Schedule
Select a title to view details.
Sunday, 20 IX
13:30 - 15:30
Check-in
15:30 - 16:00
Pizza time
16:00 - 18:00
Check-in
Monday, 21 IX
8:30 - 9:15
Breakfast
9:15 - 9:30
Opening ceremony
9:30 - 11:00
Computer assisted proofs for billiard maps (1/3)
⌄
9:30 - 11:00
Computer assisted proofs for billiard maps (1/3)
Name: Jason Mireles James
Abstract: The main topic of these lectures will be validated, high order computations of invariant manifolds for dynamical systems, and applications of these expansions. Of particular interest are dynamical systems where the equations of motion are given only implicitly. In order to have a concrete example which illustrates many of the difficulties, I will focus on stable/unstable manifolds attached to periodic orbits for billiard maps. Billiards are interesting because, while the definition of the system is physically meaningful and intuitive, the map is defined by an implicit procedure rather than an explicit formula. For such a system, it is challenging to derive series expansions of dynamically meaningful objects like invariant manifolds.
I will talk about a method for computing Fourier/Taylor/Chebyshev series expansions which exploits the discrete Fourier transform. This method works very well for numerical computations with implicitly defined maps, but introduces several layers of error (round off, truncation, and interpolation/aliasing) all of which have to be managed for a rigorous computation in a computer assisted proof. Managing these requires some nice harmonic and complex analysis, which is easiest to explain for the case of Taylor series and for planar maps like the Billiards.
As an application of the validated computations explored above, I'll show how to computer stable/unstable manifolds using the parameterization method and prove the existence of transverse heteroclinic/homoclinic connections between periodic orbits.
11:00 - 11:30
Coffee break
11:30 - 13:00
Numerical and validation of KAM tori (1/3)
⌄
11:30 - 13:00
Numerical and validation of KAM tori (1/3)
Name: Jordi Figueras
Abstract: In this course, we will study how invariant quasiperiodic tori of Hamiltonian systems and symplectic maps can be computed numerically and subsequently validated by a rigorous computer-assisted proof.
We will begin with the parameterization method, in which an invariant torus is described as an embedding satisfying a functional invariance equation. This formulation leads naturally to efficient Newton and quasi-Newton algorithms based on Fourier representations. We will discuss the role of the rotation vector, the small-divisor problem, automatic reducibility, and the practical numerical implementation of these algorithms.
The second part of the course will introduce the a posteriori approach to KAM theory. Rather than constructing a torus from an integrable approximation, an a posteriori KAM theorem starts from an approximate numerical solution and proves the existence of a true invariant torus nearby, provided that its invariance error is sufficiently small and suitable nondegeneracy and Diophantine conditions hold.
Finally, we will explain how interval arithmetic and rigorous estimates can be combined with numerical computations to verify these hypotheses on a computer. We will illustrate the complete path from a numerical approximation to a mathematically rigorous existence proof. The course will emphasize both the underlying mathematical ideas and the computational techniques needed to turn KAM theory into an effective tool.
13:00 - 14:00
Lunch
14:00 - 15:30
Numerical and validation of KAM tori (2/3)
⌄
14:00 - 15:30
Numerical and validation of KAM tori (2/3)
Name: Jordi Figueras
Abstract: In this course, we will study how invariant quasiperiodic tori of Hamiltonian systems and symplectic maps can be computed numerically and subsequently validated by a rigorous computer-assisted proof.
We will begin with the parameterization method, in which an invariant torus is described as an embedding satisfying a functional invariance equation. This formulation leads naturally to efficient Newton and quasi-Newton algorithms based on Fourier representations. We will discuss the role of the rotation vector, the small-divisor problem, automatic reducibility, and the practical numerical implementation of these algorithms.
The second part of the course will introduce the a posteriori approach to KAM theory. Rather than constructing a torus from an integrable approximation, an a posteriori KAM theorem starts from an approximate numerical solution and proves the existence of a true invariant torus nearby, provided that its invariance error is sufficiently small and suitable nondegeneracy and Diophantine conditions hold.
Finally, we will explain how interval arithmetic and rigorous estimates can be combined with numerical computations to verify these hypotheses on a computer. We will illustrate the complete path from a numerical approximation to a mathematically rigorous existence proof. The course will emphasize both the underlying mathematical ideas and the computational techniques needed to turn KAM theory into an effective tool.
15:30 - 16:00
Coffee break
16:00 - 16:30
Computer-assisted proof of non-transverse
homoclinic orbits in reversible systems
⌄
16:00 - 16:30
Computer-assisted proof of non-transverse
homoclinic orbits in reversible systems
Name: Jakub Czwórnóg
Affiliation: AGH University of Krakow
Abstract: Homoclinic orbits of equilibrium points and periodic solutions arise when their unstable and stable manifolds intersect. When these manifolds meet non-transversally, verifying the existence of such orbits becomes particularly challenging. In this talk, I will present a methodology for proving the existence of non-transverse homoclinic orbits to non-hyperbolic periodic orbits in reversible systems. The approach consists of representing periodic orbits as fixed points of a certain Poincaré map and applying cone conditions to establish bounds on strong unstable manifolds. I will present results of applying this methodology to vertical Lyapunov orbits in the Circular Restricted Three-Body Problem (CR3BP).
16:30 - 17:00
Symbolic dynamics in a pseudospectral
projection of the Cubic Ikeda Equation
⌄
16:30 - 17:00
Symbolic dynamics in a pseudospectral
projection of the Cubic Ikeda Equation
Name: Darina Serogina
Affiliation: Jagiellonian University
Abstract: There exist methods of rigorous computations for general systems of delayed differential equations (DDEs), however they cannot yet be used for proving more complicated kinds of dynamical phenomena, like chaos. Our approach is to approximate a DDE by an easier model and try to prove chaos there instead, with the hope of eventually recreating the result for the original equation. To do this, we use a pseudospectral projection, a technique that approximates a DDE by a finite-dimensional system of ordinary differential equations (ODEs), making it accessible to computer-assisted proof methods developed for ODEs. We apply this approach to the Cubic Ikeda Equation. After the projection, we use the method of covering relations for a particular Poincare map to rigorously prove the existence of a periodic orbit in the resulting ODE system. This orbit, together with a chain of coverings following a numerically approximated homoclinic connection to it, forms a set of coverings that prove existence of symbolic dynamics in the approximating ODE (chaos).
17:00 - 17:30
The Shadowing Lemma
⌄
17:00 - 17:30
The Shadowing Lemma
Name: Miłosz Zajdel
Affiliation: Jagiellonian University
Abstract: Computer-generated trajectories inevitably accumulate rounding and truncation errors, causing them to generally diverge exponentially from exact trajectories. The Shadowing Lemma tells us that near hyperbolic invariant sets, pseudo-trajectories are close to exact trajectories even in the presence of chaos. In this talk I introduce the concepts needed to state the lemma (hyperbolicity, pseudo-orbits, shadowing), present several examples of shadowing and a variant of the lemma regarding periodic orbits. I then use this variant to prove, with the help of a computer, the existence of a set on which the Hénon map is chaotic.
18:00 - ∞
Integration
Board, card, group games
Tuesday, 22 IX
8:30 - 9:30
Breakfast
9:30 - 11:00
Numerical and validation of KAM tori (3/3)
⌄
9:30 - 11:00
Numerical and validation of KAM tori (3/3)
Name: Jordi Figueras
Abstract: In this course, we will study how invariant quasiperiodic tori of Hamiltonian systems and symplectic maps can be computed numerically and subsequently validated by a rigorous computer-assisted proof.
We will begin with the parameterization method, in which an invariant torus is described as an embedding satisfying a functional invariance equation. This formulation leads naturally to efficient Newton and quasi-Newton algorithms based on Fourier representations. We will discuss the role of the rotation vector, the small-divisor problem, automatic reducibility, and the practical numerical implementation of these algorithms.
The second part of the course will introduce the a posteriori approach to KAM theory. Rather than constructing a torus from an integrable approximation, an a posteriori KAM theorem starts from an approximate numerical solution and proves the existence of a true invariant torus nearby, provided that its invariance error is sufficiently small and suitable nondegeneracy and Diophantine conditions hold.
Finally, we will explain how interval arithmetic and rigorous estimates can be combined with numerical computations to verify these hypotheses on a computer. We will illustrate the complete path from a numerical approximation to a mathematically rigorous existence proof. The course will emphasize both the underlying mathematical ideas and the computational techniques needed to turn KAM theory into an effective tool.
11:00 - 11:30
Coffee break
11:30 - 13:00
From Topological Discs to Arnold Diffusion and Blenders (1/3)
⌄
11:30 - 13:00
From Topological Discs to Arnold Diffusion and Blenders (1/3)
Name: Maciej Capiński
Abstract: In this course we will develop a geometric method based on the propagation of topological discs and cone conditions. The method provides a flexible framework for establishing the existence and properties of invariant manifolds and invariant sets, as well as for proving chaotic and symbolic dynamics.
When applied to Hamiltonian systems, these techniques can be used to construct mechanisms leading to Arnold diffusion, namely large changes in the action or energy resulting from arbitrarily small perturbations. The same geometric ideas also provide a powerful way of proving the existence of blenders, hyperbolic invariant sets whose invariant manifolds exhibit dynamical properties characteristic of higher-dimensional manifolds. The presence of blenders can lead to rich and sometimes surprising dynamical behaviour.
Throughout the course we will develop these ideas and illustrate them with applications to celestial mechanics, including computer-assisted proofs.
13:00 - 14:00
Lunch
14:00 - 15:30
Computer assisted proofs for billiard maps (2/3)
⌄
14:00 - 15:30
Computer assisted proofs for billiard maps (2/3)
Name: Jason Mireles James
Abstract: The main topic of these lectures will be validated, high order computations of invariant manifolds for dynamical systems, and applications of these expansions. Of particular interest are dynamical systems where the equations of motion are given only implicitly. In order to have a concrete example which illustrates many of the difficulties, I will focus on stable/unstable manifolds attached to periodic orbits for billiard maps. Billiards are interesting because, while the definition of the system is physically meaningful and intuitive, the map is defined by an implicit procedure rather than an explicit formula. For such a system, it is challenging to derive series expansions of dynamically meaningful objects like invariant manifolds.
I will talk about a method for computing Fourier/Taylor/Chebyshev series expansions which exploits the discrete Fourier transform. This method works very well for numerical computations with implicitly defined maps, but introduces several layers of error (round off, truncation, and interpolation/aliasing) all of which have to be managed for a rigorous computation in a computer assisted proof. Managing these requires some nice harmonic and complex analysis, which is easiest to explain for the case of Taylor series and for planar maps like the Billiards.
As an application of the validated computations explored above, I'll show how to computer stable/unstable manifolds using the parameterization method and prove the existence of transverse heteroclinic/homoclinic connections between periodic orbits.
15:30 - 16:00
Coffee break
16:00 - 17:30
Computer assisted proofs for billiard maps (3/3)
⌄
16:00 - 17:30
Computer assisted proofs for billiard maps (3/3)
Name: Jason Mireles James
Abstract: The main topic of these lectures will be validated, high order computations of invariant manifolds for dynamical systems, and applications of these expansions. Of particular interest are dynamical systems where the equations of motion are given only implicitly. In order to have a concrete example which illustrates many of the difficulties, I will focus on stable/unstable manifolds attached to periodic orbits for billiard maps. Billiards are interesting because, while the definition of the system is physically meaningful and intuitive, the map is defined by an implicit procedure rather than an explicit formula. For such a system, it is challenging to derive series expansions of dynamically meaningful objects like invariant manifolds.
I will talk about a method for computing Fourier/Taylor/Chebyshev series expansions which exploits the discrete Fourier transform. This method works very well for numerical computations with implicitly defined maps, but introduces several layers of error (round off, truncation, and interpolation/aliasing) all of which have to be managed for a rigorous computation in a computer assisted proof. Managing these requires some nice harmonic and complex analysis, which is easiest to explain for the case of Taylor series and for planar maps like the Billiards.
As an application of the validated computations explored above, I'll show how to computer stable/unstable manifolds using the parameterization method and prove the existence of transverse heteroclinic/homoclinic connections between periodic orbits.
18:00 - ∞
Sightseeing
Wednesday, 23 IX
8:30 - 9:30
Breakfast
9:30 - 11:00
Computer assisted proofs of periodic orbits based on Fourier analysis (1/3)
⌄
9:30 - 11:00
Computer assisted proofs of periodic orbits based on Fourier analysis (1/3)
Name: Jan Bouwe van den Berg
Abstract: In this lecture series, we explore the construction of computer-assisted proofs (CAPs) for periodic solutions of ordinary differential equations, delay-differential equations, and partial differential equations. Our approach is based on a Newton–Kantorovich argument formulated in an infinite-dimensional Banach space of Fourier series. This framework allows us to prove that a numerically computed approximate solution of a finite-dimensional projection indeed corresponds to an actual (nearby) solution of the full differential equation.
11:00 - 11:30
Coffee break
11:30 - 13:00
From Topological Discs to Arnold Diffusion and Blenders (2/3)
⌄
11:30 - 13:00
From Topological Discs to Arnold Diffusion and Blenders (2/3)
Name: Maciej Capiński
Abstract: In this course we will develop a geometric method based on the propagation of topological discs and cone conditions. The method provides a flexible framework for establishing the existence and properties of invariant manifolds and invariant sets, as well as for proving chaotic and symbolic dynamics.
When applied to Hamiltonian systems, these techniques can be used to construct mechanisms leading to Arnold diffusion, namely large changes in the action or energy resulting from arbitrarily small perturbations. The same geometric ideas also provide a powerful way of proving the existence of blenders, hyperbolic invariant sets whose invariant manifolds exhibit dynamical properties characteristic of higher-dimensional manifolds. The presence of blenders can lead to rich and sometimes surprising dynamical behaviour.
Throughout the course we will develop these ideas and illustrate them with applications to celestial mechanics, including computer-assisted proofs.
13:00 - 14:00
Lunch
14:00 - 15:30
From Topological Discs to Arnold Diffusion and Blenders (3/3)
⌄
14:00 - 15:30
From Topological Discs to Arnold Diffusion and Blenders (3/3)
Name: Maciej Capiński
Abstract: In this course we will develop a geometric method based on the propagation of topological discs and cone conditions. The method provides a flexible framework for establishing the existence and properties of invariant manifolds and invariant sets, as well as for proving chaotic and symbolic dynamics.
When applied to Hamiltonian systems, these techniques can be used to construct mechanisms leading to Arnold diffusion, namely large changes in the action or energy resulting from arbitrarily small perturbations. The same geometric ideas also provide a powerful way of proving the existence of blenders, hyperbolic invariant sets whose invariant manifolds exhibit dynamical properties characteristic of higher-dimensional manifolds. The presence of blenders can lead to rich and sometimes surprising dynamical behaviour.
Throughout the course we will develop these ideas and illustrate them with applications to celestial mechanics, including computer-assisted proofs.
15:30 - 16:00
Coffee break
16:00 - 16:30
Non-archimedean dynamics
⌄
16:00 - 16:30
Non-archimedean dynamics
Name: Radosław Zając
Affiliation: Jagiellonian University
Abstract: At the very beginning we will remind what non-archimedean fields are, with its primary example - p-adic numbers. Next we will build the dynamical structure on it and start exploring it: We will look at the analytic and non-analytic functions with some interesting results. Thereafter we will delve into dynamic systems in the fields of p-adic ($\mathbb{Q_p}$) and copmlex p-adic ($\mathbb{C_p}$) numebers, ending with the p-adic ergodicity. During the last part of this talk we will see some computational examples of this introduced theory.
16:30 - 17:00
KAM for periodic orbits
⌄
16:30 - 17:00
KAM for periodic orbits
Name: Laura Cara Sala
Affiliation: Universitat de Barcelona
Abstract: To analyze periodic orbits and their behavior, the classical approach is Floquet theory, which leads to linearization of the system around the periodic orbit to reduce the study of local stability to a linear system with periodic coefficients. Using Moore's approach to Floquet theory for the study of periodic orbits, in my master's thesis, we develop a theoretical framework for the convergence of Newton's method in a system with a periodic orbit, proving its existence with an explicitly computed error. We adapt the analytical techniques of KAM theory with a small KAM iterative scheme in the sense of a loss of part of the analytic domain while finding the periodic orbit. As a main result, we present a convergence theorem for proving the existence of periodic orbits when the initial error is small enough. This setup can be applied to computer-assisted proofs for the existence of periodic orbits.
17:00 - 17:30
Heat Flow of Polynomials and Auxiliary
Functions
⌄
17:00 - 17:30
Heat Flow of Polynomials and Auxiliary
Functions
Name: Thomas Neil Glover
Affiliation: University of Bristol School of Maths
Abstract: Evolving a polynomial P via the heat equation ($\partial_t-\frac{1}{2}\partial_z^2=0)$ is known to produce interesting dynamical behaviour in the zeros similar to Dyson Brownian Motion, we look at the behaviour of these zeros over a short time scale and explore potential applications to the method of auxiliary functions in Diophantine Approximation.
18:00 - ∞
Bowling
Thursday, 24 IX
8:30 - 9:30
Breakfast
9:30 - 11:00
Rotation theory on the torus (1/3)
⌄
9:30 - 11:00
Rotation theory on the torus (1/3)
Name: Pierre Antoine Guiheneuf
Abstract: Let us consider an orbit of a homeomorphism of the torus $\mathbb{S}^1 \times \mathbb{S}^1$ and observe, asymptotically, how many turns it makes in each circle per time unit. The set of all these asymptotic velocities (which are points in the plane) for all possible orbits is called the rotation set of the homeomorphism. It is a dynamical invariant that reveals a bunch of interesting properties of the homeomorphism: periodic points, entropy… I shall try to explain some of the proofs for these.
11:00 - 11:30
Coffee break
11:30 - 13:00
Computer assisted proofs of periodic orbits based on Fourier analysis (2/3)
⌄
11:30 - 13:00
Computer assisted proofs of periodic orbits based on Fourier analysis (2/3)
Name: Jan Bouwe van den Berg
Abstract: In this lecture series, we explore the construction of computer-assisted proofs (CAPs) for periodic solutions of ordinary differential equations, delay-differential equations, and partial differential equations. Our approach is based on a Newton–Kantorovich argument formulated in an infinite-dimensional Banach space of Fourier series. This framework allows us to prove that a numerically computed approximate solution of a finite-dimensional projection indeed corresponds to an actual (nearby) solution of the full differential equation.
13:00 - 14:00
Lunch
14:00 - 15:30
Computer assisted proofs of periodic orbits based on Fourier analysis (3/3)
⌄
14:00 - 15:30
Computer assisted proofs of periodic orbits based on Fourier analysis (3/3)
Name: Jan Bouwe van den Berg
Abstract: In this lecture series, we explore the construction of computer-assisted proofs (CAPs) for periodic solutions of ordinary differential equations, delay-differential equations, and partial differential equations. Our approach is based on a Newton–Kantorovich argument formulated in an infinite-dimensional Banach space of Fourier series. This framework allows us to prove that a numerically computed approximate solution of a finite-dimensional projection indeed corresponds to an actual (nearby) solution of the full differential equation.
15:30 - 16:30
Coffee break with poster session
16:30 - 17:00
Topological Invariants and Attractor Dynamics in High-Dimensional Multi-Omic Cancer Systems
⌄
16:30 - 17:00
Topological Invariants and Attractor Dynamics in High-Dimensional Multi-Omic Cancer Systems
Name: Zuzanna Kowalczyk
Abstract: Complex biological networks can be represented as high-dimensional dynamical systems where distinct phenotypic states correspond to competing attractors. In this work, we analyze high-dimensional multi-omic cancer profiles by reconstructing geometric invariants of the underlying state space. To address the high dimensionality of the data, we combine network-informed coordinate selection with Topological Data Analysis (TDA). Using Vietoris-Rips filtrations, we compute persistent homology ($H_0, H_1$) to extract stable signatures, such as persistence landscapes and Betti curves. We demonstrate that these topological invariants capture changes in phase space connectivity and cyclic structures across different cancer subtypes. The presented framework offers a solid approach for characterizing attractor geometry and transitions in biological dynamical systems.
17:00 - 17:30
Vidale-Wolfe advertising model
⌄
17:00 - 17:30
Vidale-Wolfe advertising model
Name: Anastasiia Kabaliants
Abstract: This talk is devoted to the study of the Vidale-Wolfe advertising model. Research in this area is of great importance for modern marketing: according to Statista, global advertising expenditure reached almost USD 832 billion in 2025 and increased by five percent compared to the previous year. These figures highlight the growing need for mathematical optimization methods. The model represents the relationship between sales and advertising by formulating a linear initial value problem, which can be solved analytically. By adding economically meaningful constraints on the control, we apply Pontryagin’s Maximum Principle to determine the optimal control for the model. We show that the optimal control has a bang-bang form: the maximum advertising level is applied first, followed by no advertising. Thus, we determine the optimal advertising policy and estimate the time required to achieve a desired sales level. The results demonstrate the applicability of optimal control theory to advertising models and may be useful for improving decision-making in marketing.
18:00 - ∞
Campfire
Friday, 25 IX
8:30 - 9:30
Breakfast
9:30 - 11:00
Universality of subshifts of finite type for groups. (1/3)
⌄
9:30 - 11:00
Universality of subshifts of finite type for groups. (1/3)
Name: Sebastian Barbieri Lemp
Abstract: I will explore the question of what kind of dynamical systems can be obtained as topological factors of subshifts of finite type (SFTs) on a given group. We will show that if we restrict to zero-dimensional factors, then necessarily there are computational constraints on this class. Furthermore, we will show that if the group is rich enough, then every computable action can be obtained as a factor of an SFT. I will provide an overview of the classes of groups where this property holds, and those where we know it fails. We shall use this to provide two interesting characterizations of the (still open) amenability of Thompson's group F.
These talks will include a brief and gentle introduction to computability theory.
11:00 - 11:30
Coffee break
11:30 - 13:00
Rotation theory on the torus (2/3)
⌄
11:30 - 13:00
Rotation theory on the torus (2/3)
Name: Pierre Antoine Guiheneuf
Abstract: Let us consider an orbit of a homeomorphism of the torus $\mathbb{S}^1 \times \mathbb{S}^1$ and observe, asymptotically, how many turns it makes in each circle per time unit. The set of all these asymptotic velocities (which are points in the plane) for all possible orbits is called the rotation set of the homeomorphism. It is a dynamical invariant that reveals a bunch of interesting properties of the homeomorphism: periodic points, entropy… I shall try to explain some of the proofs for these.
13:00 - 14:00
Lunch
14:00 - 15:30
Rotation theory on the torus (3/3)
⌄
14:00 - 15:30
Rotation theory on the torus (3/3)
Name: Pierre Antoine Guiheneuf
Abstract: Let us consider an orbit of a homeomorphism of the torus $\mathbb{S}^1 \times \mathbb{S}^1$ and observe, asymptotically, how many turns it makes in each circle per time unit. The set of all these asymptotic velocities (which are points in the plane) for all possible orbits is called the rotation set of the homeomorphism. It is a dynamical invariant that reveals a bunch of interesting properties of the homeomorphism: periodic points, entropy… I shall try to explain some of the proofs for these.
15:30 - 16:00
Coffee break
16:00 - 16:30
Rank One Automorphisms in Borel Dynamics
⌄
16:00 - 16:30
Rank One Automorphisms in Borel Dynamics
Name: Andrew Barsky
Affiliation: Jagiellonian University
Abstract: The class of rank one automorphisms of a measure space has been extensively studied since the 1970s. They have been recently classified up to isomorphism. They have also been studied in other contexts such as symbolic dynamics and infinite ergodic theory. We introduce the notion of a rank one automorphism in the context of Borel dynamics. We show that these automorphisms arise naturally in the theory of Bratteli diagrams as extensions from odometers. This talk is based on joint work with Sergii Bezuglyi (University of Iowa).
16:30 - 17:00
Lifts of strictly ergodic subshifts by permutative sliding block codes
⌄
16:30 - 17:00
Lifts of strictly ergodic subshifts by permutative sliding block codes
Name: Zeyu Kang
Affiliation: Uni Jena
Abstract: Permutative sliding block codes — in the sense of Hedlund — give rise to finite-to-one extensions of subshifts. We provide criteria under which minimality and unique ergodicity are preserved by this lifting procedure and illustrate the findings by means of some natural example families. As a specific example, we consider the sliding block code which maps the Thue–Morse subshift to the period-doubling subshift and show that it also lifts the Fibonacci subshift to a strictly ergodic system, which is a two-to-one extension of Fibonacci. Further examples of minimal lifts include the Tribonacci, silver mean, noble means substitutions. Moreover, Toeplitz subshifts can be used to demonstrate certain interesting phenomena, such as the existence of lifts of strictly ergodic subshifts which are minimal but fail to be uniquely ergodic.
17:00 - 17:30
Weyl connections and Anosov-like geodesic
flows
⌄
17:00 - 17:30
Weyl connections and Anosov-like geodesic
flows
Name: Tomasz Dudek
Affiliation: Jagiellonian University
Abstract: Let M be a smooth, compact Riemannian manifold without boundary, equipped with its Levi-Civita connection. It is known that if all sectional curvatures are negative, then the geodesic flow on the unit tangent bundle is Anosov: its tangent bundle splits into stable, unstable and flow directions. A Weyl connection can be viewed as a conformal analogue of the Levi-Civita connection. It is a torsion-free connection preserving a conformal structure, that is, an equivalence class of Riemannian metrics. For such connections one can introduce an analogue of sectional curvature. It has been shown by Wojtkowski that non-positive Weyl sectional curvature leads to certain Anosov-like properties of the corresponding geodesic flow. The goal of this talk is to compare the Riemannian and conformal settings, present Wojtkowski's result, and analyse the existence of invariant Weyl connections with non-positive sectional curvature on Lie groups, based on results of Wojtkowski and on my own work.
18:00 - ∞
Bar integration
Saturday, 26 IX
9:00 - 9:30
Breakfast
9:30 - 11:00
Universality of subshifts of finite type for groups. (2/3)
⌄
9:30 - 11:00
Universality of subshifts of finite type for groups. (2/3)
Name: Sebastian Barbieri Lemp
Abstract: I will explore the question of what kind of dynamical systems can be obtained as topological factors of subshifts of finite type (SFTs) on a given group. We will show that if we restrict to zero-dimensional factors, then necessarily there are computational constraints on this class. Furthermore, we will show that if the group is rich enough, then every computable action can be obtained as a factor of an SFT. I will provide an overview of the classes of groups where this property holds, and those where we know it fails. We shall use this to provide two interesting characterizations of the (still open) amenability of Thompson's group F.
These talks will include a brief and gentle introduction to computability theory.
11:00 - 11:30
Coffee break
11:30 - 13:00
Universality of subshifts of finite type for groups. (3/3)
⌄
11:30 - 13:00
Universality of subshifts of finite type for groups. (3/3)
Name: Sebastian Barbieri Lemp
Abstract: I will explore the question of what kind of dynamical systems can be obtained as topological factors of subshifts of finite type (SFTs) on a given group. We will show that if we restrict to zero-dimensional factors, then necessarily there are computational constraints on this class. Furthermore, we will show that if the group is rich enough, then every computable action can be obtained as a factor of an SFT. I will provide an overview of the classes of groups where this property holds, and those where we know it fails. We shall use this to provide two interesting characterizations of the (still open) amenability of Thompson's group F.
These talks will include a brief and gentle introduction to computability theory.
13:00 - 13:30
Closing ceremony
13:30 - 14:30