Mathematical Modeling

Ellen Zapata-Webborn discusses how mathematical research can help predict household energy use. The episode connects patterns in smart-meter data, human behaviour and the demands of electricity systems, illustrating how quantitative models can inform practical energy questions.

Gaute Einevoll talks with Tatjana Tchumatchenko about a mechanistic mathematical model of how neurons minimize energy use by deciding whether ion-channel proteins are produced locally in dendrites or in the soma. The model’s predictions agree with experimental findings.

Ulrich Sperhake and Seppe Staelens explain hypothetical boson stars and how researchers use mathematical modelling to investigate them. The discussion connects these unusual compact objects to black holes, gravity and gravitational-wave observations.

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.

Develop an analytical and computational research project with Arne Traulsen’s Department of Theoretical Biology. Possible directions include population structure, evolutionary game theory, microbial populations, ecological stochasticity, complex life cycles and infectious-disease models. The project will be developed with the incoming researcher to reflect their interests and skills. The institute’s working language is English. This vacancy belongs to the September 2026 Max Planck Postdoc Program call, which accepts applications until 13 October 2026 at 12:00 CEST through the official application platform.

Develop high-resolution air-quality models and correction algorithms suited to African conditions in a fully funded doctoral position at the African Research Centre on Air Quality & Climate, Mohammed VI Polytechnic University. The employer lists this opening in Ben Guerir and provides an application contact on its recruitment page.

Develop models of how cells sense and transmit mechanical cues, linking deformable soft materials and cell interfaces to intracellular signalling and mechanosensitive calcium responses. The project is primarily computational, with opportunities to connect models to experiments. Join Vesna Bacheva’s research at the Groningen Research Institute of Pharmacy, located within UMCG. Employment is full time for one year initially, with possible renewal for three further years. Applications close on 16 October 2026 at 23:59 Dutch local time.

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.

Develop data-driven theories of how neural circuit structure shapes computation in the Allen Institute Neural Dynamics accelerator. The scientist will combine large-scale connectivity atlases, simultaneous recordings from thousands of neurons across brain regions, and targeted perturbations during behavior. Work includes mechanistic models fitted to connectivity and activity, coarse-grained descriptions of collective dynamics, analysis of which models remain compatible with data, and design of experiments that distinguish between them. The role involves close collaboration with anatomical, electrophysiological and imaging teams, and communicating research through publications and conferences. Based in Seattle, Washington, with most hours on site. The stated annual salary range is $87,450–$108,250. Relocation assistance is offered; work visa sponsorship may be available. Remote work, when permitted, must take place in Washington State.

The study tests whether cortex preserves information during sparse-to-dense coding by targeting thalamocortical synapses to dendritic calcium-spike initiation zones, enabling output neurons to multiplex information through a 1-2-3 action-potential syntax. Evidence across long-range pathways suggests that this anatomically and biophysically distinct dendritic nexus may provide a general mechanism for transforming sparse cortical representations into dense output streams.

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.