Friday February 01, 2019 2:30 PM  3:30 PM Math Tower P131
 Boris Solomyak, University of BarIlan
On the dimension of Furstenberg measure for $SL(2,R)$ random matrix products and the Diophantine condition in matrix groupsLet $μ$ be a finitely supported measure on $SL(2,R)$ generating a noncompact and totally irreducible subgroup. Furstenberg proved that there is a unique stationary measure for the induced action on the projective line (now often called the ``Furstenberg measure''), with a positive Lyapunov exponent. In joint work with M. Hochman, we computed the Hausdorff dimension of the Furstenberg measure, assuming a Diophantine condition on the support of $μ$. I will also discuss some followup results on the Diophantine property in matrix groups and on the dimension of the support of the Furstenberg measure, joint with Y. Takahashi.

Friday February 08, 2019 2:30 PM  3:30 PM Math Tower P131
 Liviana Palmisano, Uppsala University
Newhouse LaminationsWe prove that the Newhouse phenomenon has a codimension 2 nature. Namely, there exist codimension 2 laminations of maps with infinitely many sinks. The leaves of the laminations are smooth and the sinks move simultaneously along the leaves. These Newhouse laminations occur in unfoldings of rankone homoclinic tangencies.
As consequence, in the space of polynomial maps, there are examples of:
two dimensional Hénon maps with finitely many sinks and one strange attractor,
Hénon maps, in any dimension, with infinitely many sinks,
quadratic Hénonlike maps with infinitely many sinks and one period doubling attractor,
quadratic Hénonlike maps with infinitely many sinks and one strange attractor,
two dimensional Hénon maps with finitely many sinks and two period doubling attractors,
quadratic Hénonlike maps with finitely many sinks, two period doubling attractors and one strange attractor.

Friday February 22, 2019 2:30 PM  3:30 PM Math Tower P131
 Kasra Rafi, University of Toronto
Counting of the number of simple closed curves on a surface, revisitedTBA

Friday March 01, 2019 2:30 PM  3:30 PM Math Tower P131
 Zoran Sunic, Hofstra University
Schreier spectra of some iterated monodromy groupsWe discuss calculation of spectra of several iterated monodromy groups, such as the Hanoi Towers group $H$ and one of its subgroups, the “tangled odometers group“ $T$.
The Hanoi Towers group is the iterated monodromy group of the $3$dimensional, postcritically finite, rational map $z→ z^2 – 16/(27z)$ and it models the wellknown Hanoi Towers Problem. The subgroup $T$ is the iterated monodromy group of the postcritically finite, cubic polynomial $z→ z^3/2 + 3z/2$ whose two critical points are fixed.
The groups act on the ternary rooted tree and on its boundary. The spectrum of the Schreier graphs of these actions were, in both cases, shown to consist of a countable set of isolated points and a Cantor set to which the isolated points accumulate via backward iterations of a quadratic polynomial. In both cases, the calculation is facilitated by first introducing a higher dimensional rational map, which is then shown to be semiconjugate to a onedimensional map.
Time permitting, we will also discuss the case of iterated monodromy groups of arbitrary conservative polynomials.

Friday March 08, 2019 2:30 PM  3:30 PM Math Tower P131
 Jonguk Yang, University of Michigan
TBATBA

Friday April 05, 2019 2:30 PM  3:30 PM Math Tower P131
 Malik Younsi, University of Hawaii
TBATBA

Friday April 12, 2019 2:30 PM  3:30 PM Math Tower P131
 Jing Tao, University of Oklahoma
TBATBA

Friday April 19, 2019 2:30 PM  3:30 PM Math Tower P131
 Saeed Zakeri, CUNY
TBATBA

