Sergiy Merenkov

City College of New York and CUNY Graduate Center

Title: Geometry and dynamics versus regularity for manifold automorphisms.

Abstract: I plan to discuss how regularity of automorphisms of manifolds influences the geometry and dynamics of their minimal sets and vice versa. A particular attention will be given to smooth and quasiconformal homeomorphisms of n-tori, n>=2, and hyperbolic surfaces. The results to be presented are higher dimensional versions of Denjoy's theorem on topological conjugacy for circle diffeomorphisms. 

Pekka Pankka

University of Helsinki, Finland

Title: From quasiregular mappings to quasiregular curves.

Abstract: Quasiregular mappings are a non-injective quasiconformal mappings and they may be viewed as a higher dimensional generalization of holomorphic mappings. I will first discuss some of the recent results in their global theory. Then I will discuss a new class of mappings generalizing both quasiregular mappings and holomorphic curves, called quasiregular curves.

Dzmitry Dudko

State University of New York at Stony Brook

Title:  From Denjoy's Theorem to the Renormalization Theory.

Abstract: Renormalization is a powerful tool for understanding dynamical systems on various scales. We will introduce some of the renormalization ideas, often illustrating them on pictures. In the first talk, we  will review Denjoy's Theorem on rotation number and then proceed to finer renormalization questions involving circle maps. In the second talk, we will discuss the period-doubling renormalization of real quadratic polynomials and make an analogy between the associated adding machine attractor and circle maps.

Sabya Mukherjee

Tata Institute of Fundamental  Research, India

Title: Fractals arising from antiholomorphic maps and reflection groups.

Abstract:  We will explicate topological and geometric structures of fractal sets arising from iterations of antiholomorphic rational maps (complex conjugates of rational maps of the Riemann sphere) and Kleinian reflection groups. We will also explain, mostly at the level of examples, how these conformal dynamical systems can be combined to manufacture richer systems with unusual dynamical and complex-analytic properties.