yeshiva University, 215 Lexington Ave, Room 506.

Cherry flows are smooth flows on the bi-dimensional torus with two singularities. Having a rich behavior they have been attracting a lot of research attention over the years. The first return map is one of key tools in their studies. It is a $C^2$ weakly order preserving circle map with a flat interval. In my talk, I will survey recent developments in the comprehension of the dynamics generated by such maps. I will particularly focus on functions with unbounded rotation numbers. Following that, I will deduce metric, ergodic and topological properties of Cherry flows which led to resolution of some conjectures.

### Wednesday, March 8thYakov PesinThe Pennsylvania State University

The essential coexistence phenomenon in dynamics Yeshiva University, 215 Lexington Ave, Room 506.

I will discuss two different types of essential coexistence of regular (zero Lyapunov exponents and hence, zero entropy) dynamics and chaotic (non-zero Lyapunov exponents) dynamics in the setting of smooth dynamical systems, both with discrete and continuous time. I will review some recent results in this direction, discuss some open problems and describe a new example of coexistence which demonstrates a KAM-type picture in the volume preserving category.

### Wednesday, March 29thKlaus SchmidtUniversity of Vienna and Erwin Schroedinger Institute

Algebraic Actions of the Discrete Heisenberg Group Yeshiva University, 215 Lexington Ave, Room 506.

Quite a lot is known about various notions of entropy of algebraic actions of very general groups, but establishing more detailed dynamical properties of such actions seems quite difficult – even in simple examples. In this talk I am planning to discuss properties like expansiveness, specification and entropy for principal algebraic actions of the discrete Heisenberg group. This talk is based on joint work with Doug Lind.

### Wednesday, April 5thLivio FlaminioUniversity of Lille

Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds Yeshiva University, 215 Lexington Ave, Room 506.

We prove that any ergodic affine unipotent diffeomorphisms of a compact nilmanifoldenjoys the property of asymptotically orthogonal powers (AOP). Two consequences follow: (i) Sarnak's conjecture on Möbius orthogonality holds in every uniquely ergodic model of an ergodic affine unipotent diffeomorphism; (ii) For ergodic affine unipotent diffeomorphisms themselves, the Möbius orthogonality holds on so called typical short intervals. This is joint work with K. Fraczek, J.Kulaga-Przymus and M. Lemanczyk.

### Wednesday, April 26thAnton SolomkoUniversity of Bristol

On rank and isomorphism of von Neumann special flows CUNY Graduate Center, 365 5th Ave, Room 4419, 4th Floor.

A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise smooth roof function with a non-zero sum of jumps. Such flows appear naturally as special representations of Hamiltonian flows on the torus with critical points. We consider the class of von Neumann flows with one discontinuity. I will show that any such flow has infinite rank and that the absolute value of the jump of the roof function is a measure theoretic invariant. The main ingredient in the proofs is a Ratner type property of parabolic divergence of orbits of two nearby points in the flow direction. Joint work with Adam Kanigowski.

### Sunday May 7th: Special Session on Dynamical Systems:

We are running a Special Session on Dynamical Systems at the Spring Eastern Sectional Meeting of the AMS being held at Hunter College. Our session will only be meeting on Sunday May 7th. All talks are 45 minutes and will be held in the room HE920 (Hunter East, cross to the east building on the 3rd floor).

### 5:00pmMark F DemersFairfield UniversityExponential decay of correlations for Sinai billiard flows.

More information on the meeting is available from the webpage for the meeting. Abstracts for the talks are available from from the program for Sunday.