Dynamical Systems podcasts

Daniel Levenstein discusses spontaneous activity in the hippocampus and cortex, especially during sleep, and its relationship to learning, memory and navigation. He explains how AI models can help investigate these dynamics, alongside questions about model systems, cognitive maps and the relationship between neuroscience experiments and theory.

Hosted by Paul Middlebrooks

Holly Krieger discusses arithmetic dynamics: how repeatedly applying simple mathematical rules connects number theory with dynamical systems. The conversation explores the patterns and difficult questions that arise when numbers and iteration meet, providing an accessible route into an active area of mathematical research.

Ehud Ahissar explains active perception through closed loops linking movement and sensation, drawing on work with rodent whiskers. He introduces perceptual dualism as a proposed distinction between communication within the brain and interactions with the world, and explores its implications for consciousness and neural dynamics.

Hosted by Paul Middlebrooks

Liset de la Prida discusses hippocampal sharp-wave ripples and their relationship to replay and memory. The conversation connects different ripple patterns and neuron types to population activity, asking how particular cells help shape the lower-dimensional dynamics used to describe neural computation.

Hosted by Paul Middlebrooks

Tilo Schwalger discusses population-level descriptions of neural dynamics and how mean-field models can be derived from underlying network mechanisms.

Nicolas Brunel discusses excitation-inhibition balance and mathematical explanations of irregular activity in cortical networks.

Codina Cotar discusses mathematical patterns associated with stochastic systems and anomalous diffusion, using entries in a science-and-art competition to explain the ideas. The conversation connects diffusion with familiar materials, quantum phenomena, movement and visual art, and examines how mathematical models inspire creative interpretations of nature.

Michael Breakspear and Mac Shine examine how neural dynamics change from individual cells to whole-brain systems. Their work connects gain modulation with the balance between integration and segregation, relates it to arousal pathways, and uses coarse-graining to investigate both scale-dependent coding and shared dynamical properties across neural populations.

Hosted by Paul Middlebrooks

Woodrow Shew and Keith Hengen assess whether critical dynamics form a homeostatic target for brain activity. They discuss proposed signatures and testable predictions, controversies in earlier studies, and possible relationships among criticality, sleep and neural manifolds, drawing on their review of the experimental literature.

Hosted by Paul Middlebrooks

Xiao-Jing Wang surveys theoretical neuroscience through models of cognition, working memory and decision-making. The discussion connects his textbook with the field’s history and current research, including inhibitory-cell diversity, large-scale cortical dynamics and an explanatory approach that links mechanisms across levels rather than treating them separately.

Hosted by Paul Middlebrooks

John Beggs reviews the critical-brain hypothesis and the proposal that neural activity operates near a transition between ordered and chaotic regimes. He discusses information processing, dynamic range, measurement methods, experimental evidence, criticisms and the question of whether criticality is a distinctive computational property of brains or part of a broader natural phenomenon.

Hosted by Paul Middlebrooks

Giovanni Forni discusses mathematical billiards as a tractable setting for studying dynamical systems. The conversation explores the tension between periodic motion and chaos, why seemingly elementary billiard trajectories lead to difficult questions, and which aspects remain unresolved. The interview was recorded at the European Congress of Mathematics.

Henrik Lindén discusses spinal circuits that generate rhythmic movement and the models used to understand their activity.

Eric Shea-Brown joins Paul Middlebrooks to examine what dynamical systems and dimensionality reveal about neural computation. They compare task-related activity with less constrained behaviour, consider how network connection motifs shape collective dynamics, and discuss high-dimensional activity embedded within lower-dimensional descriptions. Research examples connect predictive learning, latent representations and rich versus lazy learning regimes. The conversation also examines how theoretical neuroscientists choose useful abstractions and which assumptions about network structure and function deserve closer scrutiny.

Hosted by Paul Middlebrooks

Andrea Martin develops an account of language that combines compositional structure with physiological constraints from human brains. She discusses neural dynamics and low-dimensional manifolds as a way to connect statistical regularities with formal organization, and considers how this approach relates to the capabilities and limitations of large language models.

Hosted by Paul Middlebrooks

Earl K. Miller explores thoughts as emergent properties of prefrontal neural dynamics. The conversation covers spatial computing, working-memory capacity, oscillations, travelling waves, subspaces and silent synapses, relating changes in his scientific thinking to broader questions about the self and the limits of reductionist explanations.

Hosted by Paul Middlebrooks

Carina Curto discusses topology and mathematically tractable models of neural networks. The conversation connects population-level neural geometry with combinatorial linear-threshold networks, examining how graph structure constrains dynamics, how motifs retain properties inside larger systems, and why simpler models may help reveal principles obscured in large neural simulations.

Hosted by Paul Middlebrooks