Mathematical Modeling

Postdoctoral position in the Siegert Group developing mathematical and computational methods for analyzing complex cellular morphology in the MIND-MAP project, an interdisciplinary collaboration studying microglia dynamics and brain function. Position closes once a suitable candidate is found.

The goal of the Neural Dynamics accelerator is to understand how the brain generates flexible behavior. We aim to uncover the algorithms—implemented by dynamics in brain-wide neural circuits—that allow animals to build internal models, process information, and choose actions. We are searching for a Scientist to develop data-driven theories of how circuit structure shapes neural computation. The…

SAB 2026 investigates the mechanisms that let natural and artificial agents adapt and survive in uncertain environments. Researchers compare biological behavior with robot experiments, computer simulations and mathematical models to evaluate principles and architectures of adaptive behavior. The programme covers collective intelligence, learning and skill acquisition, artificial perception and manipulation, and physical and social constraints on behavior. A cross-kingdom intelligence symposium includes Paco Calvo, Jens Krause, Vera Meyer and Ute Schmid. The meeting runs 19–22 October 2026 in Berlin, on CEST (Europe/Berlin, UTC+2). Workshops on 19 October at TU Berlin, Marchstraße 23, start at 09:00 following registration at 08:15; afternoon workshops end at 18:30. Topics include internal world models, genetic programming and homeostatic control. Conference sessions on 20–22 October take place at Universität der Künste, Georg-Neumann-Saal, Einsteinufer 43; sessions on 20 and 21 October begin at 09:00. Consult the detailed daily programme for session and venue changes. Public registration through Pretix is open. General admission is EUR 550, or EUR 450 for students with proof of status. Fees include sessions, coffee breaks and one networking dinner; lunches, other dinners and optional social activities are self-funded. No VAT is added.

The Society for Industrial and Applied Mathematics convenes researchers developing and applying dynamical-systems methods across biology, chemistry, physics, climate science, social science, industry and data science. Themes include computational, experimental, theoretical and data-driven methods; AI-informed systems; fluid and climate dynamics; materials; networks; pattern formation; population dynamics; stochastic systems and tipping points. Minisymposium proposals are due 26 October 2026, followed by contributed lecture, poster and minisymposium-presentation abstracts on 23 November 2026.

SIAM’s computational science and engineering meeting covers mathematical models, scalable algorithms, scientific software, high-performance computing and scientific machine learning. It takes place in Pittsburgh on 22–26 February 2027. Travel-support applications are open until 30 November 2026. Abstract deadlines have passed; registration is scheduled to open in December 2026. The meeting is co-located with ACDA27 and the International Meshing Roundtable.

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.

One of the many ocean swells in the history of computational approaches to mind and brain is the rise and fall of cognitive architectures. Although supplanted by neural networks as the dominant modelling modality, cognitive architectures possess many attributes sorely coveted by the computational modeller: large, architectural-level scales, unified explanations of disparate cognitive functions in single models, and rich, hierarchical-modular decompositional structure conducive to building and modifying large computational systems. In contrast, we find in the neural network literature a proliferation of small-scale, localised models of single tasks, isolated functions, or dissected brain areas. What would it take to unify all this local knowledge into an architectural neural model? The key property that ensures (de-)compositional structure is functional encapsulation – the preservation of component behaviour in disparate contexts. Here, by analysing the behaviour of attractor networks under composition, we demonstrate that neural networks lack functional encapsulation – a property we call ‘structural flatness’. The core conclusion drawn from the analysis is this: the notion of localised, encapsulated function, essential to the more ‘cartographic’ approaches to the brain, is conceptually consistent only when applied to single networks as wholes, and not to their parts. Following from this, if the brain possesses localised, encapsulated cognitive functions, then neural networks are not the proper formalism to realise this on a grand scale; if the brain does not possess encapsulated functionality, then a critical evaluation must be made of the conceptual utility of functional localisation within computational neuroscience, and how it shapes our empirical and theoretical efforts.

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.

Sabbatical fellowship providing salary replacement (up to 50% of academic-year salary, capped at $125,000) plus up to $10,000 in leave-related expenses so mathematicians can extend a sabbatical term to a full academic year; maximum total budget $162,000 including 20% overhead.

This NIH BRAIN Initiative funding opportunity supports new or substantially advanced theories, mechanistic or predictive models, and computational or statistical methods that improve quantitative understanding of brain function across scales. Tools must address complex neural and behavioral data and be made broadly available to the neuroscience research community.

Build scalable computational pipelines for biophysical models of neurons and neural populations. Apply machine learning and statistical inference to neural recordings, construct biologically realistic networks and help shape research directions at an early-stage company working at the intersection of neuroscience and computation. On-site engagement is preferred and international candidates may apply. The advertised salary range is USD 132,000–259,000; no fixed closing date is stated.