One-Dimensional Dynamics and High-Dimensional Network Systems

20 Apr 2026, 08:00 → 24 Apr 2026, 22:40 Europe/Rome

Aula Dini (Palazzo del Castelletto)

Alice Valença De Lorenci (Imperial College London), Deniz Eroglu (Kadir Has Üniversitesi), Jeroen Lamb (Imperial College London), Stefano Marmi (Scuola Normale Superiore), Tiago Pereira (Universidade de São Paulo), Matteo Tanzi (King’s College London)

This conference aims to unite researchers in dynamical systems, fostering interdisciplinary exchange between experts in one- and low-dimensional dynamics, and those working on high-dimensional networked systems. The study of high-dimensional systems, particularly dimension reduction in network dynamics, has greatly benefited from insights from one-dimensional dynamics. Conversely, the field of complex dynamics has recorded a great activity in the push of low-dimensional descriptions to higher dimensions. By bringing together diverse perspectives, we seek both to explore recent advancements at the established intersection between these areas, and to uncover new connections.

LIST OF  SPEAKERS

Anna Miriam Benini (Università di Parma)

Fabrizio Bianchi (Università di Pisa)- On line talk                       

Henk Bruin (Universität Wien)

Kostiantyn Drach (Universitat de Barcelona, CRM-Barcelona)

Núria Fagella (Universitat de Barcelona, CRM-Barcelona)

Bastien Fernandez (LPSM, CNRS)

Ale Jan Homburg (Universiteit van Amsterdam)

Jeroen Lamb (Imperial College London)

Luna Lomonaco (IMPA)- On line talk

Stefano Luzzatto (ICTP)     

Stefano Marmi (Scuola Normale Superiore)

Marco Martens (Stony Brook University) 

Liviana Palmisano (KTH)  

Leticia Pardo-Simon (Universitat de Barcelona,CRM-Barcelona)- On line talk

Tiago Pereira (ICMC, Universidade de São Paulo)- On line talk

David Rand (University of Warwick)

Lasse Rempe (University of Manchester)

Gustavo Rodrigues Ferreira (CRM-Barcelona)

Edmilson Roque (Max Planck Institute, Dresden)

Weixiao Shen (SCMS)

Leon Staresinic (Universität Zürich)

Dmitry Turaev (Imperial College London)

Corinna Ulcigrai (Universität Zürich)               

Anna Zdunik (Uniwersytet Warszawski)

Although we do not expect to cover participants’ expenses, limited financial support may be available for younger participants presenting a poster or giving a short talk, subject to funding availability. 

The deadline to apply for funding is the 22nd Feb 2026.

The deadline for registration without funding is the 16th of March 2026

More information on the application procedure at the REGISTRATION PAGE.

The number of participants attending the Workshop is limited, therefore the registration will be confirmed after its expiration.

 

Funded by:

— FAPESP/UKRI-EPSRC grants 2023/13706-0 and EP/Z533658/1 titled Predicting Critical Transitions in      Complex Dynamical Networks: Reduction and Learning

— Serrapilheira Institute Fellowship (Grant No. Serra-1709-16124) titled Reconstructing Complex                    Networks from Data

— “Dynamics and Information Research Institute – Quantum Information (Teoria dell'Informazione),                Quantum Technologies”, in the framework of the agreement signed by Unicredit Bank and Scuola              Normale on July 31st 2014

— UKRI-EPSRC grant number UKRI1021 “Strongly Coupled Maps: Thermodynamic Limits and Rates of          Convergence”

— "BeyondTheEdge: Higher-Order Networks and Dynamics” is funded by the European Union under REA       Grant Agreement No. 101120085. 

— UKRI-EPSRC grant EP/Z002656/1 titled Reconnect - Data-driven network dynamics reconstruction to        predicting critical transitions: a random dynamics approach

book-of-abstracts.pdf

Monday 20 April

09:10 → 10:00 Registration

10:00 → 10:50 TBA

Speaker: Stefano Marmi (Scuola Normale Superiore)

10:50 → 11:40 TBA

Speaker: Weixiao Shen (SCMS)

11:40 → 12:10 Coffee break

12:10 → 13:00 Wild Sets with Collet-Eckmann Points and Infinitely Many Sinks:Stability and Coexistence

In two dimensional unfoldings of homoclinic tangencies, the parameter space contains codimension one laminations whose leaves consist of maps with invariant non hyperbolic Cantor sets. I will describe the geometry and dynamics of these Cantor sets. They are wild both in the senses of Hofbauer–Keller and Newhouse, yet contain Collet–Eckmann points with dense orbits. As a consequence, wildness and non uniform chaotic hyperbolicity coexist on a single invariant set and persist along codimension one parameter families.

Furthermore, each leaf of the lamination also contains maps with infinitely many sinks accumulating on the Cantor set containing the Collet–Eckmann point. The construction is based on a generalized renormalization scheme for two dimensional systems, which will be outlined in the talk.

Speaker: Liviana Palmisano (KTH)

14:30 → 15:20 Intermingled basins for skew product systems

In the context of skew product systems, I'll revisit some constructions of maps with multiple attractors that have intermingled basins, and I'll discuss some novel constructions.

Speaker: Ale Jan Homburg (University of Amsterdam)

15:20 → 15:45 Short Talk: A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.

Convener: Vincent Goverse (Imperial College London)

15:45 → 16:15 Coffee break

16:15 → 17:05 Algebraic correspondences: Where rational dynamics meets Kleinian groups- on line talk

The analogies between the iteration of holomorphic maps and the action of Kleinian groups were first systematically explored by Dennis Sullivan in the mid-1980s. In the landmark paper, where he famously proved Fatou's conjecture—that rational maps on the Riemann sphere have no wandering domains—Sullivan introduced what is now known as Sullivan's Dictionary. This conceptual framework draws deep parallels between the definitions, theorems, and conjectures of holomorphic dynamics and those of Kleinian group theory.
Sullivan emphasized striking similarities between the Fatou set $F_f$ and Julia set $J_f$ of a holomorphic map $f$ on the Riemann sphere $\widehat{\mathbb{C}}$, and the ordinary set $\Omega(G)$ and limit set $\Lambda(G)$ of a finitely generated Kleinian group $G$ acting on $\widehat{\mathbb{C}}$. His proof of the no wandering domains theorem was directly inspired by methods used to establish Ahlfors’ Finiteness Theorem in the setting of Kleinian groups, highlighting the profound conceptual bridges between the two fields.
Both rational maps and finitely generated Kleinian groups can be regarded as special cases of holomorphic correspondences. An $n$-to-$m$ holomorphic correspondence on $\widehat{\mathbb{C}}$ is a multivalued map $\mathcal{F}: z \mapsto w$ defined implicitly by a polynomial relation $P(z, w) = 0$.
In 1994, Shaun Bullett and Christopher Penrose introduced the first family of correspondences that contains matings between quadratic rational maps and the modular group, and proved that, for a particular parameter, the correspondence is a mating : it behaves as the modular group on an open subset \Omega, and as a polynomial (and its inverse) in the complement.
Since then, the field of correspondences which are matings between rational maps and Kleinian groups grew considerably.
In this talk, I will give an overview of the subject.

Speaker: Luna Lomonaco (IMPA)

17:05 → 17:30 Short Talk: Non-statistical skew products with one-dimensional fibers

Convener: Raul Steven Rodriguez Chavez (ICTP and PUC-Rio)

Tuesday 21 April

09:30 → 10:20 Geometry and dynamics of developmental decision making.

I will discuss new work about the use of dynamical systems to understand the early development of an embryo, in particular the way that cells transition from a pluripotent stem cell state to become specialised, complex, functional cells such as neurons, heart cells or the cells in a flower petal. I will describe how a dynamical systems viewpoint leads to new analysis methods for state-of-the-art single-cell data that quantifies the activity of essentially all genes in the cells in a given tissue, such as the early heart. And how ideas from catastrophe and bifurcation theory are used to construct a model of how the cells transition through a complex network of intermediate cells states before adopting their end state. I will also discuss how this leads to new mathematical results and conjectures about how boundary conditions on parameter space force complex bifurcation structures in the interior of the parameter space.

Speaker: David Rand (University of Warwick)

10:20 → 11:10 Universality in Transcendental Dynamics

The Mandelbrot set is a fractal object encoding the dynamical behaviour of the family of quadratic polynomials z^2+c, where c is a parameter varying over the complex plane. It surprisingly appears also in the parameter spaces of all (reasonable) rational maps and in such sense, it also encodes the dynamical behaviour of this much larger class. The explanation is intricate and relies on the concept of renormalization: essentially, renormalization isolates and extrapolates the behaviour of a rational functions near its critical values, and brings it back to analogous behaviours for quadratic polynomials. In this work we present an analogous object for transcendental maps, which arises from a model family and yet encodes the dynamical behaviour of all (reasonable) families of transcendental meromorphic maps.
This is joint work with M. Astorg and N. Fagella.

Speaker: Anna Miriam Benini (Università di Parma)

11:10 → 11:40 Coffee break

11:40 → 12:30 The Tandelbrot set and the dynamics of tangent-like mappings

The well-know theory of polynomial-like mappings describes the dynamics and bifurcations of proper maps defined in a region containing critical points. If instead we are in a purely transcendental setting, that is, in the presence of an (omitted) asymptotic value and no critical points, we then speak of tangent-like mappings. The model family is known as the generalized tangent family and its bifurcation locus is the boundary of the Tandelbrot set. In this talk we will introduce these concepts and see how they can be used to build a transcendental renormalization theory. This is joint work with Mathieu Astorg and Anna Miriam Benini.

Speaker: Núria Fagella (Universitat de Barcelona)

12:30 → 12:55 Short Talk: The Arti-Mazur zeta function for interval maps.

Convener: Jorge Olivares-Vinales (SCMS, Fudan University)

12:30 The Arti-Mazur zeta function for interval maps.

In this talk, I will discuss recent work characterizing the rationality of the Artin–Mazur zeta function for unimodal maps. I will then present examples showing that this characterization fails for multimodal maps, and therefore for polynomial maps of higher degree. If time permits, I will also explain how these examples connect to Thurston’s conjecture on the structure of isentropes for polynomial maps

Speaker: Jorge Olivares-Vinales (SCMS, Fudan University)

14:30 → 15:20 Learning network dynamics from data through compressive sensing techniques

Networks of coupled dynamical systems are fundamental models across the sciences, from physics to neuroscience. Despite their success, the governing equations of such systems are often unknown, limiting our ability to predict and control their dynamics. In many applications, only time series data from the network is accessible, and learning the governing equations from data becomes an inverse problem. In this talk, inspired by compressive sensing techniques, I will show how learning network dynamics from data can be formulated as a convex optimization problem. By exploiting structural information encoded in the network dynamics, such as sparsity, statistical properties, and symmetries, we characterize the minimum amount of data required for learning the network dynamics exactly (and robustly). We illustrate these ideas using networks of coupled chaotic maps and oscillators.

Speaker: Edmilson Roque (Max Planck Institute, Dresden)

15:20 → 15:45 Short Talk: Adiabatic invariant actions for partially integrable systems

Convener: Amir Khodaeian Karim (Imperial College London)

15:45 → 16:15 Coffee break

16:15 → 17:05 Thermodynamics through potential theory- on line talk

I will describe how tools from potential theory can be used to obtain a very precise statistical description of the dynamics of polynomials and rational maps. In particular, I will explain how the complex setting often allows one to overcome the need for strong a priori hyperbolicity assumptions. This talk is based on joint works with Tien-Cuong Dinh.

Speaker: Fabrizio Bianchi (Università di Pisa)

17:05 → 17:55 Universal finite-type entire functions

A transcendental entire function is said to be of finite type if it has only finitely many critical values (images of critical points) and asymptotic values (non-algebraic singularities of inverse branches). Functions of finite type are of significant interest in complex analysis and complex dynamics.
Eremenko and Lyubich showed that the class S of finite-type entire functions is stratified by finite-dimensional complex parameter space, consisting of functions all of which have the same topological mapping behaviour. For example, one such parameter space is given by pre- and post-compositions of the sine function with affine maps.
It is a natural question what can happen as functions in a given parameter space degenerate. For example, what are the possible limits of a sequence of functions in such a parameter space that leaves any compact subset thereof? In joint work with Prochorov, we show that this limiting behaviour can be extremely complicated. In fact, we show that, for any given finite set S, there exists a universal function for this set: A transcendental entire function f such that the possible pre-compositions of f with affine maps accumulate on all entire functions with the same singular values. In particular, the parameter space of such a universal function f accumulates on all
Moreover, using Bishop's technique of quasiconformal folding, we show that the pre-compositions in question accumulate even on every (not necessarily entire) finite-type map defined on a simply-connected domain and having singular set S. Given time, I will discuss consequences of this result for transcendental dynamics, in particular for the important problem of extending Thurston's characterisation of post-critically finite rational maps to the setting of transcendental dynamics.

Speaker: Lasse Rempe (University of Manchester)

20:00 → 22:00 SOCIAL DINNER-- La Pergoletta

Wednesday 22 April

10:20 → 11:10 IETs rotation numbers and rigidity

Rigidity is a central question investigated in one dimensional dynamics: we say that a class of one dimensional maps is rigid when a topological conjugacy between two of them has automatically further regularity properties. In this talk we want to highlight how a notion of 'combinatorial rotation number' borrowed from the study of Interval exchange transformations (IETs) can help investigate rigidity in different settings, by discussing two recent results for multi-critical circle maps and affine interval exchange maps (AIETs) respectively.
For multi-critical circle maps, assuming exponential convergence of renormalization, we show that two maps with the same signature, under a full measure condition of the latter, are C^(1+a) conjugated (joint work with Estevez and Trujillo). In the setting of AIETs, we describe a class of AIETs which are C^10 but not C^1 conjugated (joint work with Trujillo). In both works, a crucial role in the proofs is played by suitable 'Diophantine-like' conditions (on the signature, or on the IET rotation number) which control combinatorics and exploits the classical Rauzy-Veech induction for IETs.

Speaker: Corinna Ulcigrai (Universität Zürich)

11:10 → 11:40 Coffee break

11:40 → 12:30 Dynamics in the real world.

An experiment in cell biology inspired a general method to use the tools/ideas from the theory for dynamical systems to build models for real world processes.

Speaker: Marco Martens (Stony Brook University)

12:30 → 12:55 Short Talk: Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

Convener: Rubio Gunawan The (SISSA)

12:30 Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

We construct an example of a smooth circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization lemma of independent interest, which gives a canonical way to construct a full branch map given its induced map.

Speaker: Rubio Gunawan The (SISSA)

14:30 → 15:20 Teichmüller spaces and normal forms for wandering domains- on line talk

Wandering domains of entire functions exhibit a wide range of dynamical behaviour, and a useful way to study this is through the associated dynamical Teichmüller space T(U,f). In this talk, I will discuss how the structure of this space depends on the grand orbit relation in the wandering domain. I will show that if the grand orbit relation is discrete, then T(U,f) is infinite-dimensional, answering a question of Fagella–Henriksen. I will then present normal forms for the dynamics on wandering domains, giving global linearising coordinates in the discrete case and power-like dynamics between annuli in the indiscrete case. This is joint work with N. Fagella and G. R. Ferreira.

Speaker: Leticia Pardo Simon (Universitat de Barcelona)

15:20 → 15:45 Short Talk: Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$

Convener: Alden Paige (The University of Manchester)

15:20 Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$

It is known that every positive primitive Pythagorean triple can be uniquely express in the form $M_{a_1} \ldots M_{a_n} v$, where each $M_{a_i}$ is one of three specific matrices, and $v$ is either $(3,4,5)^T$ or $(4,3,5)^T$. Motivated by a desire to compute this code for any given triple, Romik presented an ergodic dynamical system on the positive quadrant of the unit circle, and conjugated this to the unit interval. Later, Cha (et al.) presented a method for computing Berggren trees for some quadratic forms on $\mathbb{R}^3$ that satisfy certain conditions. In this talk, I present a methodology for constructing 1-D dynamical systems from these Berggren trees following the outline of Romik's paper, and give their absolutely continuous invariant measures by adapting Keane's method of computing the Gauss measure for the continued fraction map. Time permitting, I will also show how the Farey map may be exhibited as an example.

Speaker: Alden Paige (The University of Manchester)

15:45 → 16:15 Coffee break

16:15 → 17:15 POSTER SESSION

Conveners: Amir Khodaeian Karim (Imperial college), Bella Figliaggi (USP), Rubio Gunawan The (SISSA)

Thursday 23 April

09:30 → 10:20 Rigidity and density of hyperbolicity: from polynomials to transcendental maps

In this talk, I will introduce a large class of transcendental entire maps to which we can transfer several central results in polynomial dynamics; this includes many of the available results on rigidity and density of hyperbolicity. This transfer is done via our main tool: dynamically meaningful polynomial approximations, which we establish in the near-degenerate regime. If time permits, I will also outline further implications for Transcendental Thurston Theory. Based on joint work, partially in progress, with Dzmitry Dudko.

Speaker: Kostiantyn Drach (CRM-Barcelona)

10:20 → 11:10 A simple model for the population dynamics in OTC wholesale fresh product markets

The purpose of this talk is to introduce a dynamical model for the time evolution of buyers populations in over-the-counter (OTC) wholesale fresh product markets and to the present the results of its mathematical analysis. The dynamics is governed by immediate reactions of buyers and sellers to changes in basic indicators. Buyers are influenced by some degree of loyalty to their regular suppliers. Yet, at times, they also prospect for better offers. On the other hand, sellers primarily aim at maximising their profit. Yet, they can be also prone to improving their competitiveness in case of clientele deficit.
The analysis reveals that the dynamics spontaneously self-regulates in time and generates (transient) oscillatory behaviours that prevent any seller to dominate permanently its competitors (and to be permanently dominated). Long-term behaviours are also investigated, with focus on asymptotic convergence to equilibrium. In particular, in the simplest case of 2 competing sellers, a normal-form-like analysis in the neighbourhood of an elliptic fixed point proves that such convergence holds under suitable, yet economically meaningful, assumptions on the model’s characteristics.

Speaker: Bastien Fernandez (Laboratoire de Probabilités, Statistique et Modélisation)

11:10 → 11:40 Coffee break

11:40 → 12:30 Lorenz attractor in the Lorenz map

It is known that the dynamics of a Lorenz-like attractor are described by a singular one-dimensional map (the quotient of the Poincare map over the strong-stable invariant foliation). For Lorenz attractors emerging out of a variety of homoclinic bifurcations, this map takes a universal form — it is a C^1-small perturbation of the map
X --> |1 - c X^b|
where the parameter c can be arbitrary, and 0 < b < 1, so the map has an infinite derivative at zero and positive Schwarzian. We give a complete description of the attractors for this family of maps and for all its low-regularity perturbations. In particular, we determine the region in the parameter plane (b,c) for which the Lyapunov exponent is positive for all orbits. The main difficulty is that for small values of b the map is contracting for long series of consecutive iterations, but we show that the expansion always prevails. This is a joint work with Klim Safonov.

Speaker: Dmitry Turaev (Imperial College London)

12:30 → 12:55 Short Talk: High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms

Convener: Dmitrii Mints (Imperial College London)

12:30 High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphism

Our research is aimed at studying the dynamics of smooth multidimensional diffeomorphisms from the Newhouse domain, that is, open regions in the space of maps where systems with homoclinic tangencies are dense. We prove that in the space of smooth and real-analytic multidimensional maps in any neighborhood of a map such that it has a bi-focus periodic orbit whose invariant manifolds are tangent, there exist open regions (which are subdomain of the Newhouse domain) where maps with high order homoclinic tangencies of corank 2 (invariant manifolds forming the tangency have a plane of common tangent vectors) are dense and maps having universal two-dimensional dynamics are residual. This is a joint work with D. Turaev.

Speaker: Dmitrii Mints (Imperial College London)

14:30 → 15:20 Hausdorff measure for continued fraction iterated function system

Speaker: Anna Zdunik (Uniwersytet Warszawski)

abstract2_Pisa.pdf

abstract_talk_pisa.pdf

15:20 → 15:45 Short Talk: A Tensorization Approach to Overcoming the Curse of Dimensionality in High-Dimensional Coupled Systems

Convener: Giuseppe Tenaglia (Imperial college London)

15:20 A Tensorization Approach to Overcoming the Curse of Dimensionality in High- Dimensional Coupled Systems

Perturbations of high-dimensional systems are notoriously delicate: even when their magnitude vanishes with the dimension, their cumulative effect may remain significant due to the curse of dimensionality.
We study a class of uncoupled noisy systems perturbed by the introduction of a hole whose size decreases as the dimension grows. Although the perturbation becomes asymptotically small, its impact is amplified by dimensional growth.
Exploiting the product structure through tensorization, we prove that, if the uncoupled dynamics is noisy enough, the perturbed dynamics admits an equilibrium measure that stays uniformly close in W 1,2 to that of the unperturbed system

Speaker: Giuseppe Tenaglia (Imperial college London)

15:45 → 16:15 Coffee break

16:15 → 17:05 The Topological Boshernitzan-Kornfeld Conjecture

Interval Translations Maps (ITMs) are a natural generalisation of the well-known Interval Exchange Transformations (IETs). They are obtained by dropping the bijectivity assumption for IETs. As such, they are exactly the finite piecewise isometries of the interval. There are two types of ITMs, finite-type and infinite-type ones. They are classified by their non-wandering sets: it is a finite union of intervals for finite-type maps, and contains a Cantor set for infinite-type maps.

One of the basic questions in the field is: How prevalent is each type of map in the parameter space? In this work, we show that the set of finite-type maps contains an open and dense subset of the parameter space of ITMs with a fixed number of intervals, which resolves in positive the topological version of a long-standing conjecture due to Boshernitzan and Kornfeld.

This is a joint work with Kostiantyn Drach and Sebastian van Strien.

Speaker: Leon Staresinic (Universität Zürich)

17:05 → 17:55 Equilibrium States for Doubly Intermittent Maps

We study the existence and uniqueness of equilibrium states for various potentials for a class of doubly intermittent maps. This is joint work with J.Alves, V. Ramos and J. Siqueira.

Speaker: Stefano Luzzatto (ICTP)

Friday 24 April

09:30 → 10:20 Ergodic properties of sums of visits to $[0,1/2)$ by quadratic irrational rotations.

The visit sums and averages of orbits under irrational rotations has been of interest since at least the seminal work of Kesten in the 1960. Recent work by Avila et al. revisted the problem in the case that the rotation number is a quadratic irrational, showing that the typical behaviour is slightly different from what Kesten proved for typical rotation numbers. Their method is based on $\Z$-extension (skew-products) over the rotation and certain renormalization techniques. We recently generalized their method so as to include samples of Ehrenfest wind-tree model as well. Using purely combinatoric methods, it is possible to give precise statements about visit sums for particular orbits, or actually the orbit of 0. This orbit is actually non-typical in view to the results of Avila et al. The talk is based on joint work with Charles Fourgeron, Davide Ravotti, Dalia Terhesiu, and with Robert Fokkink.

Speaker: Henk Bruin (University of Vienna)

10:20 → 11:10 Mixing and ergodicity of non-autonomous circle dynamics

Thanks to the work of Aaronson, Doering and Mañé, Craizer, and many others, we know that the properties of an inner function and its dynamics in the unit disc are closely related to the dynamics of its boundary extension. If, however, we consider compositions of inner functions, i.e. non-autonomous dynamics in the unit disc, less is known about its relation to the corresponding non-autonomous dynamical system on the unit circle given by composing the boundary extensions. In this talk, we will tackle this problem from the point of view of ergodic theory. We will discuss necessary and sufficient conditions for mixing and ergodicity, construct examples and counterexamples, and present some consequences of ergodicity. This is joint work with Artur Nicolau (UAB).

Speaker: Gustavo Rodrigues Ferreira (Centre de Recerca Matemàtica)

11:10 → 11:40 coffee break

11:40 → 12:05 Short Talk: Reconstructing resonant phase oscillator interactions from noisy time series

Convener: Bengi Dönmez (Vrije Universiteit Amsterdam)

12:05 → 12:30 Revealing Dynamics, Communities, and Criticality from Data

Complex systems consist of interacting units connected through intricate networks. Predicting sudden changes in their dynamics is essential to mitigate the consequences of large-scale disruptions. This task is inherently challenging, as it requires forecasting behavior in parameter regimes where no data are available.
We address this problem for networks with chaotic local dynamics by reconstructing both the individual dynamics and a statistical description of their interactions directly from data. We show that the network behavior admits a decomposition into an emergent deterministic
component and a fluctuation term. While such fluctuations are traditionally treated as noise and filtered out, we demonstrate that they are in fact essential for uncovering the underlying interaction structure such as community structures. This enables the early prediction of synchronization transitions in networks with community structure, even when the system operates far from the transition regime.

Speaker: Tiago Pereira (Universidade de São Paulo)

12:30 → 13:00 TBA

Speaker: Jeroen Lamb (Imperial College London)