04.11.2026 11:00 Panagiotis Andreou (TUM): Homogeneity Fusion Estimation in Grouped Network Autoregressive and Factor Models
We study models for multivariate time series evolving on networks with latent group structure under two complementary network-density regimes. When the network is sparse, we focus on the Grouped Network Vector Autoregression (GNAR) model, capturing dynamics through group-specific transition coefficients. We consider joint estimation of the unobserved network, group memberships, and coefficients. When the network is dense, the GNAR model is akin to a weak factor model with group-specific loadings. We develop a likelihood-based framework for loadings estimation in this setting, covering both known and latent group structures, as well as suitable PCA-based alternatives. This is joint work with Changryong Baek and Vladas Pipiras.
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05.11.2026 14:00 Giacomo Borghi (TUM): Particle approximation of replicator-mutator dynamics
Interacting systems where particles duplicate and mutate are ubiquitous in many application domains, including biological modeling, evolutionary optimization, and multimodal sampling. In the talk, we review the paradigmatic example of the replicator-mutator particle system and show its convergence towards a PDE with a source term and a diffusive term. The central, novel tool is a Wasserstein distance with bounded ground cost, resembling the Wasserstein-Fisher-Rao distance.
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10.11.2026 16:15 Jakob Möller: Velocity Averaging (or not…) and Quantum Kinetic Theory
Velocity averaging is a class of regularity results for the transport equation which says that macroscopic observables attached to the distribution function solution of a kinetic equation are more regular than the distribution function itself. It has important applications to the existence theory for the Boltzmann and Vlasov equations, and to hydrodynamic limits of the Boltzmann equation. This talk will discuss the possibility of applying velocity averaging in the context of quantum dynamics. Our analysis of this problem will lead us to discuss the so-called Madelung quantum hydrodynamic equations and the magnetic or gauge-invariant Wigner transform due to Stratonovich.
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12.11.2026 14:00 Giuseppe Bruno (U Bern): tbd
tbd
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16.11.2026 16:30 Jonas Köppl: Continuous symmetry breaking in discrete interacting particle systems?
Unlike finite-state Markov chains, interacting particle systems on infinite graphs may admit multiple stationary measures, and even convergence to one of these is not guaranteed. One particular obstruction is the existence of time-periodic orbits, where the system returns to its initial distribution after a fixed period without being stationary, thereby spontaneously breaking the continuous time-translation symmetry. The conditions under which such noisy systems can maintain sufficient spatial order to sustain such time-periodic behaviour have been a contentious issue in the physics literature and a mathematical treatment of such broken-symmetry, macroscopically time-dependent states has been mostly limited to mean-field like approximations.
In this talk, we present some recent progress on two questions: (a) in which spatial dimensions d is such time-periodic behaviour possible? (b) What quantitative properties, such as the rate of decay of truncated correlations, can we infer from the existence of a time-periodic orbit?
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