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: * Anatole Katok is at Penn State for the semester.

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.

Currently Scheduled Talks for Fall 2017:

Nattalie Tamam Tel Aviv University

Divergent trajectories in arithmetic homogeneous spaces of rational rank two Yeshiva University, 215 Lexington Ave, Room 312. The seminar has changed rooms.

In the theory of Diophantine approximations, singular points are ones for which Dirichlet’s theorem can be infinitely improved. It is easy to see that all rational points are singular. In the special case of dimension one, the only singular points are the rational ones. In higher dimensions, points lying on a rational hyperplane are also obviously singular. However, in this case there are additional singular points. In the dynamical setting the singular points are related to divergent trajectories. In the talk I will define obvious divergent trajectories and explain the relation to rational points. In addition, I will present the more general setting involving Q-algebraic groups. Lastly I will discuss results concerning classification of divergent trajectories in Q-algebraic groups.

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Edward Belbruno Yeshiva University and Princeton University

Stochastic Regularization of the Big Bang Singularity Yeshiva University, 215 Lexington Ave, Room 312. The seminar is in a different room than last year. Note the special date and time.

The Friedmann differential equations, that model the expansion of the universe, are not defined at the Big Bang Singularity. These equations are modified by including random perturbations modeled by Brownian motion. A method is described on how to regularize these differential equations using stochastic methods. It is proven that solutions exist from a contracting universe to an expanding one if and only if a key parameter takes on a value from a special set of co-prime numbers at the Big Bang. It is also proven that the universe expansion variable can perform random fluctuations.

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Liviana Palmisano University of Bristol

The rigidity conjecture Yeshiva University, 215 Lexington Ave, Room 312. The seminar is in a different room than last year. The talk starts at 5:30pm.

A central question in dynamics is whether the topology of a system determines its geometry, whether the system is rigid. Under mild topological conditions rigidity holds in many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. We will discuss the case of circle maps with a flat interval. The class of maps with Fibonacci rotation numbers is a $C^1$ manifold which is foliated with co dimension three rigidity classes. Finally, we summarize the known non-rigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes.

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Claude Schochet The Technion, Israel

A Case Study in Non-Commutative Topology Yeshiva University, 215 Lexington Ave, Room 312.

Non-commutative topology uses the tools of C*-algebras and algebraic topology to study phenomena from classical topology, geometry, functional analysis, and physics. In this talk we show how the same C*-algebra arises from quantum mechanics, rotations of the circle, and a flow on a torus. We then demonstrate how it is possible to retrieve information from the model using K-theory for C*-algebras. This is the opposite of a survey talk: the focus will be exclusively upon one example. No knowledge of C*-algebras or K-theory will be assumed. Graduate students are especially welcome!

Past Semesters:

Spring 2017 Fall 2016 Spring 2016