Current & Upcoming

The geometry of a complex network shapes the way the network processes, transmits, and organizes information. But what exactly is the geometry of a network, and how can we uncover it? In this talk, I will show how foundational concepts originated from Riemannian manifolds provide powerful tools for analysing and understanding the structure of complex data. We see that by leveraging geometric insights, we can detect a family of regular equivalence classes (as a fundamental network similarity measure), uncover hidden community structures in social networks, identify bottlenecks in chemical reactions, and explain phenomena such as over-squashing in (simplicial) neural networks.

Probabilistic principal component analysis (PPCA) and factor analysis (FA) are methods for understanding the principal directions along which given data is distributed. Both classes of models have been used extensively in various fields such as psychology and sociology, and for applications including classification problems. This talk will present an effective model-selection method for PPCA and FA and, in particular, for determining the effective dimension of a noisy data set. The main technique is based on resolution of singularities for real schemes arising from these models. This is joint work with Mathias Drton and Andrew McCormack.

How do cells and tissues encode and exchange information to coordinate multicellular behaviour? Our work on somitogenesis showed that the temporal organization of signalling matters for development: the relative timing between oscillating pathways is functionally important for embryonic segmentation. We then asked whether temporal signalling could also regulate cell fate in a homeostatic tissue. In the intestinal epithelium, we found that changing the frequency of signalling oscillations alters cell-type composition, establishing frequency encoding as a mechanism of tissue homeostasis. More recently, we turned to communication between embryonic and maternal tissues during human implantation. While initially aiming to study signalling between these tissues, we made an unexpected observation: embryonic and endometrial cells form heterokaryons. Following this finding mechanistically led us to identify Syncytin-2/MFSD2A as a mediator of this interaction. Together, these studies explore how information is encoded within tissues and exchanged between them to coordinate multicellular behaviour.

Halloween requires the presence of blood and horror (as well as drinks and sometimes bats). In my talk I will cover all four aspects. Bed bugs binge drink (about three times their body weight), and they only drink blood. For females, drinking blood comes with sex, which, as I will present, denotes the horror part (if that is insufficient for horror, I will bring a picture from a heavily infested room). Sex is traumatic for females – copulatory wounding occurs at every mating - and I will quantify the trauma and show what females do about that. Traumatic insemination also lead to some unusual sperm biology. I will examine some of the sperm biology separately for the two genetically separated clades of bed bugs that either drink human or bat blood. Human and bat blood produce bed bug sperm that differ predictably in lipid profiles, and in sperm metabolism. This contrasts with Drosophila, where we find that, in the testes, sperm are protected from incorporating dietary lipids but instead take them up from lipid vesicles in the seminal fluid (called microcarriers). Sperm then shuttle dietary sterols to the offspring where they seem to enhance offspring growth, possibly because sterols are the precursor for the insect growth hormone.

Eukaryotic cells produce thousands of different lipids—collectively known as the lipidome—whose composition is tailored to cellular needs. Lipids are distributed unevenly throughout biological systems, where they accumulate locally, forming membranes with specific compositions and thereby determining the identity and functional specialization of organelles. Due to their hydrophobicity, lipids cannot move freely out of cellular membranes through the cell’s aqueous environment and require transporters—lipid transfer proteins, or LTPs—to carry them. LTPs are soluble molecular machines responsible for transporting lipids, and they are found in all kingdoms of life. They have diverse structures, but many share a common mode of action: they extract specific lipids from membrane bilayers and load them into a hydrophobic pocket, forming water-soluble protein-lipid complexes that isolate cargoes from the aqueous phase. In addition to their cargo, some LTPs mobilize auxiliary lipids that function as exchange currencies or cofactors. They facilitate the uptake or release of the cargo, which would determine the direction of transport and its coupling to metabolism. However, for most LTPs, the identity of cargo and auxiliary lipids remains unknown. The fundamental biochemistry of LTPs remains poorly understood, limiting our ability to study how they function within cells. Our goal is to begin addressing this gap; I will present a recent systematic analysis of the lipid binding properties of human LTPs and discuss the general principles that we have derived from it.

When can we change the diagonal of a matrix without changing its spectrum? We completely answer this question over an algebraically closed field of characteristic zero or larger than the size of the matrix: A square matrix A admits a nonzero diagonal matrix D such that A and A+D have the same spectrum if and only if there are two principal minors of A of the same size that are not equal. This relates to the classical additive inverse eigenvalue problem in numerical analysis and has implications for existence and rigidity results in the theory of Floquet isospectrality of discrete periodic operators in solid state physics. The proof employs new techniques involving Hilbert schemes of points and the infinitesimal structure of the Hilbert--Chow morphism. This is joint work with John Cobb and Matt Faust.

TBA