Complex Analysis and Dynamics Seminar at CUNY's GC

Complex Analysis and Dynamics Seminar

Department of Mathematics

Graduate Center of CUNY

Friday: 2:00 pm - 3:00 pm

Room 6417


Organizers: David Aulicino, Jun Hu (On Leave), Sudeb Mitra, Dragomir Saric

Spring 2026: Upcoming Seminars

February 27: Andreas Wieser (Institute for Advanced Study)
Effective equidistribution results for semisimple periodic orbits in homogeneous spaces

In her fundamental work from the early 90's, Ratner showed that unipotent flows on homogeneous spaces exhibit strong rigidity properties. In particular, she classified orbit closures and invariant measures for such flows. These classification results allowed Mozes and Shah to study the distribution of periodic orbits qualitatively.

In this talk, we discuss joint work with Einsiedler, Lindenstrauss, and Mohammadi establishing equidistribution results for periodic orbits of semisimple groups with polynomially effective rates. These results form a central component of a large program effectivizing Ratner's theorems. We also outline the dynamical ideas essential to our proof.

March 6: Petr Naryshkin (Institute for Advanced Study)
TBA

March 13: Martin Schmoll (Clemson University)
TBA

April 17: Yunping Jiang (Graduate Center and Queens College)
TBA

April 24: Benjamin Dozier (Cornell University)
TBA

May 1: Constantin Kogler (Institute for Advanced Study)
On dimension and absolute continuity of self-similar measures

A similarity is a map from $\mathbb{R}^d$ to itself that uniformly scales distances. When one repeatedly applies randomly chosen contracting similarities, the resulting process converges to a limiting probability distribution known as a self-similar measure. These measures form a fundamental class of examples within the broader topic of stationary measures, which appear in numerous areas of mathematics. Two central problems in the study of self-similar measures are to determine their Hausdorff dimension and to understand when they are absolutely continuous, meaning that they admit a density with respect to Lebesgue measure. I will present previous results on these questions as well as joint work with Samuel Kittle. Indeed, we establish numerous novel explicit examples of absolutely continuous self-similar measures. In fact, we give the first inhomogeneous examples in dimension 1 and 2 and construct examples for essentially any given rotations and translations, provided they have algebraic coefficients. Moreover, we strengthen Varju's result for Bernoulli convolutions and Lindenstrauss-Varju's result in dimension $\geq 3$. Addressing the dimension of self-similar measures, we generalise Hochman's result to contracting on average measures and show the exact overlaps conjecture for complex Bernoulli convolutions.

May 8: Megan Roda (Institute for Advanced Study)
TBA

May 15: Sudeb Mitra (Graduate Center and Queens College)
TBA

Spring 2026: Previous Seminars

February 6: Barak Weiss (Tel Aviv University)
Horocycle dynamics on the moduli space of translation surfaces, in the rank one setting

In ongoing joint work with Jon Chaika and Florent Ygouf, we establish a Ratner-type orbit closure theorem for the horocycle flow on rank one loci, in the moduli space of translation surfaces. The question of describing horocycle invariant ergodic measures is still open, and contrary to Ratner's work, we describe all orbit-closures without a corresponding measure classification theorem. I will give a crash course on the structure of these moduli spaces, emphasizing rel foliations and rel deformations. Then I will describe our approach to the problem, and indicate some of the main difficulties.

February 13: David Aulicino (Brooklyn College and Graduate Center of CUNY)
Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces

We consider generic translation surfaces of genus $g>0$ with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order $d$. Given a translation surface, the number of cylinders with waist curve of length at most $L$ grows like $L^2$. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by $L^2$, the limit as $L$ goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points $n$. All necessary background will be given. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.

February 20: Chenxi Wu (University of Wisconsin)
Topological Entropy and Artin Mazur zeta function for non Archimedean rational maps

This is about my collaborations with Yunping Jiang, Hongming Nie and Liang-Chung Hsia. For a rational map over a non Archimedean local field (for example, the field of p adic rationals or the field of formal Laurent series, the latter is related to the degeneration of complex Julia sets due to DeMarco-McMullen) where the omega limit set of critical points does not contain other critical points, we developed an algorithm for the calculation of the reciprocal of its Artin-Mazur zeta function, and also its topological entropy via symbolic dynamics.

Previous Semesters:

For information about the history of our seminar, please visit: History.