Week 09.02.2026 – 15.02.2026

Topology plays a critical role in regulating the three-dimensional organization of DNA across a wide range of length scales. At the kilobase-pair scale, various biological processes generate over- and underwinding of the DNA double helix, a phenomenon known as DNA supercoiling. To accommodate excess torsional stress, DNA undergoes large-scale configurational rearrangements, resulting in the formation of plectonemes. We recently studied the emergence and coexistence of multiple plectonemic domains using a statistical-mechanical model that builds on the classical two-phase description of stretched, supercoiled DNA. Despite its simplicity, the resulting theory shows excellent agreement with Monte Carlo simulations of the twistable wormlike chain model. 
At the megabase scale, we investigated microscopy data of interphase chromosomes obtained using multiplexed fluorescence in situ hybridization (FISH). By analyzing distance distributions and associated scaling laws, we found that, for a given genomic locus, chromatin can adopt two distinct conformational states, indicating the coexistence of different topological organizations, which we denote as phase α and phase β. These phases exhibit distinct scaling behavior: the α phase is consistent with a crumpled-globule–like organization, whereas the β phase corresponds to a more extended yet confined conformation, such as a looped domain architecture.

Twenty years ago, Luczak and Winkler proved that a uniformly random plane d-ary tree with n nodes can be constructed from a uniformly random one with n-1 nodes, by adding leaves at a well-chosen place. I will discuss generalizations of this construction to other models of discrete random trees under log-concavity type assumptions, as well as the continuum counterpart of the problem. Along the way, we will see that the Aldous' Continuum Random Tree can be "grown by the leaves", and that the resulting dynamics is the scaling limit of the Luczak-Winkler process.

With recent advances in wavefront shaping techniques for imaging and telecommunications, the question of a theoretical description of coherently controlled waves in complex media has become increasingly important. Indeed, these waves elude incoherent propagation theories such as radiative transport theory. Moreover, macroscopic approaches such as random matrix theory lack the flexibility to incorporate realistic experimental conditions such as quasiballistic effects, complex geometries, absorption, or incomplete wave control. In this work, I introduce a general theoretical framework for shaped waves valid under these conditions. At the heart of this theory lies a transport equation similar to the radiative transport equation but for a matrix function. This equation captures not only the statistical distribution of transmission eigenvalues in random media, but also the intensity profile of transmission eigenstates, whose sinusoidal shape remained unexplained for a decade.

We introduce a novel measure of dependence that captures the extent to which a random variable Y is determined by a random vector X. The measure equals zero precisely when Y and X are independent, and it attains one exactly when Y is almost surely a measurable function of X. We further extend this framework to define a measure of conditional dependence between Y and X given Z. We propose a simple and interpretable estimator with computational complexity comparable to classical correlation coefficients, including those of Pearson, Spearman, and Chatterjee. Leveraging this dependence measure, we develop a tuning-free, model-agnostic variable selection procedure and establish its consistency under appropriate sparsity conditions. Extensive experiments on synthetic and real datasets highlight the strong empirical performance of our methodology and demonstrate substantial gains over existing approaches.

See: https://www.londonmathfinance.org.uk/seminar

See: https://www.londonmathfinance.org.uk/seminar