Past

A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here I will discuss a proposal for a `hydrodynamic' origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. In particular I will discuss how in maximally chaotic systems there is a suppression of exponential growth in commutator squares of generic few-body operators. This suppression appears to indicate that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems.

There are various aspects of the AdS/CFT correspondence that are rather mysterious. For example, how does the gravitational theory know about a discrete boundary spectrum or how does it know moments of the partition function factorize, given the existence of connected (wormhole) geometries? In this talk I will discuss some recent efforts with Andreas Blommaert and Luca Iliesiu on these two puzzles in two dimensional dilaton gravities. These gravity theories are simple enough that we can understand and propose a resolution to the discreteness and factorization puzzles. I will show that a tiny but universal bilocal spacetime interaction in the bulk is enough to ensure factorization, whereas modifying the dilaton potential with tiny corrections gives a discrete boundary spectrum. We will discuss the meaning of these corrections and how they could be related to resolutions of the same puzzles in higher dimensions. 

This event will take place on Teams. A link will be available 30 minutes before the session begins.

Sebastien Racaniere is a Staff Research Engineer at DeepMind. His current main interest is in the use of symmetries in Machine Learning. This offers diverse applications, for example in Neuroscience or Theoretical Physics (in particular Lattice Quantum Chromodynamics). Past interests, still in Machine Learning, include Reinforcement Learning (i.e. learning from rewards), generative models (i.e. learn to sample from probability distributions), and optimisation (i.e. how to find 'good' minima of functions)

The morphogenesis of branched tissues has been a subject of long-standing interest and debate. Although much is known about the signaling pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial patterning, are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we show that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Finally, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying matrix. This inflationary branching-arresting random walk model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the matrix into which it expands.

Let $F$ be a finite field or a $p$-adic field. One method of constructing irreducible representations of $G = GL_2(F)$ is to consider spaces on which $G$ naturally acts and look at the representations arising from invariants of these spaces, such as the action of $G$ on cohomology groups. In this talk, I will discuss how this goes for abstract representations of $G$ (when $F$ is finite), and smooth representations of $G$ (when $F$ is $p$-adic). The first space is an affine algebraic variety, and the second a tower of rigid spaces. I will then mention some recent results about how this tower allows us to construct new interesting $p$-adic representations of $G$, before explaining how trying to adapt these methods leads naturally to considerations about certain geometric properties of these spaces.

The Persistent Homology Transform, and the Euler Characteristic Transform are topological analogs of the Radon transform that can be used in statsistical shape analysis. In this talk I will consider an interesting variant called the Extended Persistent Homology Transform (XPHT) which replaces the normal persistent homology with extended persistent homology. We are particularly interested in the application of the XPHT to binary images. This paper outlines an algorithm for efficient calculation of the XPHT exploting relationships between the PHT of the boundary curves to the XPHT of the foreground.

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Here we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome

Climate- and weather prediction centres such as the Met Office rely on efficient numerical methods for simulating large scale atmospheric flow. One computational bottleneck in many models is the repeated solution of a large sparse system of linear equations. Preconditioning this system is particularly challenging for state-of-the-art discretisations, such as (mimetic) finite elements or Discontinuous Galerkin (DG) methods. In this talk I will present recent work on developing efficient multigrid preconditioners for practically relevant modelling codes. As reported in a REF2021 Industrial Impact Case Study, multigrid has already led to runtime savings of around 10%-15% for operational global forecasts with the Unified Model. Multigrid also shows superior performance in the Met Office next-generation LFRic model, which is based on a non-trivial finite element discretisation.

The experimental evidence of the existence of a feedback between growth and stress in tumors poses challenging questions. First, the rheological properties (the constitutive equations) of aggregates of malignant cells are to identified. Secondly, the feedback law (the "growth law") that relates stress and mitotic and apoptotic rate should be understood. We address these questions on the basis of a theoretical analysis of in vitro experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression.
Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern.
The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

The Teichmüller space for a closed surface of genus g is the space of marked complex/hyperbolic structures on the surface. Teichmüller space also identifies with the space of Fuchsian representations of the fundamental group into PSL(2,R) (mod conjugation). Higher Teichmüller theory concerns special representations of surface (or hyperbolic) groups into higher rank Lie groups of non-compact type.

TBA.

In this talk we will show the application of (multilayer) network science to a wide spectrum of problems related to the ongoing COVID-19 pandemic, ranging from the molecular to the societal scale. Specifically, we will discuss our recent results about how network analysis: i) has been successfully applied to virus-host protein-protein interactions to unravel the systemic nature of SARS-CoV-2 infection; ii) has been used to gain insights about the potential role of non-compliant behavior in spreading of COVID-19; iii) has been crucial to assess the infodemic risk related to the simultaneous circulation of reliable and unreliable information about COVID-19.

References:

Assessing the risks of "infodemics" in response to COVID-19 epidemics
R. Gallotti, F. Valle, N. Castaldo, P. Sacco, M. De Domenico, Nature Human Behavior 4, 1285-1293 (2020)

CovMulNet19, Integrating Proteins, Diseases, Drugs, and Symptoms: A Network Medicine Approach to COVID-19
N. Verstraete, G. Jurman, G. Bertagnolli, A. Ghavasieh, V. Pancaldi, M. De Domenico, Network and Systems Medicine 3, 130 (2020)

Multiscale statistical physics of the pan-viral interactome unravels the systemic nature of SARS-CoV-2 infections
A. Ghavasieh, S. Bontorin, O. Artime, N. Verstraete, M. De Domenico, Communications Physics 4, 83 (2021)

Individual risk perception and empirical social structures shape the dynamics of infectious disease outbreaks
V. D'Andrea, R. Gallotti, N. Castaldo, M. De Domenico, To appear in PLOS Computational Biology (2022)

Las Vergnas and Meyniel conjectured in 1981 that all the $t$-colorings of a $K_t$-minor free graph are Kempe equivalent. This conjecture can be seen as a reconfiguration counterpoint to Hadwiger's conjecture, although it neither implies it or is implied by it. We prove that for all positive $\epsilon$, for all large enough $t$, there exists a graph with no $K_{(2/3 + \epsilon)t}$ minor whose $t$-colorings are not all Kempe equivalent, thereby strongly disproving this conjecture, along with two other conjectures of the same paper.

How can one integrate singular functions over fractals? And why would one want to do this? In this talk I will present a general approach to numerical quadrature on the compact attractor of an iterated function system of contracting similarities, where integration is with respect to the relevant Hausdorff measure. For certain singular integrands of logarithmic or algebraic type the self-similarity of the integration domain can be exploited to express the singular integral exactly in terms of regular integrals that can be approximated using standard techniques. As an application we show how this approach, combined with a singularity-subtraction technique, can be used to accurately evaluate the singular double integrals that arise in Hausdorff-measure Galerkin boundary element methods for acoustic wave scattering by fractal screens. This is joint work with Andrew Gibbs (UCL) and Andrea Moiola (Pavia).

The aim of this talk is to present some recent developments of Geometric Measure Theory on non smooth spaces with lower Ricci Curvature bounds, mainly related to the first and second variation formula for the area, and their applications to the isoperimetric problem on non compact manifolds. The reinterpretation of some classical results in Geometric Analysis in a low regularity setting, combined with the compactness and stability theory for spaces with lower curvature bounds, leads to a series of new geometric inequalities for smooth, non compact Riemannian manifolds. The talk is based on joint works with Andrea Mondino, Gioacchino Antonelli, Enrico Pasqualetto and Marco Pozzetta.

In this talk, we present our study of Brown’s definition of the probabilistic zeta function of a finite lattice, and propose a natural alternative that may be better-suited for non-atomistic lattices. The probabilistic zeta function admits a general Dirichlet series expression, which need not be ordinary. We investigate properties of the function and compute it on several examples of finite lattices, establishing connections with well-known identities. Furthermore, we investigate when the series is an ordinary Dirichlet series. Since this is the case for coset lattices, we call such lattices coset-like. In this regard, we focus on partition lattices and d-divisible partition lattices and show that they typically fail to be coset-like. We do this by using the prime number theorem, establishing a connection with number theory.

Distribution dependent equations (or McKean—Vlasov equations) have found many applications to problems in physics, biology, economics, finance and computer science. Historically, equations with either Brownian noise or zero noise have received the most attention; many well known results can be found in the monographs by A. Sznitman and F. Golse. More recently, attention has been paid to distribution dependent equations driven by random continuous noise, in particular the recent works by M. Coghi, J-D. Deuschel, P. Friz & M. Maurelli, with applications to battery modelling. Furthermore, the phenomenon of regularisation by noise has received new attention following the works of D. Davie and M. Gubinelli & R. Catellier using techniques of averaging along rough trajectories. Building on these ideas I will present recent joint work with L. Galeati and F. Harang concerning well-posedness and stability results for distribution dependent equations driven first by merely continuous noise and secondly driven by fractional Brownian motion.

Let X be a closed Riemannian manifold, and represent the algebra C(X) of continuous functions on X on the Hilbert space L^2(X) by multiplication.  Inspired by the heat kernel proof of the Atiyah-Singer index theorem, I'll explain how to describe K-homology (i.e. the dual theory to Atiyah-Hirzebruch K-theory) in terms of parametrized families of operators on L^2(X) that get more and more 'local' in X as time tends to infinity.

I'll then switch perspectives from C(X) -- the prototypical example of a commutative C*-algebra -- to noncommutative C*-algebras coming from discrete groups, and explain how the underlying large-scale geometry of the groups can give rise to approximate 'decompositions' of the C*-algebras.  I'll then explain how to use these decompositions and localization in the sense above to compute K-homology, and the connection to some conjectures in topology, geometry, and C*-algebra theory.

Donaldson-Thomas (DT) theory is an enumerative theory which produces a virtual count of stable coherent sheaves on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will explain the role of d-critical locus structure in the definition of motivic DT invariant, following the definition by Bussi-Joyce-Meinhardt. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint works with Sheldon Katz. The results have substantial overlap with recent work by Ricolfi-Savvas, but techniques used here are different. 

 I will present a scenario where the early universe is in a topological phase of gravity.  I will discuss a number of analogies which motivate considering gravity in such a phase. Cosmological puzzles such as the horizon problem provide a phenomenological connection to this phase and can be explained in terms of its topological nature. To obtain phenomenological estimates, a concrete realization of this scenario using Witten's four dimensional topological gravity will be used. In this model, the CMB power spectrum can be estimated by certain conformal anomaly coefficients. A qualitative prediction of this phase is the absence of tensor modes in cosmological fluctuations.