Collective cell migration is a fundamental process driving essential biological phenomena, including tissue morphogenesis, wound healing, and cancer metastasis. A key driver of these coordinated movements is cellular heterogeneity—be it in size, adhesive properties, signaling, etc. 2D models fail to capture the full interaction between cells, and 3D models can be computationally prohibitive. Based on cellular sub-element modeling, we present a pseudo-3D model to understand the movement of cells in tight groups.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

I will talk about a model for a population that is structured in space and that diffuses heterogeneously. The model is based on a KPP equation with a “q-diffusion”, which is a framework that unifies various standard linear diffusion regimes: Fickian diffusion (q = 0), Stratonovich diffusion (q = 1/2), Fokker-Planck diffusion (q = 1). I will explore how the ability of persistence and how the asymptotic spreading speed depend on the parameter q and on the phase shift between the growth rate r(x) and the diffusion coefficient D(x). Those results demonstrate that persistence and spreading properties generally depend on q: for example, appropriate configurations of r(x) and D(x) can be constructed such that q-diffusion either enhances or diminishes the ability of persistence and the spreading speed with respect to the traditional Fickian diffusion. This work underscores the importance of carefully selecting diffusion models in ecological and epidemiological contexts, highlighting their potential implications for persistence, spreading, and control strategies. Joint work with Y.-J. Kim and L. Roques.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Grid cells, with their striking hexagonal firing patterns, are neurons which play a key role in the internal navigational system of mammals. This talk will concern a nonlocal Fokker- -Planck-type PDE which emerged in a pursuit to better understand the effects of noise on grid cell activity. When this model produces hexagonal neuronal network activity which persists when translated in accordance with the mammal's movement in physical space, the model is in a setting which enables the mammal's ability to orientate itself. But under which conditions could such activity emerge in the model?

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Pancreatic cancer is one of the deadliest cancers, and despite decades of research, treatments remain largely ineffective. To make progress, scientists must look beyond the cancer cells themselves and examine everything surrounding them. This work uses mathematical models as a virtual laboratory to study two hidden forces that shape how pancreatic cancer grows: the nerves that infiltrate the tumor and the progressive hardening of the surrounding tissue. Nerves are not passive bystanders; some slow tumor growth, while others accelerate it. Meanwhile, tissue stiffening acts as armor around the tumor, making it harder for treatments to penetrate and be effective. By building mathematical models of these interactions, this work helps explain why the same treatment can succeed in one patient and fail in another and opens the door to more personalized therapeutic strategies.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Many partial differential equations describe how a macroscopic density of particles/cells evolves in time. So, it is a natural question to ask whether there’s a microscopic (deterministic) model, which focuses on the interaction between each particles, that leads to a given macroscopic PDE. For second-order aggregation–diffusion equations, this connection has been proved, starting with the porous medium equation in 2001. In this work, we extend that framework to a fourth-order equation, that has applications in cell–cell adhesion in biological systems. This is a joint work with Alejandro Fernandez- Jimenez.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Many biological systems exhibit intermittent dynamics across a wide range of scales, where individuals alternate between distinct behavioral states over time, such as motion and rest, or directed and undirected movement. Examples include microswimmers such as bacteria, microalgae, and amoebae, as well as animal groups such as schools of fish and flocks of sheep. In this talk, I will present one unifying model to describe such systems. First, I will discuss the modeling of intermittent biased motion in microswimmers subjected to an external signal c(x). I will outline the minimal ingredients required for a model to reproduce directed motion of particles toward (or away from) the source of the signal. In the second part, I will focus on intermittent collective dynamics in animal groups, particularly small groups of sheep and large schools of fish. In both systems, transitions can occur between a collective stationary state and a collective moving state, despite the very different biological contexts involved. I will show how both scenarios can be described within a common theoretical framework based on active particles with discrete internal states. Finally, I will discuss the strengths and limitations of this approach, and explain why it provides a particularly effective description of these biological systems.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Population dynamics are often observed as distributions of individuals with respect to structuring variables such as size or age. The associated inverse problem consists of inferring the underlying vital rates (recruitment/birth, growth, and death) which are typically complex, nonparametric functions due to limited prior knowledge. Physics- Informed Neural Networks (PINNs) provide a natural framework for such problems by combining neural networks as universal function approximators with mechanistic constraints encoded in differential equations. In this talk, we showcase the ability of PINNs to solve inverse problems in the context of size-structured population dynamics governed by coupled PDE-ODE models, in two biological contexts: oocyte dynamics in fish ovaries and adipocyte dynamics in adipose tissue.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

In this talk, we study the long-time dynamics of two mesoscopic models for neuronal populations, with a particular focus on the role of synaptic delay and network connectivity. At this scale, the system is described by a probability density representing the distribution of neuronal states, such as the membrane potential or the time elapsed since the last discharge. More precisely, we analyze the behavior of the NNLIF (Nonlinear Noisy Leaky Integrate-and-Fire) model, formulated as a nonlinear Fokker--Planck type equation, and the age-structured model based on the time-since-last-discharge description. While entropy dissipation methods provide a natural analytical framework, they encounter significant limitations, especially in regimes of strong connectivity. We present alternative approaches based on two main ideas: first, the analysis of simplified discrete models, which provide fast and intuitive insight into the nonlinear dynamics; and second, a linearization around equilibrium combined with a reformulation of the problem as a Volterra-type integral equation. These techniques allow us to better understand the influence of delay and connectivity on the long-time behavior of the system. This talk is based on joint works with José A. Cañizo, Alejandro Ramos-Lora, and Nicolás Torres.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)