Fri, 30 Oct 2026

11:00 - 12:00
L4

Growth accelerations are the key to the niche

Dr Oliver Meacock
(School of Biosciences University of Sheffield)
Abstract
The relationship between organisms and their environment is the heart of ecology. Microbes exemplify this relationship, modifying their shared chemical environment to engage in cooperative exchanges, kill each other with deadly toxins and compete over limited resources. Understanding the environment-organism coupling - the topic of niche theory - is therefore key to manipulating microbiota. 
Much of our understanding of the niche comes from rate-based frameworks. For example, resource competition is typically described using the logistic equation, which states that growth rates tend to zero as population densities increase toward their carrying capacity. The mechanisms driving these population dynamics are implicit, with the underlying resource dynamics abstracted out of the model.
Starting from mechanistically-explicit consumer-resource models, I will argue that growth accelerations (resulting from the combination of the timescales of both environmental and population dynamics) provide a more powerful understanding of the niche than rate-based perspectives. Exploiting an exact homology between the equations describing consumer-resource systems and the generalised Lotka-Volterra (gLV) model, I will demonstrate that basic concepts such as density-dependence and context-dependencies of interactions can be accurately captured with an accelerational lens. Moreover, derived frameworks such as Modern Coexistence Theory (MCT) can be readily translated into an accelerational form, enabling their integration into mechanistic frameworks. Finally, I will exploit this homology to explain how obligatory mutualistic exchanges between bacteria can be reconciled with ecosystem stability, contrasting with predictions from the gLV model.


 

Fri, 16 Oct 2026

11:00 - 12:00
L4

Emergent phenomena in protein complexes out of equilibrium: from topologically-protected states to computation

Dr Jaime Agudo-Canalejo
(Dept of Physics & Astronomy UCL)
Abstract
Protein complexes, typically made up of a small number of identical subunits, are very common in biology. These subunits can additionally undergo post-translational modifications, such as phosphorylation and dephosphorylation, resulting in a high dimensional state space for the protein complex. Importantly, such modifications are catalyzed by enzymes that are driven out of equilibrium by the consumption of a fuel such as ATP. I will discuss, from a theoretical perspective, how very simple enzyme-catalyzed operations at the single subunit level can result in emergent behaviour at the level of the entire protein complex. First, I will discuss how topologically-protected edge currents emerge and become enhanced in arbitrarily high-dimensional stochastic systems representing the state of the complex, extending previous results for two-dimensional stochastic systems [1]. Second, I will discuss how enzymes that act on a subunit in a context-dependent manner provide a molecular implementation of stochastic cellular automata,  that can be exploited to engineer molecular-scale computing devices, such as an error-tolerant memory or a finite-state machine [2].
 
[1] E. Tang, J. Agudo-Canalejo, and R. Golestanian, Phys. Rev. X 11, 031015 (2021)
[2] J. Kocka, K. Husain, and J. Agudo-Canalejo, PRX Life 4, 013036 (2026)
Fri, 19 Jun 2026
13:00
L4

Simplicial Novikov Homology

Vidit Nanda
Abstract

I will describe a circle-valued Morse theory for simplicial complexes. The central objects of study are partial matchings which admit certain zigzag cycles; these cyclic matchings lift canonically to acyclic matchings on the infinite cyclic cover of the underlying simplicial complex. From the lifted acyclic matchings, we obtain a finitely generated Morse chain complex defined over the Novikov ring, which consists of power series in one variable with finite negative support. We then establish a quasi-isomorphism between this Morse-Novikov complex and the simplicial chain complex of the cyclic cover, duly completed over the Novikov ring. As a pleasant consequence, we can define new computable invariants to detect (obstructions to) the fiberedness of tame knots.

Wed, 24 Jun 2026

11:00 - 13:00
L4

Wasserstein Limits for Empirical Measures of Markov Processes

Fengyu Wang
(University of Swansea)
Abstract

In this talk we summary some recent progress on limit theorems for the Wasserstein distance of empirical measures of Markov processes. For symmetric diffusion processes on Riemannian manifold possibly with reflecting or killing boundary, the sharp convergence rate is derived with renormalization limit formulated by using the spectrum of the generator. Moreover, a general framework is established to estimate the convergence rate in Wasserstein distance of empirical measures for ergodic Markov processes.

Wed, 10 Jun 2026
11:00
L4

A short course on Rough Stochastic Differential Equations (RSDEs) and Applications (Lecture 3/3)

Prof. Peter Friz
(TU Berlin)
Abstract

Recent advances at the interface of stochastic analysis, rough path theory, stochastic filtering, stochastic control, and mean-field systems have led to a rapidly developing framework for analyzing stochastic dynamics conditioned on common/observation noise. This mini course  will survey how rough stochastic differential equations, introduced in 2021 by A. Hocquet, K. Lê and the speaker, lead to a unifying perspective across several areas of applied probability. (Additional coauthors include F. Bugini, J. Dause, W. Stannat, H. Zhang and P.Zorin-Kranich).

 

 

 

Further Information

This mini course will develop in three lectures on the Wednesdays 20/5, 3/6, 10/6 at 11am in L4

Wed, 03 Jun 2026
11:00
L4

A short course on Rough Stochastic Differential Equations (RSDEs) and Applications (Lecture 2/3)

Prof. Peter Friz
(TU Berlin)
Abstract

Recent advances at the interface of stochastic analysis, rough path theory, stochastic filtering, stochastic control, and mean-field systems have led to a rapidly developing framework for analyzing stochastic dynamics conditioned on common/observation noise. This mini course  will survey how rough stochastic differential equations, introduced in 2021 by A. Hocquet, K. Lê and the speaker, lead to a unifying perspective across several areas of applied probability. (Additional coauthors include F. Bugini, J. Dause, W. Stannat, H. Zhang and P.Zorin-Kranich).

 

 

Further Information

This mini course will develop in three lectures on the Wednesdays 20/5, 3/6, 10/6 at 11am in L4

Wed, 20 May 2026
11:00
L4

A short course on Rough Stochastic Differential Equations (RSDEs) and Applications (Lecture 1/3)

Prof. Peter Friz
(TU Berlin)
Abstract
Recent advances at the interface of stochastic analysis, rough path theory, stochastic filtering, stochastic control, and mean-field systems have led to a rapidly developing framework for analyzing stochastic dynamics conditioned on common/observation noise. This mini course  will survey how rough stochastic differential equations, introduced in 2021 by A. Hocquet, K. Lê and the speaker, lead to a unifying perspective across several areas of applied probability. (Additional coauthors include F. Bugini, J. Dause, W. Stannat, H. Zhang and P.Zorin-Kranich).
 



 

Further Information

This mini course will develop in three lectures on the Wednesdays 20/5, 3/6, 10/6 at 11am in L4

Thu, 11 Jun 2026
15:00
L4

Von Neumann Equivalence Rigidity

Daniel Drimbe
(University of Iowa)
Abstract
The notion of measure equivalence for discrete groups was introduced by Gromov as a measurable counterpart to the geometric notion of quasi-isometry. Measure equivalence is closely connected to the theory of II_1 factors: if groups G and H are measure equivalent, then they admit free ergodic probability measure preserving actions whose associated von Neumann algebras are stably isomorphic. Also, two groups G and H are said to be W*-equivalent if their group von Neumann algebras are stably isomorphic.  
 
More recently, an even coarser equivalence relation between groups, termed von Neumann equivalence, was introduced by Ishan, Peterson, and Ruth; it is implied by both measure equivalence and W*-equivalence. In joint work with Stefaan Vaes, we established a unique factorization theorem for direct products of hyperbolic groups up to von Neumann equivalence.
Fri, 15 May 2026
13:00
L4

Geometry and excluded-volume effects in particle systems

Maria Bruna
(Oxford University)
Abstract

I will discuss stochastic systems of interacting particles with non-overlapping constraints, which give rise to so-called excluded-volume interactions. The aim is to derive effective macroscopic equations governing the evolution of particle densities from the underlying microscopic dynamics. When particles possess nontrivial size or shape, geometric constraints become essential: they complicate the coarse-graining process and strongly influence the emergent behaviour of the system. I will present two representative examples, hard spheres and infinitely thin needles, highlighting how geometry enters the macroscopic description

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