10:00 -11:00 Dmitry Turaev: Ergodic averaging for partially-integrable systems

Coffee break

11:30 – 12:00 Manuel Garzón: Low-energy dynamics in generic potential fields

12:00 – 12:30 Dmitry Mints: High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms

12:30 – 13:00 Cédric Oms: Dynamics on b-symplectic manifolds

Lunch break

15:00 – 16:00 Maria Przybylska: Integrability of a charged rigid body in a constant electromagnetic field

16:00 – 16:30 Pavel Korchagin: Staggered and unstaggered nonlinear modes for DNLS equation with competing nonlinearities

16:30 – 17:00 Dmitry Sinelshchikov: Metrisable oscillators and (super)integrable two-dimensional metrics

10:00 -11:00 Vladimir Dragović: Finite groups of random walks and periodic four-bar links

Coffee break

11:30 – 12:30 Marina Gonchenko: Reversible perturbations of degenerate resonances

12:30 – 13:00 Carlota Maria Cuesta Romero: Existence of undercompressive travelling waves of a non-local generalised Korteweg-de Vries-Burgers equation

Lunch break

15:00 – 16:00 Maira Aguiar: The Role of Homologous Reinfections in Complex Dengue Epidemic Dynamics

16:00 – 16:30 Miguel Aguilera: Spectral Control of the Memory Capacity in Associative Neural Networks Storing Dynamical Attractors

16:30 – 17:00 Ivan Garashchuk: Optimization methods for finding complex dynamicsin models with high number of parameters

17:00 – 17:30 Enrique C Gabrick: Complex dynamics in seasonal infectious diseases: chaos, multistability and crisis

20:00 Conference Dinner

10:00 -11:00 Juan Belmonte: Mathematical modeling of CAR-T Cell therapy: Dynamics, treatment scheduling and resistance across tumor contexts

Coffee break

11:30 – 12:30 Roberto Barrio: Dynamics in mean-field neural models: applications

12:30 – 13:00 Carter Hinsley: Kneading in flows

Lunch break

15:00 – 16:00 Daniele De Martino: Mathematical Modeling of Bacterial Metabolic Adaptation: Diauxie, Co-consumption, and Heterogeneity 

16:00 – 16:30 Thierry Tran: Dealing with Uncertainty In Food Fermentation Systems

16:30 – 17:00 Kepa Ruiz-Mirazo: Extending consumer-resource models to explore the evolution of proto-metabolic cell ecologies

17:00 – 17:30 Svana Rogalla Closing the gap: An elastic model recapitulates the kinetics of embryonic wound healing

18:00 - 19:00 Excursion to Bilbao

Dengue transmission is shaped by multiple viral serotypes, temporary cross-immunity (TCI), antibody-dependent enhancement (ADE), and repeated exposure in endemic populations. Classical multi-strain models usually assume lifelong protection against reinfection with the same serotype. However, recent evidence suggests that homologous dengue reinfections, although rare, can occur. Their population-level consequences remain poorly understood.

We extend a two-infection, two-strain dengue model with TCI and ADE-mediated transmission differences to include homologous reinfections. Homologous reinfection is represented by two parameters: relative susceptibility to reinfection with the same serotype and relative infectiousness during homologous reinfection. Using equilibrium analysis, bifurcation diagrams, simulations, and phase-space projections, we examine how these parameters affect dengue dynamics under intermediate and long TCI durations, with and without seasonality.

The results indicate that rare homologous reinfection pathways can influence long-term dengue dynamics when interacting with immune history, TCI, ADE-mediated transmission differences, and seasonal variation. Incorporating such pathways may improve understanding of recurrent outbreaks and irregular incidence patterns in highly exposed populations.

In this talk we study the dynamics of two recently introduced mean-field models representing the behavior of

heterogeneous all-to-all coupled quadratic integrate-and-fire neural networks.

Firstly we study the phenomena that when there are synaptic dynamics in the model, which allows a delay in synaptic transmission, it seems to reduce the emergence of

chaotic dynamics by increasing the synaptic time constant and maintains a phase-locked state in the form of bursting dynamics in the mean-field model. We examine in depth the different dynamical

behaviors that can be found in both mean-field models (spiking, bursting, and Rossler-like chaotic behaviors) and study in detail the bifurcations underlying their appearance and disappearance.

Moreover, we relate the disappearance of various behaviors with the recently introduced geometric bifurcations.

And secondly, we focus on the use of mean-field models in a theoretical study of tonic-clonic epileptic seizures. These are a particularly important class of epilepsy and have previously been theorised to arise in systems with an instability from one temporal rhythm to another via a quasi-periodic transition. We show that a recently introduced class of next generation neural field models has a sufficiently rich bifurcation structure to support such behaviour. 

Chimeric Antigen Receptor T-cell therapy has transformed the treatment of several hematological malignancies and is currently being explored for solid tumors, where major challenges remain. In this talk, I will present an overview of recent work on mathematical models for CAR-T cell therapy, with emphasis on how dynamical systems can help understand treatment response, resistance mechanisms, and therapy scheduling.

I will discuss three complementary modeling approaches. First, a model for malignant gliomas treated with CAR-T cells in combination with chemotherapy, where resistant tumor subpopulations, treatment timing, and in silico trials are used to explore therapeutic protocols. Second, a delay differential equation model for CAR-T therapy in glioblastoma, designed to capture the time required for immune activation and expansion. Third, a model for leukemia incorporating healthy B-cell influx, CAR-T persistence, oscillatory dynamics, and explicit treatment thresholds.

Together, these studies illustrate how mathematical oncology can provide mechanistic insight into CAR-T dynamics, identify key parameters controlling treatment outcome, and support the rational design of future therapeutic strategies.

We present our solutions to two long standing open problems, one from probability theory formulated by Malyshev

in 1970 and another one from a crossroad of geometry and dynamics, going back to Darboux in

1879. The Malyshev problem is of finding effective, explicit necessary and sufficient conditions in

the closed form to characterize all random walks in the quarter plane with a finite group of the

random walk of order 2n, for all n ≥ 2. We also describe all n-periodic Darboux transformations for 4-bar link problems

for all n ≥ 2, thus completely solving the Darboux problem, that he solved for n = 2.

This is based on a joint work with Milena Radnovic.

We study the dynamics of a charged rigid body with stationary charge distribution in external constant electric and magnetic fields. The total charge of the body vanishes and the charge distribution is described by symmetric matrix of the 'electrostatic inertia' of the body. The equations of motion are derived and it is shown that they are Hamiltonian with respect to a certain degenerated Poisson structure. Integrability of this system is analysed using Kovalevskaya method, the Ziglin theorem concerning the splitting of separatrices and the differential Galois theory. The non-integrability theorems under general assumptions and some integrable cases are presented.

Work in collaboration with Andrzej J. Maciejewski 

We introduce action variables for a class of partially integrable Hamiltonian systems and show that if a partially integrable system is ergodic on almost every common level of the integrals, then the actions are adiabatic invariants - they preserve with a good accuracy for a very long time when the parameters of the system change slowly. The reason is that the actions are integrals of the corresponding  averaged systems; interestingly, in the non-ergodic case, the averaged system may be non-integrable and display dynamics unrelated to the dynamics of the full slow-fast system.