Tuesday June 05, 2018 2:30 PM  3:30 PM Math Tower P131
 Yair Minsky, Yale University
WeilPetersson geometry, Dehn filling and branched surfacesWe study pseudoAnosov mapping classes with bounded normalized WeilPetersson translation distance (and unbounded genus). In analogy with a result of FarbLeiningerMargalit for Teichmuller translation distances, we show all such mapping classes fit together into a finite collection of cusped hyperbolic 3manifolds, where the cusps are filled to become either vertical (transverse to fibers) or horizontal (parallel to fibers). After a reduction using work of Schlenker, KojimaMcShane and BrockBromberg, the argument uses the theory of branched surfaces in 3manifolds. This is joint work with Chris Leininger, Juan Souto and Sam Taylor.

Tuesday June 12, 2018 2:30 PM  3:30 PM Math Tower P131
 Yusheng Luo, Harvard University
On the inhomogeneity of the Mandelbrot setWe will show that the Mandelbrot set is totally locally conformally inhomogeneous: the only orientation preserving conformal map $f:U → V$ with $U\cap ∂ M \neq \emptyset$ and satisfying $f(U\cap∂ M) ⊂ ∂ M$ is the identity map. The proof uses the study of the local conformal symmetries of the Julia sets: we will show in many cases, the dynamics can be recovered from local conformal structures of the Julia sets.

Thursday June 21, 2018 1:30 PM  2:30 PM Math Tower P131
 Roland Roeder, IUPUI
Limiting Measure of LeeYang Zeros for the Cayley TreeI will explain how to use detailed properties of expanding maps of the circle (ShubSullivan rigidity, LedrappierYoung formula, large deviations principle, ...) to study the limiting distribution of LeeYang zeros for the Ising Model on the Cayley Tree. No background in mathematical physics is expected of the audience. This is joint work with Ivan Chio, Caleb He, and Anthony Ji.

Friday August 31, 2018 2:30 PM  3:30 PM Math Tower P131
 Mahan Mj, TIFR Mumbai
A survey of CannonThurston MapsWe shall survey the theory of CannonThurston Maps. These form a connecting link between the hyperbolic geometry and the complex dynamics of Kleinian groups. We shall also discuss a generalization to geometric group theory and end with some open problems.

Friday September 07, 2018 2:30 PM  3:30 PM Math Tower P131
 Mark Pollicott, University of Warwick
Dynamical Zeta functionsThe famous Selberg zeta function can be interpreted as a complex function defined in terms of closed orbits on a compact
surface with constant negative curvature. We want to discuss generalizations of this: firstly to surfaces of variable negative curvature; and secondly to higher Teichmuller theory.

Friday September 14, 2018 2:30 PM  3:30 PM Math Tower P131
 Peter Veerman, Portland State University
Strange Convex SetsGiven a closed convex set $Ω∈\mathbb{R}^n$, the metric projection of a given point $x∈\mathbb{R}^n$ is given by the unique point $Π(x)∈Ω$ that minimizes the (Euclidean) distance $\lbrace\vert yx\vert\ \vert\ y∈Ω\rbrace$ between $Ω$ and $x$. Most mathematicians tend to think of convex sets in $\mathbb{R}^n$ as very tame objects. It is therefore surprising that it is easy to construct a compact convex set $Ω$ in $\mathbb{R}^2$ with the following strange property [Shapiro, 1994]: There is a point $x\notinΩ$ and a vector $v$ such that the directional derivative $$\lim_{t→ 0}\frac{Π(x+vt)Π(x)}{t}$$ fails to exist. Note that for example convex polygons are not strange in this sense.
We revisit and modify that construction to obtain a convex curve in $\mathbb{R}^2$ that is $C^{1,1}$ or differentiable with Lipschitz derivative. We show that the convex set bounded by this curve has the property that the directional derivative of the projection is not defined. This construction can be made $C^n$ for $n≥ 2$ except at a single point, and such that directional differentiability still fails.

Friday September 21, 2018 2:30 PM  3:30 PM Math Tower P131
 NguyenBac Dang, Stony Brook University
Spectral gap in the dynamical degrees of tame automorphisms preserving an affine quadric threefoldIn this talk, I will present the tame automorphisms group preserving an affine quadric threefold. The main focus of my talk is the understanding of the degree sequences induced by the elements of this group. Precisely, I will explain how one can apply some ideas from geometric group theory in combination with valuative techniques to show that the values of the dynamical degrees of these tame automorphisms admit a spectral gap.Finally I will apply these techniques to characterize when the Lyapounov exponents of a random walk on this particular group are strictly positive.

Friday September 28, 2018 2:00 PM  3:00 PM Math Tower P131
 Dragomir Saric, Queens College
Asymptotics of moduli of curves and applicationsIn a joint work with H. Hakobyan, we prove that each Teichmuller geodesic in the universal Teichmuller space has a unique limit point on Thurston boundary. The main result depends on asymptotic estimates of moduli of curves. Another application of the asymptotics, in a joint work with A. Basmajian and H. Hakobyan, is to give a sufficient condition on FenchelNielsen coordinates for infinite surfaces to guarantee that the surfaces have ergodic geodesic flows, i.e. of type $O_G$. In a joint work with H. Miyachi, we show that the Teichmuller disk in the universal Teichmuller space extends by continuity to a closed disk in Thurston bordification. Thurston boundary to arbitrary Teichmuller spaces are recently introduced in a joint work with F. Bonahon.

Friday October 05, 2018 2:30 PM  3:30 PM Math Tower P131
 Lasse RempeGillen, University of Liverpool
Taming wild entire functionsThe study of the dynamics of transcendental entire functions has a long history, going back to Fatou. It has recently garnered much interest, partly due to intriguing connections with other areas of holomorphic dynamics. While some examples and families have been wellunderstood since the 1980s, only recently tools have become available to advance a detailed understanding of large and very general classes of transcendental entire functions.
In this talk, I will discuss some of these developments. In particular, I will discuss analogues of the local connectivity of Julia sets, which play a crucial role in polynomial dynamics. In joint work with Sixsmith (and partly with Alhamd), we introduce a notion of "docile" entire functions, and show in particular that a large class of functions, known as "strongly geometrically finite functions", are docile. I will also discuss work in progress with Sixsmith, with the goal of bringing the "puzzle" techniques of Yoccoz to bear on transcendental dynamics.
In the course of the discussion, I intend to also touch upon work of Mihaljevic, and joint work with Albrecht and Benini (concerning the dynamics of entire functions of finite order), with Benini (concerning an analogue of the DouadyHubbard landing theorem), and with Pfrang (on Hubbard trees).

Friday October 12, 2018 2:30 PM  3:30 PM SCGP 102
 Alena Erchenko, Ohio State University
Flexibility of Lyapunov exponents on the circle and the torusThere are several interesting classes of measures. For two special classes of dynamical systems, we will concentrate on the invariant measure that is absolutely continuous with respect to the Lebesgue measure and the measure of maximal entropy. First, we show that Lyapunov exponents with respect to these two probability measures for smooth expanding circle maps of a fixed degree $≥ 2$ take on all values that satisfy some wellknown inequalities. Then, we demonstrate a similar result for positive Lyapunov exponents with respect to these two measures for Anosov areapreserving diffeomorphisms on a twotorus that are homotopic to a fixed areapreserving Anosov automorphism (work in progress).

Friday October 26, 2018 2:30 PM  3:30 PM Math Tower P131
 Vasiliki Evdoridou, The Open University
Singularities of inner functions associated to entire maps in the class $\mathcal{B}$Let $f$ be a transcendental entire function and $U$ be an unbounded, invariant Fatou component of $f$. We can associate an inner function, $g$ say, to the restriction of $f$ to $U$. We consider two classes of functions in $\mathcal{B}$ having finitely many tracts. We show that if $f$ belongs to either of these two classes the number of singularities of $g$ on the unit circle is equal to the number of tracts of $f$. This is joint work with N. Fagella, X. Jarque and D. Sixsmith.

Friday November 02, 2018 2:30 PM  3:30 PM Math Tower P131
 Yotam Smilansky, The Hebrew University of Jerusalem
Multiscale substitution schemes and Kakutani sequences of partitionsSubstitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. In this talk we will use new path counting results for directed weighted graphs to show that such sequences of partitions are uniformly distributed, thus extending Kakutani's original result. Furthermore, we will describe certain limiting frequencies associated with sequences of partitions, which relate to the distribution of tiles of a given type and the volume they occupy.

Friday November 09, 2018 2:30 PM  3:30 PM Math Tower P131
 Dimitrios Ntalampekos, Stony Brook University
Removability of planar sets: old and new resultsRemovability of sets for quasiconformal maps and Sobolev functions has applications in Complex Dynamics, in Conformal Welding, and in other problems that require "gluing" of functions to obtain a new function of the same class. We, therefore, seek geometric conditions on sets that guarantee their removability. In this talk, I will give a survey of old results and discuss some very recent results on the (non)removability of the Sierpiński gasket and of Sierpiński carpets.
A first result is that the Sierpiński gasket is removable for continuous functions of the class $W^{1,p}$ for $p>2$. The method used applies to more general fractals that resemble the Sierpiński gasket, such as the Apollonian gasket and generalized Sierpiński gasket Julia sets.
Then, I will sketch a proof that the Sierpiński gasket is nonremovable for quasiconformal maps and thus for $W^{1,p}$ functions, for $1≤ p≤ 2$. The argument involves the construction of a nonEuclidean sphere, and then the use of the BonkKleiner theorem to embed it quasisymmetrically to the plane.

Friday November 16, 2018 2:30 PM  3:30 PM Math Tower P131
 Dimitry Turaev, Imperial College
On wandering domains near homoclinic tangtenciesGiven a map, we define a wandering domain as an open region such that the diameter of its images by the iterations of the map shrinks to zero but the corresponding limit set is not a periodic point. It is known that many finitely smooth twodimensional diffeomorphisms have wandering domains while it is not known if a polynomial diffeomorphism of a plane can have one. We discuss wandering domains whose limit sets are homoclinic tangencies. We show the existence of real analytic planar diffeomorphisms with wandering domains and discuss how to find wandering domains for polynomial diffeomorphisms of the threedimensional space.

Friday November 30, 2018 2:30 PM  3:30 PM Math Tower P131
 Christopher J. Leininger, University of Illinois at UrbanaChampaign
Polygonal billiards, Liouville currents, and rigidityA particle bouncing around inside a Euclidean polygon gives rise to a biinfinite "bounce sequence" (or "cutting sequence") recording the (labeled) sides encountered by the particle. In this talk, I will describe recent work with Duchin, Erlandsson, and Sadanand, in which we prove that the set of all bounce sequencesthe "bounce spectrum"essentially determines the shape of the polygon. This is consequence of our main result about Liouville currents on surfaces associated to nonpositively curved Euclidean cone metrics. In the talk I will explain the objects mentioned above, how they relate to each other, and give some idea of the proof of the main theorem.

Friday December 07, 2018 2:30 PM  3:30 PM Math Tower P131
 Zoran Sunic, Hofstra University
TBATBA

