Thu, 30 Jan 2025

12:00 - 13:00
L3

Spontaneous shape transformations of active surfaces

Alexander Mietke
(Department of Physics)
Further Information

Alexander Mietke is a theoretical physicist working on active and living matter. He frequently collaborates with experimentalists who study processes at the cell, tissue and organism scale to identify minimal physical principles that guide these processes. This often inspires new theoretical work on topics in non-equilibrium soft matter physics, more broadly in the self-organization of mechanical and chemical patterns in active matter, the emergent shape dynamics of membranes and active surfaces, liquid crystals in complex geometries, chirality in active systems, as well as in developing coarse-graining and inference approaches that are directly applicable to experimental data. 

Abstract

Biological matter has the fascinating ability to autonomously generate material deformations via intrinsic active forces, where the latter are often present within effectively two-dimensional structures. The dynamics of such “active surfaces” inevitably entails a complex, self-organized interplay between geometry of a surface and its mechanical interactions with the surrounding. The impact of these factors on the self-organization capacity of surfaces made of an active material, and how related effects are exploited in biological systems, is largely unknown.

In this talk, I will first discuss general numerical challenges in analysing self-organising active surfaces and the bifurcation structure of emergent shape spaces. I will then focus on active surfaces with broken up-down symmetry, of which the eukaryotic cell cortex and epithelial tissues are highly abundant biological examples. In such surfaces, a natural interplay arises between active stresses and surface curvature. We demonstrate that this interplay leads to a comprehensive library of spontaneous shape transformations that resemble stereotypical morphogenetic processes. These include cell-division-like invaginations and the autonomous formation of tubular surfaces of arbitrary length, both of which robustly overcome well-known shape instabilities that would arise in analogue passive systems.

 

 

Thu, 23 Jan 2025

12:00 - 13:00
L3

Optimal design of odd active solids

Anton Souslov
(University of Cambridge)
Further Information

Anton Souslov is an Associate Professor of Theoretical Statistical Physics working on the theory of soft materials, including mechanical metamaterials, active matter, topological states, and polymer physics.

Abstract

Active solids consume energy to allow for actuation and shape change not possible in equilibrium. I will first introduce active solids in comparison with their active fluid counterparts. I will then focus on active solids composed of non-reciprocal springs and show how so-called odd elastic moduli arise in these materials. Odd active solids have counter-intuitive elastic properties and require new design principles for optimal response. For example, in floppy lattices, zero modes couple to microscopic non-reciprocity, which destroys odd moduli entirely in a phenomenon reminiscent of rigidity percolation. Instead, an optimal odd lattice will be sufficiently soft to activate elastic deformations, but not too soft. These results provide a theoretical underpinning for recent experiments and point to the design of novel soft machines.

 

 

Mon, 16 Jun 2025
15:30
L3

Kinetic Optimal Transport

Prof Jan Maas
(IST Austria)
Abstract

We present a kinetic version of the optimal transport problem for probability measures on phase space. The central object is a second-order discrepancy between probability measures, analogous to the 2-Wasserstein distance, but based on the minimisation of the squared acceleration. We discuss the equivalence of static and dynamical formulations and characterise absolutely continuous curves of measures in terms of reparametrised solutions to the Vlasov continuity equation. This is based on joint work with Giovanni Brigati (ISTA) and Filippo Quattrocchi (ISTA).

Mon, 02 Jun 2025
15:30
L3

Variance renormalisation of singular SPDEs

Dr Máté Gerencsér
(TU Wien )
Abstract

Scaling arguments give a natural guess at the regularity condition on the noise in a stochastic PDE for a local solution theory to be possible, using the machinery of regularity structures or paracontrolled distributions. This guess of ``subcriticality'' is often, but not always, correct. In cases when it is not, a the blowup of the variance of certain nonlinear functionals of the noise necessitates a different, multiplicative renormalisation. This led to a general prediction and the first results in the case of the KPZ equation in [Hairer '24]. We discuss recent developments towards confirming this prediction. Based on joint works with Fabio Toninelli and Yueh-Sheng Hsu.

Mon, 19 May 2025
15:30
L3

Quantitative Convergence of Deep Neural Networks to Gaussian Processes

Prof Dario Trevisan
(University of Pisa)
Abstract

In this seminar, we explore the quantitative convergence of wide deep neural networks with Gaussian weights to Gaussian processes, establishing novel rates for their Gaussian approximation. We show that the Wasserstein distance between the network output and its Gaussian counterpart scales inversely with network width, with bounds apply for any finite input set under specific non-degeneracy conditions of the covariances. Additionally, we extend our analysis to the Bayesian framework, by studying exact posteriors for neural networks, when endowed with Gaussian priors and regular Likelihood functions, but we also provide recent advancements in quantitative approximation of trained networks via gradient descent in the NTK regime. Based on joint works with A. Basteri, and A. Agazzi and E. Mosig.

Mon, 12 May 2025
15:30
L3

TBC

TBC
Mon, 05 May 2025
15:30
L3

Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions

Dr. Ana Djurdjevac
(Freie Universität Berlin)
Abstract

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with Itô noise, for particle systems exhibiting mean-field interactions both in the drift and the noise terms. Global existence and uniqueness of solutions to the corresponding SPDEs are established via the variational approach to SPDEs. To estimate the weak error, we employ the Kolmogorov equation technique on the space of probability measures. This work generalizes previous results for independent Brownian particles — where Laplace duality was used. In particular, we recover the same weak error rate as in that setting. This paper builds on joint work with X. Ji., H. Kremp and  N.  Perkowski.

Mon, 10 Mar 2025
15:30
L3

Recent progress on quantitative propagation of chaos

Dr Daniel Lacker
(Columbia University)
Abstract

When and how well can a high-dimensional system of stochastic differential equations (SDEs) be approximated by one with independent coordinates? This fundamental question is at the heart of the theory of mean field limits and the propagation of chaos phenomenon, which arise in the study of large (many-body) systems of interacting particles. This talk will present recent sharp quantitative answers to this question, both for classical mean field models and for more recently studied non-exchangeable models. Two high-level ideas underlie these answers. The first is a simple non-asymptotic construction, called the independent projection, which is a natural way to approximate a general SDE system by one with independent coordinates. The second is a "local" perspective, in which low-dimensional marginals are estimated iteratively by adding one coordinate at a time, leading to surprising improvements on prior results obtained by "global" arguments such as subadditivity inequalities. In the non-exchangeable setting, we exploit a surprising connection with first-passage percolation.

Mon, 03 Mar 2025
15:30
L3

Spin glasses with multiple types

Dr Jean-Christophe Mourrat
(ENS Lyon)
Abstract

Spin glasses are models of statistical mechanics in which a large number of elementary units interact with each other in a disordered manner. In the simplest case, there are direct interactions between any two units in the system, and I will start by reviewing some of the key mathematical results in this context. For modelling purposes, it is also desirable to consider models with more structure, such as when the units are split into two groups, and the interactions only go from one group to the other one. I will then discuss some of the technical challenges that arise in this case, as well as recent progress.

Mon, 24 Feb 2025
15:30
L3

Sharp bounds for parameter-dependent stochastic integrals

Dr Sonja Cox
(University of Amsterdam)
Abstract

We provide sharp bounds in the supremum- and Hölder norm for parameter-dependent stochastic integrals. As an application we obtain novel long-term bounds for stochastic partial differential equations as well as novel bounds on the space-time modulus of continuity of the stochastic heat equation. This concerns joint work with Joris van Winden (TU Delft).

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