Seminars

Galaxy images and spectra map large-scale cosmic structure and constrain fundamental physics. While galaxy-clustering bias models are well developed, forthcoming datasets can also trace the intergalactic medium and recover complementary cosmic-web information. Jamie Sullivan discusses models for both neutral and ionized intergalactic material. Neutral-hydrogen work includes the environments of Lyman-alpha emitters at redshifts 2.5–5, relevant to future DESI extensions and Spec-S5, together with the measured Lyman-alpha forest and an observationally practical compression of its bispectrum. Ionized-gas research studies momentum through an effective-field-theory kinetic Sunyaev–Zel’dovich bispectrum, and density through fast-radio-burst clustering and cross-correlations. Together, these approaches aim to map intergalactic modes alongside galaxy tracers and improve precision cosmological constraints.

This seminar investigates Anderson localization in subwavelength elastic periodic systems with random perturbations. For the unperturbed structure, layer-potential methods recast the eigenvalue problem as boundary integral equations, yielding asymptotic expressions for subwavelength eigenvalues and establishing a band gap above the subwavelength band. A Floquet transform then brings the perturbed problem into a periodic formulation and produces equations for resonant frequencies under general perturbations. Numerical experiments on monomer and dimer structures test agreement with the analysis. Increasing the strength and number of random perturbations demonstrates localization, providing a mathematical basis for elastic metamaterial design.

How do humans stabilize an inverted pendulum, and why does a balanced pole eventually fall? Drawing on 25 years of fingertip pole-balancing research, this talk examines neural correction delays: longer poles move more slowly relative to the nervous system’s response time. Delay-differential models can stabilize the upright position, yet skilled people still experience falls. The proposed explanation is microchaos arising from interactions among delay, sensory dead zones and frequency-dependent force encoding. A region of transient falling solutions lies next to stable microchaotic dynamics. Such microchaos is absent in virtual frontal-plane balancing tasks, while models of standing postural sway lack the corresponding transient regime. The comparison suggests that human falls, unlike pole falls, are more plausibly associated with medical events or slips and trips.

To orchestrate complex behaviors in mammals, the cerebral cortex must continuously transmit its processing results to subcortical regions. While internal cortical processing relies on highly selective sparse codes, these descending cortical output streams employ an enigmatic dense code, characterized by high firing rates and low feature selectivity. This dense population code presents a profound paradox: how can downstream regions extract precise, cognitively relevant signals when most cortical output neurons can be active at any moment? We address this paradox by testing the hypothesis that cortex does not lose information when switching to a dense code. Instead, it utilizes a mechanism for sparse-to-dense coding transformations discovered by my laboratory: thalamocortical synapses target specifically the dendritic initiation zone for calcium action potentials (APs), which enables cortical output neurons to transmit multiple information streams simultaneously via a multiplexed 1-2-3 AP syntax. I will provide first evidence that this remarkable synaptic specificity and coding syntax generalize across long-range pathways. Information coupling via an anatomically and biophysically distinct dendritic nexus may hence be a ubiquitous mechanism for sparse-to-dense coding transformations in cortex. Dissecting these mechanistic origins of cortical output streams is only now possible due to a unique in vivo – in silico approach, perfected over two decades, that my laboratory developed for bridging the gaps between dendritic and population-level computations

Lenka Zdeborová introduces the Rules-and-Facts model, in which some observations follow a shared rule while others are isolated exceptions requiring memorization. The framework studies when a learner can acquire the rule and retain those exceptions simultaneously. Its results emphasize how capacity is organized and deployed, rather than capacity alone. The talk examines how regularization and the geometry of kernels or learned feature maps can reserve resources for memorization without undermining rule learning. It connects the balance between abstraction and memory to architectural and algorithmic choices, providing a theoretical account of neural networks that both generalize and recall specific facts.

Mark Harnett presents work on how synaptic organization, nonlinear dendritic processing, and neuronal activity patterns interact to support computation, flexibility, and learning in the adult mammalian neocortex. The Brain and Cognitive Sciences colloquium is followed by a reception.

Leonid Berlyand discusses mathematical models for the onset of cell motion driven by myosin contraction. A two-dimensional free-boundary PDE model links cell-shape evolution to diffusion and Keller–Segel-type transport. The talk examines linear stability, a stability-determining eigenvalue and the way nonlinear diffusion changes the bifurcation from supercritical to subcritical. It also considers the curvature of the bifurcation curve, connections to bistability, and the role of non-self-adjoint operators. An example illustrates why a spectral gap alone need not guarantee stability. This is an in-person Analysis of Fluids and Related Topics seminar at Princeton.

Rani Borbara presents brain-wide recordings from more than 150 freely moving C. elegans to examine how anatomical connectivity becomes functional organization during behavior. Cross-animal models map cell-class conditional dependencies and test how synapses, gap junctions, neuromodulation and shared brain states shape circuit dynamics.

Stanford Neurosciences Seminar Series talk by Emery Brown (Massachusetts Institute of Technology, Neuroscience Statistics Research Lab) on deciphering the dynamics of the unconscious brain under general anesthesia, hosted by the Wu Tsai Neurosciences Institute.

This seminar discusses a proof-of-concept gravitational-waveform model described in arXiv:2511.10522. It augments post-Newtonian equations using physics-informed neural-network methods and universal differential equations. The talk also covers ongoing development of a precessing surrogate model designed to evaluate in less than one millisecond while covering a broader portion of the LVK frequency band.

Daphna Shohamy and Ashok Litwin-Kumar bridge experimental and computational neuroscience to explain how the brain assigns significance to memories, how dopamine shapes memory-guided decisions, and how bodily signals influence learning. Isabel Low moderates a public discussion and question session.

Kirk Public Lecture at the Isaac Newton Institute by Yoshiko Ogata (Kyoto University) on how macroscopic properties of matter emerge from quantum particle interactions and the classification of topological order from an operator-algebraic perspective in mathematical physics.

Luca Mrini presents work in progress on quantising singular configuration spaces using the non-smooth calculus of metric-measure spaces. The framework generalises smooth quantum mechanics through Hilbert spaces, position and momentum operators, Hamiltonians, unitary dynamics, and observable algebras. A method for bounding mass gaps after symplectic reduction uses the curvature of the unreduced configuration space. Examples include the harmonic oscillator constrained to zero angular momentum, lattice Yang–Mills theory, and fractional-dimensional Laakso spaces. The talk closes with prospective applications to the Yang–Mills mass-gap problem and quantum gravity.

Isaac Newton Institute seminar in the 'Mathematics of many-body entanglement' (MMB) programme: Ignacio Cirac of the Max-Planck-Institut für Quantenoptik speaks on the preparation of tensor network states.

Large recurrent networks are important models in several fields, including neuroscience, machine learning, physics, and applied mathematics. Yet their dynamics are difficult to study directly, because high-dimensional nonlinear systems can exhibit rich behavior that is hard to summarize in terms of individual trajectories. In this talk, I will discuss an approach that seeks to understand such dynamics through the structure of the network’s equilibria. I will focus on a random balanced network of threshold-linear units that undergoes a transition from a single stable equilibrium to extensive chaos as the disorder strength crosses a critical value. Using a combination of Kac–Rice theory, replica calculations, numerical root-finding, and dynamical mean-field theory, we show that the chaotic regime contains an exponentially large number of equilibria. These equilibria are all saddles, but with only a fractionally small number of unstable directions. Surprisingly, despite the completely random connectivity, the equilibria are not scattered randomly through phase space. Instead, they are strongly correlated and confined to a comparatively small region. The chaotic attractor lies within this same region, suggesting a direct geometric link between the organization of unstable equilibria and the collective structure of the dynamics. This picture helps explain why networks with extensive chaos can nevertheless display dynamics dominated by a relatively small number of collective modes. More broadly, the results suggest that the geometry of equilibria provides a useful complementary perspective to dynamical mean-field theory for understanding high-dimensional neural dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-27. Recording duration: 00:46:40.

Traditional work in the study of human reward-based learning involves designing an experimental task---often inspired by Reinforcement Learning (RL) theory---and fits a small set of computational models---often inspired by RL algorithms---to that dataset. For example, researchers often model human behavior on bandit tasks using variants of Q-learning. While this approach has been highly productive, leading to landmark discoveries such as the dopamine reward prediction error hypothesis, it also has limitations. This talk focuses on the lack of generalizability of such models: Even if they closely fit behavior on the original task, models derived from the one-task-one-model paradigm usually predict behavior on other tasks quite poorly. I argue that this lack of generalizability is a fundamental problem for the cognitive sciences: we intuitively expect our models to be robust to superficial task differences, such as variations in the number of choice options, reward probabilities, or the exact kind of non-stationarity. I will propose potential solutions to this problem along two dimensions: the behavioral dataset and the computational model. Regarding computational models, I will introduce work in which we moved beyond the limitations of hand-crafted one-off models by employing flexible, data-driven methods. These methods allowed us to compare classes of models instead of individual model instances, allowing us to cover the space of possible models more exhaustively, and innovate cognitive mechanisms very efficiently. For the behavioral dataset, we move from using single learning tasks to a comprehensive task space that encompasses most existing paradigms in the literature, while closing the gaps between them in a near-continuous fashion. Our results suggest that more general models in conjunction with broader datasets can pave the road toward increasingly general models of human reward-based learning and decision making, and a persistent departure from many aspects of RL theory. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-20. Recording duration: 00:51:19.

Networks of interconnected neurons display diverse patterns of activity. Relating these patterns to the structure of the network is a central goal of theoretical neuroscience. Classic neural field and rate models have been powerful tools for this purpose due to their analytical tractability. Here, we show that the recently-developed combinatorial threshold-linear network (CTLN) model is a mean-field theory for excitatory-inhibitory Hawkes networks, with clustered connectivity, in an inhibition-stabilized regime. This mapping allows us to leverage powerful analytical results for CTLN networks to predict diverse macroscopic dynamics of clustered Hawkes networks, including metastability between various macroscopic fixed points, limit cycles, and chaotic attractors. We will then examine an extension of this approach to models with nonlinear dendritic dynamics, focusing on dendritic calcium spikes.We uncover a marked point process mean-field theory for these n etworks and use this to examine how somatic vs dendritic-targeting connectivity shapes the mean-field equilibrium phase diagram. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-13. Recording duration: 00:54:14.

Neural oscillations are often proposed to support brain computation by routing information, organizing cell assemblies, or shaping coding dynamics. Yet these ideas usually assume rhythms that are strong, sustained, and regular, whereas in vivo oscillations are often weak, transient, noisy, and variable in frequency and phase. In this talk, I will argue that such “no-metronome” oscillations are not just noisy fluctuations, but coordinated complex dynamics with functional consequences. Combining analyses of neural activity recordings during actual behavior (mice and non-human-primate LFPs and human EEG) with computational modelling, I will discuss evidence that transient oscillatory events can carry task-relevant information and support flexible communication through spatiotemporally structured relationships across populations, timescales, and frequencies. Together, these results suggest that oscillatory weakness and weirdness are not just imperfections, noise to average-out, but part of the functional repertoire of neural computation Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-06. Recording duration: 00:40:47.

Reward expectations – one’s prediction about the likelihood of future outcomes - play a central role in shaping the satisfaction derived from those outcomes. Most existing research treats expectations as static, assuming they remain fixed in time. However, real-life expectations are often dynamic, fluctuating as new information becomes available. For example, during a soccer game, your expectations of seeing your team winning will likely rise and fall as the game unfolds. In the main part of this talk, I will present a series of studies demonstrating that human expectations can be tracked at sub-second timescales. Using slot machines as a case study, we leverage the continuous deceleration of the reels to elicit moment-by-moment fluctuations in rewardexpectations. To capture these dynamics, we take complementary approaches: we use the high temporal resolution of electroencephalography (EEG) to track neural signatures of evolving expectations, and we develop a novel behavioral paradigm (“Slot or Not”) designed to measure changes in expectations via betting behavior. Across four studies, we show that expectations fluctuate continuously and can be tracked both behaviorally and neurally. Extending these findings, a subsequent intracranial study shows that the human orbitofrontal cortex (OFC) encodes the moment-by-moment changes of reward expectations. In the second part of this talk, I will return to the relationship between expectations andsatisfaction. If expectations shape satisfaction, and if they are best conceptualized as dynamic trajectories rather than static quantities, a key question arises: does the trajectory leading up to an outcome influence how that outcome is evaluated? I will outline a new research direction aimed at formalizing this relationship using computational modeling. This is ongoing work, and I welcome feedback on how best to formalize these ideas. Finally, I will discuss potential extensions of this framework to psychopathology, asking whether alterations in dynamic expectations may characterize conditions such as Major Depressive Disorder and Gambling disorder. Together, this work introduces a new framework for studying expectations as dynamic processes, offering a richer understanding Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-29. Recording duration: 00:42:25.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.