http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Thu, 04 Sep 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Jim Yorke (UMD) - http://yorke.umd.edu/
Abstract: A graph can summarize some of the basic properties of any dynamical system. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our goal has been to define a meaningful concept of graph of almost any dynamical system. As a result, we base our definition of ``chain graph'' on ``epsilon-chains'', defining both nodes and edges of the graph in terms of chains. In particular, nodes are often maximal limit sets and there is an edge between two nodes if there is a trajectory whose forward limit set is in one node and its backward limit set is in the other. Our initial goal was to prove that every ``chain graph'' of a dynamical system is, in some sense, connected, and we prove connectedness under mild hypotheses.
]]> http://www-math.umd.edu/research/seminars.html Thu, 18 Sep 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Jon Chaika (The University of Utah) - https://www.math.utah.edu/~chaika/ 
Abstract: Consider a point mass traveling in a polygon. It travels in a straight line, with constant speed, until it hits a side, at which point it obeys the rules of elastic collision. What can we say about this? When all the angles of the polygon are rational multiples of pi, the unit tangent bundle is foliated by invariant surfaces and we know a lot about it. In the case when at least one of the angles is irrational, it is much less understood, though from approximating with the rational case we know a couple of things. Kerckhoff, Masur and Smillie proved that there exists a billiard in an irrational polygon where the billiard flow is ergodic with respect to the natural measure.  This talk will present two results both concerning weak mixing:

1) A strengthening of Kerckhoff, Masur and Smillie’s result: There exists a polygon where billiard flow is weakly mixing with respect to the natural volume on the unit tangent bundle.

2) A classification of the rational polygons where the billiard flow is weakly mixing with respect to the natural area on the invariant surfaces that foliate the unit tangent bundle.

Open questions will be presented and no previous knowledge of billiards nor translation surfaces will be assumed. This is joint work with Giovanni Forni and Francisco Arana-Herrera.
]]> http://www-math.umd.edu/research/seminars.html Thu, 25 Sep 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Adam Kanigowski (UMD) - 
Abstract: Kolmogorow (K) and Bernoulli are two abstract properties that describe chaoticity of a system. It is known that Bernoulli implies K and that K does not imply Bernoulli in general. We will discuss these two properties in the setting of partially hyperbolic systems. We will discuss some classical and recent results and also state some open questions.
]]> http://www-math.umd.edu/research/seminars.html Tue, 30 Sep 2025 14:00:00 EDT Where: Kirwan Hall 1311
Speaker: Fan Yang (Wake Forest) - https://yangfan.sites.wfu.edu/
Abstract: Given a diffeomorphism preserving a one-dimensional expanding foliation $\mathcal F$ with homogeneous exponential growth, we construct a family of reference measures on each leaf of the foliation with controlled Jacobian and a Gibbs property. We then prove that for any measure of maximal u-entropy, its conditional measures on each leaf must be equivalent to the reference measures. When the measure of maximal u-entropy is a Gibbs $\mathcal F$-state (i.e., when the reference measures are equivalent to the leafwise Lebesgue measure), we prove that the log-determinant of $f$ must be cohomologous to a constant. We will discuss several applications, including the strong and center foliations of Anosov diffeomorphisms, factor over Anosov diffeomorphisms, and perturbations of the time-one map of geodesic flows on surfaces with negative curvature. Joint with J. Buzzi, Y. Shi, and J. Yang.

]]> http://www-math.umd.edu/research/seminars.html Thu, 02 Oct 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Rigoberto Zelada (University of Warwick) - 
Abstract: 
We will define and discuss the concept of \textit{group of rigidity} (associated with a collection of finitely many sequences). As we will see, groups of rigidity play an instrumental role in answering questions stemming from the theory of generic Lebesgue preserving automorphisms of $[0,1]$, IP-ergodic theory, multiple recurrence, and spectral theory. A simple statement which epitomizes the type of results that one can obtain with the help of groups of rigidity is the following:\\
For any $(b_1,...,b_\ell)\in \mathbb N^\ell$ one has that there is no vector $(a_1,...,a_\ell)\in \mathbb Z^\ell$ orthogonal to $(b_1,...,b_\ell)$ with some  $|a_j|=1$ if and only if there is an increasing sequence $(n_k)_{k\in \mathbb N}$ in $\mathbb N$ with the property that  for every $F\subseteq \{1,...,\ell\}$ there is a $\mu$-preserving transformation $T_F:[0,1]\rightarrow [0,1]$ ($\mu$ denotes the Lebesgue measure) such that 
$$
\lim_{k\rightarrow\infty}\mu(A\cap T_F^{-b_jn_k}B)=\begin{cases}
\mu(A\cap B),\,\text{ if }j\in F,\\
\mu(A)\mu(B),\,\text{ if }j\not\in F,
    \end{cases}
$$
for every pair of measurable sets $A,B\subseteq [0,1]$. Part of this talk is based
on joint work with Vitaly Bergelson.
]]> http://www-math.umd.edu/research/seminars.html Thu, 09 Oct 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Sovanlal Mondal (The Ohio State University) - https://sites.google.com/view/sovanlalmondal/home

Abstract: 
In 1988, Bourgain introduced the random method to establish the existence of sparse sequences of integers along which the pointwise ergodic theorem holds. He also proved that the mean ergodic theorem holds along randomly generated sublacunary sequences (that is, sequences whose consecutive term ratios converge to 1). In this talk, we will demonstrate that there exist randomly generated sublacunary sequences along which the pointwise ergodic theorem may fail, even for indicator functions. We will also discuss some recent results concerning ergodic theorems along return times in rapidly mixing systems.
Part of this talk is based on joint work with Madhumita Roy and Máté Wierdl.
]]> http://www-math.umd.edu/research/seminars.html Thu, 23 Oct 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Kosma Kasprzak (Jagiellonian University) -
Abstract: One of the ways to generalize the classical concept of ergodic averages is as follows: instead of considering average values of some function $f$ along the whole orbit $(T^n(x))$, consider them only along a subsequence $(T^{a_n}(x))$. We focus on the case when $(a_n)=(P(n))$ for some polynomial $P$, and let $(X, T)$ be a uniquely ergodic topological system. We are then interested in the property that such ergodic averages along $(a_n)$ converge for every $x\in X$ to the integral of $f$. This is a very delicate property, and not many examples of such systems are known.
We will see a new method for establishing this kind of property for $(a_n)=(n^2)$, by assuming a strong rigidity condition on $X$, in particular obtaining weakly mixing examples. Here by rigidity we mean the existence of a sequence $(T^{q_n})$ of iterates of $T$ converging to the identity map on $X$ — we will in particular require a uniform, quantitative form of this convergence.
The method uses a lot of input from number theory about the distribution of square residues in arithmetic progressions, and interestingly it does not seem to yield results for polynomials of larger degree. We will discuss the reason for this, as well as examples of systems satisfying the required rigidity condition.
]]> http://www-math.umd.edu/research/seminars.html Thu, 30 Oct 2025 15:30:00 EDT Where: Kirwan Hall 1311
Speaker: Bassam Fayad (UMD) -
Abstract: We show that any real-analytic Hamiltonian system with 5 or more degrees of freedom, that is locally integrable around an elliptic equilibrium can be perturbed so (in fixed complex-analytic domains) such that the equilibrium becomes Lyapunov unstable.

Joint work with Jaime Paradela Diaz, Maria Saprykina, and Tere Sera.
]]> http://www-math.umd.edu/research/seminars.html Thu, 06 Nov 2025 15:30:00 EST Where: Kirwan Hall 1311
Speaker: Francisco Arana-Herrera (Rice University) - https://farana.rice.edu/
Abstract:  The classical dynamics of billiard flows on rational polygons has been
successfully studied by reduction to straight line flows on
translation surfaces. Nevertheless, the quantum counterpart of this
picture remains much less understood. We will discuss joint work with
Athreya and Forni studying quantizations of straight line flows on
translation surfaces and applications to some classical problems of
Furstenberg in ergodic theory.
]]> http://www-math.umd.edu/research/seminars.html Tue, 18 Nov 2025 14:00:00 EST Where: Kirwan Hall 1311
Speaker: Enrique Pujals (CUNY) - https://sites.google.com/site/enriquepujalsgc/home
Abstract: For mild dissipative of the disk, we will show that any ergodic measure is either metric isomorphic to an odometer or it is contained in a homoclinic class. That result will be used to decompose the non-wandering set into different maximal transitive pieces. The main technique used is a (new) closing lemma that we will outline the proof. This is a joint work with Sylvain Crovisier.
]]> http://www-math.umd.edu/research/seminars.html Thu, 20 Nov 2025 15:30:00 EST Where: Kirwan Hall 1311
Speaker: Sébastien Labbé (Université de Bordeaux) - http://www.slabbe.org
Abstract:  In the aperiodic tilings proposed by Penrose in 1974, the
ratio of tile frequencies is equal to the golden ratio. Several
aperiodic tilings discovered since then, such as Ammann's tilings
(1980s) or Jeandel-Rao's tilings (2015), are also associated with the
golden ratio. This is also the case for the aperiodic monotile called
"hat" discovered in 2023, whose ratio of frequencies of the two
orientations of the monotile is well-defined and is equal to the 4th
power of the golden ratio. In this presentation, we will explain how
one-dimensional symbolic dynamics can be used to understand and obtain
new results in the theory of aperiodic tilings. We also propose a new
family of aperiodic tilings that goes beyond the golden ratio. This is
associated with the metallic means, that is, the positive roots of the
polynomials $x^2-nx-1$ for any positive integer $n$.

The first part will be a general introduction to the topics. In the
second part, we will focus on the metallic mean Wang tiles introduced
recently in https://doi.org/10.1017/fms.2025.10069 and
https://doi.org/10.1017/fms.2025.10098

]]> http://www-math.umd.edu/research/seminars.html Thu, 04 Dec 2025 15:30:00 EST Where: Kirwan Hall 1311
Speaker: Jennifer Jones-Baro (University of Denver) -
Abstract: The stabilized automorphism group of a dynamical system (X,T) is the group of all self-homeomorphisms of X that commute with some power of T. While this is an algebraic object, we show that it captures rich dynamical information. We begin by characterizing the stabilized automorphism groups of odometers and Toeplitz subshifts, establishing an invariance property in these settings. We then extend our results to a broader class of minimal systems, proving that if two such systems have isomorphic stabilized automorphism groups and each has a non-trivial rational eigenvalue, then they must share the same set of rational eigenvalues. We further identify a class of systems for which the assumption of having a non-trivial rational eigenvalue can be removed. Finally, we generalize a known result for mixing shifts of finite type to include all irreducible shifts of finite type.
]]> http://www-math.umd.edu/research/seminars.html Thu, 11 Dec 2025 15:30:00 EST Where: Kirwan Hall 1311
Speaker: Jaime Paradela Diaz (UMD) -
Abstract: In a joint work with M. Guardia we construct symplectic blenders in two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robust, strong form of topological instability.
]]> http://www-math.umd.edu/research/seminars.html Thu, 05 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Omri Solan (Institute for Advanced Study) - https://www.ias.edu/scholars/omri-solan
Abstract: A translation surface is a closed surface that is obtained by gluing edges of a polygon in parallel. The group $GL_2(R)$ acts on the collection translation surfaces of a fixed genus $g$. For a fixed translation surface $S$ and $t>0$, we obtain a probability measure on the collection of translation surfaces by rotating $S$ with a uniform angle and then multiplying by diag$(e^t, e^-t)$. Alternatively, we can talk on expanding a piece of horospherical orbit. We prove equidistribution of this sequence of measures as $t \to \infty$. This resolves a conjecture of Forni, and extends a result of Eskin and Mirzakhani that (in particular) showed our result with a Cesàro average. We will also discuss an application of this result to billiards with rational angles.
]]> http://www-math.umd.edu/research/seminars.html Tue, 10 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Barak Weiss (Tel Aviv University) - https://www.math.tau.ac.il/~barakw/
Abstract: 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.
]]> http://www-math.umd.edu/research/seminars.html Thu, 12 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Federico Rodriguez Hertz (Pennsylvania State University ) -
Abstract: In joint work with Pablo Carrasco we push the theory ofthermodynamic formalism from hyperbolic systems to partially hyperbolic systems in different forms. In the meantime we find several interesting open problems and dynamical proofs of some (to us) interesting results, for example we show Burger-Monod theorem on vanishing of second bounded cohomology for higher rank lattices. The goal of the talk is to discuss this development.
]]> http://www-math.umd.edu/research/seminars.html Thu, 19 Feb 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Karen Butt (University of Chicago) - https://math.uchicago.edu/~kbutt/
Abstract: Given a closed negatively curved manifold, we consider the extent to which dynamical data associated to its closed geodesics (equivalently, periodic orbits of its geodesic flow) determines the underlying metric up to isometry. For instance, the lengths of closed geodesics, marked by their free homotopy classes, are conjectured to characterize the underlying metric up to isometry. In this talk, we consider a dynamically flavored variant of this marked length spectrum rigidity problem. We introduce the marked Poincare determinant, which associates to each free homotopy class of closed curves a number which measures the unstable volume expansion of the geodesic flow along the associated closed geodesic. Our main result is that near hyperbolic metrics in dimension 3, this invariant determines the metric up to homothety. This is joint work with Erchenko, Humbert, Lefeuvre, and Wilkinson.
]]> http://www-math.umd.edu/research/seminars.html Tue, 03 Mar 2026 14:00:00 EST Where: Kirwan Hall 3206
Speaker: Piotr Oprocha (University of Ostrava) - https://oprocha.eu/
Abstract: A very useful technique called BBM (Brown-Barge-Martin), incorporates inverse limits and natural extensions of the underlying bonding maps to embed attractors (for homeomorphisms) in manifolds. The original idea goes back to the paper of Barge and Martin, where the authors constructed strange attractors from a wide class of inverse limits. One of the crucial steps for this technique to work is the usage of Brown's approximation theorem.

Recently, this technique found several interesting applications and extensions. In this talk we will present a few possible applications of BBM technique in a construction of concrete examples of dynamical systems on surfaces. If time permits, we will relate BBM to Anosov-Katok fast approximation method and construction of smooth diffeomorphisms.

The talk is based on joint work(s) with Jernej Cinc and Michal Kowalewski.
]]> http://www-math.umd.edu/research/seminars.html Thu, 12 Mar 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Andreas Wieser (Institute for Advanced Study) - https://awieser1.github.io/
Abstract: 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.
]]> http://www-math.umd.edu/research/seminars.html Thu, 26 Mar 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Emilio Corso (Pennsylvania State University) - https://www.emiliocorso.com/
Abstract: Starting with the pioneering work of Furstenberg and Kesten in the sixties, the quest for non-commutative analogues of classical limit theorems in probability theory has gathered continuous attention ever since. We will discuss aspects of the study of random walks driven by actions of discrete countable groups by isometries of metric spaces, with a focus on those possessing certain hyperbolic-like features, which are most clearly on display for actions on Gromov-hyperbolic spaces and for the dynamics of the mapping class group on the Teichmüller space of a closed oriented surface. The emphasis is on large deviations for the process of renormalized distances from the origin: we prove existence of a large deviation principle, with identification of the rate function as an appropriate Fenchel-Legendre transform, for a broad class of isometric group actions encompassing the two aforementioned examples, as well as many others of relevance in geometric group theory and geometric topology. This at once extends recent work of Boulanger, Mathieu, Sert and Sisto, and provides a more streamlined argument for their result. Quantitative refinements of the main result, afforded by thermodynamic formalism in the subadditive and superadditive regime, will also be presented.
]]> http://www-math.umd.edu/research/seminars.html Thu, 02 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Rohil Prasad (Princeton) - https://r0hilp.github.io/
Abstract: Let $H$ be a smooth and proper Hamiltonian function on $\mathbb{R}^4$. I will discuss a proof that almost every regular level set of $H$ contains at least two closed orbits of the Hamiltonian flow. The proof uses holomorphic curve techniques from symplectic geometry. The techniques also apply, for example, to the problem of finding closed magnetic geodesics on the two-sphere, which I will discuss if there is time to do so.
]]> http://www-math.umd.edu/research/seminars.html Thu, 16 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Scott Schmieding (Penn State University) - https://s-schmieding.github.io/
Abstract: I'll discuss the notion of invariant random compacts for group actions. Then after some background, I'll discuss the notions of IC-rigidity and weak IC-rigidity for actions. Then I'll mention some applications of these ideas, including to dilations of subsets of the circle. I will also mention a number of questions. This is joint work with Bryna Kra.
]]> http://www-math.umd.edu/research/seminars.html Thu, 23 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Davi Obata (Brigham Young University) - https://sites.google.com/mathematics.byu.edu/davi-obata

Abstract: We study Anosov diffeomorphisms on T^3 with a decomposition E^s+E^c+E^u, where E^c expands uniformly. For such systems, u-Gibbs measures are invariant measures whose conditional measures along W^u leaves are absolutely continuous. Our motivating problem is to try to understand when such measures are SRB (conditional measures along W^cu leaves are absolutely continuous). In this talk, I will survey what is known for this problem in the case that E^s and E^u are not jointly integrable (joint work with S. Alvarez, M. Leguil and B. Santiago); and an ongoing work on the jointly integrable case (with S. Crovisier and the aforementioned collaborators). For the jointly integrable case, the proof relies on constructing a "horocycle flow" and studying its ergodic properties.
]]> http://www-math.umd.edu/research/seminars.html Thu, 30 Apr 2026 14:00:00 EDT Where: Kirwan Hall 3206
Speaker: Giovanni Canestrari (University of Toronto, Canada) -
Abstract: After introducing the problem of linear response, we consider a chaotic Sinai billiard with a hole in the boundary of the table and we derive a linear response formula for the physical conditional invariant probability measure as the hole opens. We will also mention a result on linear response for similar 'singular' perturbations
]]>