• Artem Chernikov awarded the Bessel Research Award by the Humboldt Foundation

    This award is given annually to internationally renowned academics from outside of Germany in recognition of their research accomplishments.  This award is named after Bessel and funded by the German ministry of education and research. Congratulations Atrem Chernikov.  https://www.humboldt-foundation.de/en/apply/sponsorship-programmes/friedrich-wilhelm-bessel-research-award  Read More

  • Mapping the Mind

    Junior computer science and mathematics double major Brooke Guo analyzes neural connections to understand the causes of complex brain conditions like schizophrenia.  When Brooke Guo arrived at the University of Maryland as a freshman in 2022, she knew she wanted to help people and work in a health-related field someday.… Read More

  • Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More

  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More

  • 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More
  • 1
  • 2
  • 3
  • 4
  • 5

This workshop is cosponsored by the dynamical systems groups at Maryland and Penn State, and has been held twice each year, beginning in Fall 1991. The Fall meetings are held at Penn State and the Spring meetings are held at the Department of Mathematics of the University of Maryland, College Park. Our spring meetings have been partially supported by the National Science Foundation from their beginning in 1992 through the present.

Links to previous conference programs and upcoming conference:

Chernov Lectures (D. Dolgopyat)

Title: Exponentially mixing systems

Lecture 1: Limit theorems
Lecture 2: Bernoulli property
Lecure 3: Exponential mixing for random transformations

Abstract: Exponential mixing is arguably the most chaotic property for
deterministic systems.
In this lecture series I will discuss recent progress in understanding
the statistical properties
of exponentially mixing systems and outline open question.

 

T. Bénard

Title: Equidistribution of random walks on homogeneous spaces.

Abstract: I will explain why a random walk on a simple homogeneous space equidistributes toward the Haar measure with an explicit rate, provided that the walk is not trapped in a finite invariant set and that the distribution driving the walk is Zariski-dense and has algebraic coefficients. The argument relies on a multislicing theorem which extends Bourgain’s projection theorem and is of independent interest. Joint work with Weikun He.

 
M. Cekic

Title: Speed of mixing on Abelian covers of isometric extensions of Anosov flows

Abstract: I will report on a recent work with Lefeuvre and Muñoz-Thon. We prove a complete asymptotic expansion of the correlation function in inverse powers of the time variable, for flows which arise as Abelian extensions, that is, extensions to Z^d-covers, of certain partially hyperbolic flows. This includes the frame flow of a Z^d-Abelian cover of a negatively curved closed Riemannian manifold (M, g), if the frame flow on (M, g) is ergodic. As a special case, our theorem also applies to Z^d-extensions of Anosov flows. The proof uses Fourier series in Z^d (Floquet theory), (microlocal) anisotropic Sobolev spaces tailored to the dynamics, as well as the semiclassical Borel-Weil calculus on principal bundles.

 
J. Chaidez

Title: The conformally symplectic dynamics of characteristic foliations

Abstract: Any hypersurface in a contact manifold comes equipped with a natural dynamical system, called the characteristic foliation. Special cases include the suspension flow of a contactomorphism and the Liouville flow on a Liouville manifold. One may view the characteristic foliation as a type of conformally symplectic dynamical system.

In this talk, I will explain some recent studying the dynamics of characteristic foliations using tools from (partially) hyperbolic dynamics and ergodic theory. I will also explain several applications to contact topology, including the proof that convex hypersurfaces are not dense in the $C^2$-topology in dimension five (in sharp contrast to the seminal works of Giroux in dimension three and Honda-Huang in the $C^0$-topology). This talk covers ongoing joint work with Michael Huang (USC), Dishant Pancholi (Chennai) and Yasha Eliashberg (Stanford). 
 
 
M. Gidea
 
Title: Invariant Manifolds for Conformally Symplectic Dynamical Systems

Abstract: Conformally symplectic systems appear naturally in physics (e.g., mechanical systems with dissipative force proportional to the velocity), celestial mechanics (e.g., spin-orbit models), non-equilibrium thermodynamics problems (e.g., thermostats), etc. We focus on conformally symplectic maps, which transform the symplectic form into a multiple of itself by a conformal factor. We show that the topology of the underlying manifold presents obstructions to the possible conformal factors.

We also study geometric properties  of normally hyperbolic manifolds(NHIMs)  for conformally symplectic maps. We show that conditions among rates and the conformal factor are equivalent to the NHIM being symplectic. We also show that the hyperbolicity rates satisfy pairing rules similar to those for Lyapunov exponents of periodic orbits.

Then, we show that the scattering map -- which relates the past asymptotic trajectory of a homoclinic orbit to the future asymptotic trajectory --  is symplectic.

Finally, we present  some applications to the Arnold diffusion problem for Hamiltonian systems with small dissipation.
 
B. Kalinin
 
Title: Rigidity of strong and weak foliations.

Abstract: We consider a perturbation $f$ of a hyperbolic toral automorphism $L$ and a dominated splitting of the stable foliation of $f$ into weak and strong parts. We discuss rigidity results related to exceptional properties of these weak and strong foliations. This talk is based on a joint work with Victoria Sadovskaya.

If the strong foliation of $f$ is mapped to the linear one by the conjugacy $h$ between $f$ and $L$, we  obtain smoothness of $h$ along the weak foliation and regularity of the joint foliation of the strong and unstable foliations. If the weak foliation is sufficiently regular, we  obtain smoothness of the conjugacy along the strong foliation and regularity of the joint foliation of the weak and unstable foliations. If both conditions hold then we get smoothness of $h$ along the stable foliation and regularity of the unstable one. We also deduce a rigidity result for the symplectic case, where high enough Holder exponent of $h$ implies its smoothness. The main theorems are obtained in a unified way using our new result on relation between holonomies and normal forms.
 
O. Khalil
 
Title: Strong spectral gap on geometrically finite hyperbolic manifolds

Abstract: Geometrically finite hyperbolic manifolds generalize finite-volume ones by allowing infinite volume with controlled geometry at infinity, and are heavily studied in geometry, dynamics, and spectral theory. Work of Lax–Phillips, Patterson, and Sullivan from the 80s shows that their Laplacians have discrete spectrum below that of the universal cover. This result is intimately tied to the Anosov property of the geodesic flow. A natural question is whether a similar phenomenon holds for the Casimir operator on the frame bundle, where the underlying frame flow is no longer Anosov. I will report on joint work with Dubi Kelmer and Pratyush Sarkar where we take a first step in this direction by proving that the Casimir admits a spectral gap under the necessary condition that the topological entropy exceeds half the volume entropy, confirming a conjecture of Amir Mohammadi and Hee Oh. No prior familiarity with these objects will be assumed.
 
M. Saprykina
 
Title:  Lyapunov unstable approximation of integrable Hamiltonians
 
Abstract:  We prove that any real-analytic Hamiltonian with a locally integrable non-degenerate and not locally convex elliptic equilibrium, can be perturbed within the real analytic category, while preserving the Birkhoff normal form at the equilibrium up to any arbitrary order, so that the equilibrium becomes Lyapunov unstable. This result is joint with Bassam Fayad, Jaime Paradela and Tere Seara.
 
SHORT TALKS:
 
G. Bixler 
Title:Local rigidity of some actions of rank-one Lie groups
Abstract: An action is \emph{locally rigid} if it is conjugate to every nearby action. Many actions of higher-rank Lie groups are known to be locally rigid, but actions of rank-one Lie groups have been less studied. I prove that a certain family of such actions, related to complex-hyperbolic geometry, are locally rigid. This extends Masayuki Asaoka's earlier work in the real-hyperbolic setting. My main technical result is a periodic Lyapunov spectrum rigidity theorem for ``half-complex-hyperbolic'' Anosov flows; this theorem extends part of Clark Butler's thesis.
 
M. Brown
Title: Expanding Maps on Flowers, Interval Exchange Transformations, and Ergodic Optimization
Abstract: I will discuss subsystems of expanding maps on the circle that are contained in flowers, showing they have at most linear complexity and relating them to embeddings of a certain class of interval exchange transformations. Flowers for expanding maps were first introduced by Brémont and Harriss-Jenkinson in the context of ergodic optimization. I will discuss how our results extend Bullett and Sentenac’s work on Sturmian systems, and also a connection to recent work of Gao et al. on ergodic optimization.
 
S. Durham
Title: Rapid mixing for random walks on nilmanifolds 
Abstract: Consider a random walk on a nilmanifold generated by a finite collection of translations. We say that the walk is rapid mixing if correlations between smooth observables decay superpolynomially. We show that for all nilmanifolds there exists an m, such that almost any m translations generate a rapid mixing walk. In certain specific cases, we show that m may be taken to be 2. This is joint work with Dima Dolgopyat and Minsung Kim.
 
G.Dvorkin
Title: Generalized constructions of  SRB measures.
Abstract: SRB measures are a special class of measures, which are in some sense the closest invariant measures to the volume in the non-volume preserving situation. In particular, SRB measures are physical: their basin has positive volume. One of the central questions in the modern dynamics is whether SRB measures exist and how to construct them. The first construction of SRB was done by Sinai for Anosov systems and was obtained by averaging the volume under the evolution of the system and taking a weak limit (push-forward construction). Later by Pesin and Sinai it was shown that the push-forward construction can be started not from the volume itself, but from the leaf volume on some submanifold with sufficiently good expansion properties. Moreover, Sinai conjectured that the construction can be started from any subset of such a submanifold of a positive volume. We prove this conjecture under one of the most general hyperbolic conditions -- effective hyperbolicity (this is a joint work with Yakov Pesin). Moreover, I will discuss what is going on if  the initial set is changing in time and how these types of constructions can be used to study Viana's conjecture.
  
A. Maldonado
Title: Rigidity in products of Anosov flows
Abstract: Irreducible higher rank Anosov actions often exhibit strong rigidity properties. Katok and Spatzier conjectured that such actions are always smoothly conjugate to algebraic actions. This conjecture, without additional assumptions, was shown to be false by Vinhage. To construct his counterexample, he began with products of Anosov flows, which despite being reducible at first, can give rise to irreducible actions via nontrivial time changes. In this talk, we present two rigidity results for time changes of products of Anosov flows related to stabilizers of periodic orbits. In our first theorem, stabilizers are used to detect when two time changes are conjugate, while in our second theorem they detect when the resulting action is reducible. This is joint work with Miri Son.
 
N. Martinez Ramos
Title: Asymptotic behavior of the spectral radius of locally constant strongly irreducible cocycles
Abstract: In 1986, Cohen posed a question on whether given a sequence $g_{1}, g_{2}, \dots$ of i.i.d. matrices in GL(d,R), the sequence $n^{-1} \log\rho(g_{n}\dots g_{1})$ would converge to the top Lyapunov exponent, where $\rho(g)$ is the spectral radius. Several positive results have been obtained in this direction, with the strongest one being proved by Aoun and Sert in 2021, asserting that the limit exists almost surely under finiteness of the second moment.More generally, in the case of an ergodic measure preserving system $(\Sigma, \mathcal{B}, \mu, T)$ and $A:\Sigma\to\text{M}_{d\times d}$ a measurable linear cocycle, Morris proved in 2014 that the limsup of $n^{-1} \log\rho(A(T^{n-1}x)\dots A(x))$ converges almost surely to the top Lyapunov exponent of the cocycle. However, the limit of this sequence does not exist in general, as shown by Avila and Bochi in 2002. In this talk, I will establish some conditions under which $\text{GL}(d,\mathbb{R})$-valued cocycles over a subshift of finite type, equipped with an equilibrium state, exhibit exponential asymptotics for the spectral radius. To that end I will use a definition of strong irreducibility which fits the case of locally constant cocycles and I will develop some large deviations estimates which will allow us to use the strategy developed by Benoist and Quint. 
 
T. O'Hare
Title: Effective Equidistribution for Contact Anosov flows in Dimension Three
Abstract: A classical theorem of R. Bowen states that the family of normalized measures over geodesic packets in hyperbolic surfaces equidistributes towards the measure of maximal entropy. In a joint work with Asaf Katz, we quantify this equidistribution in the general setting of contact flows in dimension 3, recovering an exponential equidistribution rate. When these periodic orbit measures are weighted by a potential function, we show that they exponentially equidistribute towards the appropriate equilibrium state. Our estimate is based on Zeta function analysis approach of Pollicott-Sharp together with Dolgopyat’s method. We also recover weaker (polynomial) bounds for general transitive Anosov flows.
 
I. Park
Title: Smooth Local Linearization of SL(n,\R)-Actions Near Fixed Points
Abstract: Let a Lie group $G$ act smoothly on a manifold $M$ with a fixed point $p$. The classical linearization problem asks whether the action near $p$ is locally conjugate to the induced linear representation $\rho\colon G \to \mathrm{GL}(T_pM)$. Smooth linearization is known in the following cases: (a) $G$ is compact (Bochner, Cartan), (b) the action is analytic (Kushnirenko; Guillemin--Sternberg, 1960s), and (c) $G =\text{SL}(n,\mathbb{R}) $ with $\dim M = n$ (Cairns--Ghys, 1997). Cairns--Ghys also constructed non-linearizable examples, suggesting that linearizability depends more on the dimension of $M$. In joint work with Miri Son, however, we propose that the key factor is the representation $\rho$. More precisely, for $G =\text{SL}(n,\mathbb{R})$, we prove smooth linearizability for $\rho = (\mathrm{Std.}) \oplus (\mathrm{Triv.})^m$ for all $m \ge 0$, and construct non-linearizable examples for $\rho = (\mathrm{Adj.})$ or $(\mathrm{Sym}^2)$. In this talk, we review earlier results, discuss applications to the classification of Lie group actions, and outline some ideas in the proof.
 
S. Pavez Molina
Title: Local Smooth Rigidity of Anosov diffeomorphisms in $T^{3}$.
Abstract: A small C^1 perturbation of an Anosov diffeomorphism is known to be topologically conjugate to the original system via a bi-Hölder homeomorphism. A fundamental question is under what conditions this conjugacy can be promoted to a smooth one. It is known that a necessary condition for smoothness is the matching of the periodic data of the diffeomorphisms. In this talk, I will focus on this smooth rigidity problem in the case of the three-dimensional torus, where the presence of complex eigenvalues introduces significant difficulties. Building on the progress made by Kalinin, Sadovskaya, Gogolev, Guysinski, and Rodríguez Hertz, the remaining open case concerns pairs of Anosov diffeomorphisms close to a linear model whose Jacobian data are not cohomologous to a constant. I will present a positive answer to this question by establishing local smooth rigidity for small perturbations of hyperbolic automorphisms of $\mathbb{T}^3$ with complex spectrum. This is joint work with James Marshall Reber.
 
E. Shuvaeva
Title: Avila-Gouëzel-Yoccoz Balls in the Teichmüller Space of Quadratic Differentials
Abstract: The AGY metric was first introduced by Avila, Gouëzel and Yoccoz as a metric on the space of Abelian differentials and used to prove that the Teichmüller flow is exponentially mixing on connected components of its strata. Later, it was established that this metric serves as a useful tool in the study of Teichmüller Dynamics due to its controlled behavior both locally and close to infinity. This talk presents some new boundedness results. In particular, I will provide estimates on the AGY norms of the vectors of a certain relative cohomology basis that captures the geometry of the flat metric and show that the Masur-Veech volume of any AGY ball of a sufficiently small radius in the principal stratum of quadratic differentials is uniformly bounded.

Confirmed speakers:

Thimothée Bénard 

Mihajlo Cekic

Julian Chaidez

Marian Gidea

Boris Kalinin

Osama Khalil 

Jaime Paradela

Maria Saprykina

 SCHEDULE:

Thursday:

2pm-3pm -- M. Saprykina
3:30pm-4:30pm -- J. Paradela
Friday:
9-10 --  D.Dolgopyat
10-10:30 coffee break
10:30-11:30 -- M. Cekic
11:30-12:30 -- M. Gidea
12:30-2-- Lunch break
2-5  -- Brin Award Ceremony
Saturday: 
9-10 -- D. Dolgopyat
10-10:30 -- coffee break
10:30 -11:30 -- O. Khalil
11:30-12:30 --short talks (2 rounds)
12:30-2 -- Lunch Break
2-3 -- J. Chaidez
3-3:30 -- coffee break
3:30-4:00  -- short talks (1round)
4:00-5:00 - T. Benard
Sunday:
9-10 -- D. Dolgopyat
10:30-11:00 short talks (1 round)
11:00-12:00 -- B. Kalinin

Beginning in Fall 1991, the dynamics groups of the University of Maryland and Pennsylvania State University have jointly sponsored two annual three to four day meetings in dynamical systems and related topics: a spring meeting here in College Park, and a fall meeting in State College. These meetings, though primarily regional, also attract participants outside the region and the country; the conference archives indicate their scope.

All the talks will take place in the Colloquium Room (3rd floor) in the Math Department (Kirwan Hall) at UMD.

 

Chernov lectures will be given by Dmitry Dolgopyat (UMD).

The 15th Michael Brin prize in dynamical systems will be awarded Friday April 10, 2026.

 

 

Confirmed speakers:

TBA

 

  1. Dynamics at Maryland

Subcategories

2015 Dynamics Conference

2025 Dynamics Conference

  • 1
  • 2