L1

Quantum field theories (QFTs) in d dimensions that posses a (d-1)-form symmetry are conjectured to decompose into disjoint “universes”, each of which is itself a (local and unitary) QFT. I will give an overview of our current understanding of decomposition, and then discuss how this phenomenon occurs in the fusion of condensation defects of certain 3d QFTs. This gives a “microscopic” explanation of why in these instances, the fusion coefficient can be taken as an integer rather than a general TQFT.

I will describe a procedure, known as holomorphic twist, to isolate protected quantities in supersymmetric quantum field theories. The resulting theories are holomorphic, interacting and have infinite dimensional symmetries, analogous to the holomorphic half of a 2D CFT. I will explain how to study quantum corrections to these symmetries and other  higher operations.
As a surprise, we find a novel UV manifestation of
confinement, dubbed "holomorphic confinement," in the example of pure
SU(N) super Yang-Mills.

According to the correspondence principle, classical physics emerges in the limit of large quantum numbers. We examine three examples of the semiclassical description of conformal field theory data: large charge boundary operators in the O(2) model, large spin impurities in the free triplet scalar field theory and large charge Wilson lines in QED. By simultaneously taking the coupling to zero and quantum numbers to infinity, we can connect the microscopic to the emergent classical description smoothly.

What sets the size and form of living organisms is still, by large, an open question. During this talk, I will illustrate how we are addressing this question by examining the links between spatial scales, from subcellular to organ, both experimentally and theoretically. First, I will present how we are deriving continuous plant growth mechanical models using homogenisation. Second, I will discuss how directionality of organ growth emerges from cell level. Last, I will present predictions of fluctuations at multiple scales and experimental tests of these predictions, by developing a data analysis approach that is broadly relevant to geometrically disordered materials.

Hypergraphs for multiscale cycles in structured data

Iris Yoon

Understanding the spatial structure of data from complex systems is a challenge of rapidly increasing importance. Even when data is restricted to curves in three-dimensional space, the spatial structure of data provides valuable insight into many scientific disciplines, including finance, neuroscience, ecology, biophysics, and biology. Motivated by concrete examples arising in nature, I will introduce hyperTDA, a topological pipeline for analyzing the structure of spatial curves that combines persistent homology, hypergraph theory, and network science. I will show that the method highlights important segments and structural units of the data. I will demonstrate hyperTDA on both simulated and experimental data. This is joint work with Agnese Barbensi, Christian Degnbol Madsen, Deborah O. Ajayi, Michael Stumpf, and Heather Harrington.

Minmax Connectivity and Persistent Homology 

Ambrose Yim

We give a pipeline for extracting features measuring the connectivity between two points in a porous material. For a material represented by a density field f, we derive persistent homology related features by exploiting the relationship between dimension zero persistent homology of the density field and the min-max connectivity between two points. We measure how the min-max connectivity varies when spurious topological features of the porous material are removed under persistent homology guided topological simplification. Furthermore, we show how dimension one persistent homology encodes a relaxed notion of min-max connectivity, and demonstrate how we can summarise the multiplicity of connections between a pair of points by associating to the pair a sub-diagram of the dimension one persistence diagram.

Consider the injection of a fluid onto an impermeable surface for an infinite length of time... Does the injected fluid reach a finite height, or does it keep on growing forever? The classical theory of gravity currents suggests that the height remains finite, causing the radius to grow outwards like the square root of time. When the fluid resides within a porous medium, the same is thought to be true. However, recently I used some small scale experiments and numerical simulations, spanning 12 orders of magnitude in dimensionless time, to demonstrate that the height actually grows very slowly, at a rate ~t^(1/7)*(log(t))^(1/2). This strange behaviour can be explained by analysing the flow in a narrow "inner region" close to the source, in which there are significant vertical velocities and non-hydrostatic pressures. Analytical scalings are derived which match closely with both numerics and experiments, suggesting that the blob of fluid is in fact ever-growing, and therefore becomes unbounded with time.

It has been known for some time that the contact sets between
self-avoiding idealised tubes (i.e. with exactly circular, normal
cross-sections) in various highly compact, tight structures comprise
double lines of contact. I will re-visit those results for two canonical
examples, namely the orthogonal clasp and the ideal trefoil knot. I will
then show experimental and 3D FEM simulation data for deformable elastic
tubes (obtained within the group of Pedro Reis at the EPFL) which
reveals that the ideal contact set lines bound (in a non-rigorous sense)
the actual contact patches that arise in reality.

[1] The shapes of physical trefoil knots, P. Johanns, P. Grandgeorge, C.
Baek, T.G. Sano, J.H. Maddocks, P.M. Reis, Extreme Mechanics Letters 43
(2021), p. 101172, DOI:10.1016/j.eml.2021.101172
[2]  Mechanics of two filaments in tight orthogonal contact, P.
Grandgeorge, C. Baek, H. Singh, P. Johanns, T.G. Sano, A. Flynn, J.H.
Maddocks, and P.M. Reis, Proceedings of the National Academy of Sciences
of the United States of America 118, no. 15 (2021), p. e2021684118
DOI:10.1073/pnas.2021684118

We present a framework to generate and evaluate thematic recommendations based on multilayer network representations of knowledge graphs (KGs).  We represent the relative importance of different types of connections (e.g., Directing/acting) with an intuitive salience matrix that can be learnt from data, tuned to incorporate domain knowledge, address different use cases, or respect business logic. We apply an adaptation of the personalised PageRank algorithm to multilayer network models of KGs to generate item-item recommendations. These recommendations reflect the knowledge we hold about the content, and are suitable for thematic or cold-start settings.

Evaluating thematic recommendations from user data presents unique challenges. Our method only recommends items that are 'thematically' related; that is, easily reachable following connections in the KG. We develop a variant of the widely-used Normalised Discounted Cumulative Gain (NDCG) to evaluate recommendations based on user-item ratings, respecting their thematic nature.

We apply our methods to a KG of the movie industry and MovieLens ratings and in an internal AB test. We learn the salience matrix and demonstrate that our approach outperforms existing thematic recommendation methods and is competitive with collaborative filtering approaches.

The applied, numerical and asymptotic analysis of acoustic, electromagnetic and elastic scattering by smooth scatterers (e.g. a cylinder or a sphere) is a classical topic in applied mathematics. However, many real-world applications involve highly non-smooth scatterers with geometric structure on multiple length scales. Examples include acoustic scattering by trees and other vegetation in the modelling of urban noise propagation, electromagnetic scattering by snowflakes and ice crystal aggregates in climate modelling and weather prediction, and elastic scattering by cracks and other interfaces in seismic imaging and hydrocarbon exploration. In such situations it may be more appropriate to model the scatterer not by a smooth surface but by a fractal, a geometric object with self-similarity properties and detail on every length scale. Well-known examples include the Cantor set, Sierpinski triangle and the Koch snowflake. In this talk I will give an overview of our recent research into acoustic scattering by such fractal structures. So far our work has focussed on establishing well-posedness of the scattering problem and integral equation reformulations of it, and developing and analysing numerical methods for obtaining approximate solutions. However, there remain interesting open questions about the high frequency (short wavelength) asymptotic behaviour of solutions, and whether the self-similarity of the scatterer can be exploited to derive more efficient approximation techniques.

Many microorganisms must navigate strange biological environments whose physics are unique and counter-intuitive, with wide-ranging consequences for evolutionary biology and human health. Mucus, for instance, behaves like both a fluid and an elastic solid. This can affect locomotion dramatically, which can be highly beneficial (e.g. for mammalian spermatozoa swimming through cervical fluid) or extremely problematic (e.g. the Lyme disease spirochete B. burgdorferi swimming through the extracellular matrix of human skin). Mathematical modeling and numerical simulations continue to provide new fundamental insights about the biological world in and around us and point toward new possibilities in biomedical engineering. These complex fluid phenomena can either enhance or retard a microorganism's swimming speed, and can even change the direction of swimming, depending on the body geometry and the properties of the fluid. We will discuss analytical and numerical insights into swimming through model viscoelastic (Oldroyd-B) and liquid-crystalline (Ericksen-Leslie) fluids, with a special focus on the important and in some cases dominant roles played by the presence of nearby boundaries.