Week 30.03.2026 – 05.04.2026

We analyze continuity equations with Stratonovich stochasticity on a smooth closed and compact Riemannian manifold M with metric h. The velocity field u is perturbed by Gaussian noise terms W_1(t), . . . ,W_N (t) driven by smooth spatially dependent vector fields a_1(x), . . . , a_N (x) on M . The velocity u belongs to L^1_t W^{1,2}_x with div_h u bounded in L^p_{t,x} for p > d + 2, where d is the dimension of M (we do not assume div_h u ∈ L^∞_{t,x}).
We show that by carefully choosing the noise vector fields a_i (and the number N of them), the initial-value problem is well-posed in the class of weak L^2 solutions, although the problem can be ill-posed in the deterministic case because of concentration effects.
The proof of this “regularization by noise” result reveals a link between the nonlinear structure of the underlying domain M and the noise, a link that is somewhat hidden in the Euclidean case (a_i constant). To our knowledge, this is the first instance of “regularization by noise” phenomena beyond R^d. The proof is based on an a priori estimate in L^2, which is obtained by a duality method, and a weak compactness argument.
This is a joint work with Kenneth Karlsen (UiO).

Pattern formation is ubiquitous in biological development. Tissue patterns are often formed as organisms grow in size. I will discuss examples of how growth affects the physics of pattern formation. My first example will be the arrangement of chromatophores on the squid mantel, as an instance of disordered packing on a growing surface. I will then present a two-species toy model to explore potential universal behavior in these systems. I will conclude by using similar ideas to understand stripe pattern stability in clownfish mutants.

References:

Ross RJ, Masucci GD, Lin CY, Iglesias TL, Reiter S, Pigolotti S. Hyperdisordered cell packing on a growing surface. Physical Review X. 15(2):021064 (2025).
Ross RJ, Pigolotti S. Coarsening and universality on a growing surface. arXiv preprint arXiv:2411.09172 (2024).
Klann M, Miura S, Lee SH, Vianello SD, Ross R, Watanabe M, Gairin E, Liang Y, Hutto HW, McCluskey BM, Herrera M et al. Cell-cell communication as underlying principle governing color pattern formation in teleost fishes. Nature Communications (2026).

Much of the causal inference literature relies on the Stable Unit Treatment Value Assumption (SUTVA), which rules out interference between individuals. However, in many public health settings, this assumption does not hold. For example, in the context of a prevention program, one person’s vaccination status may indirectly influence the infection risk of their contacts within a social network. In addition to unmeasured confounding, estimating causal effects in these settings can be complicated by several factors, including homophily bias, unmeasured contextual confounding, autocorrelation, and uncertainty about the underlying network structure. In this talk, I’ll present recent methodological developments aimed at addressing these challenges, focusing in particular on work from my thesis and its application to substantive research questions in education and public health. I’ll also touch on ongoing challenges and future directions in this area of research.