Past

Clean markings on surfaces were a key component in Masur and Minsky's hierarchy machinery, which proved to be a powerful tool in the study of mapping class groups. In this talk, I will briefly discuss the connection between clean markings and hierarchies, and I will explain how a natural analogue can be constructed for finite-type Artin groups.

We present a new dynamical way of establishing local laws for sparse random matrices, the Bernoulli flow method. It is based on a Markovian jump process, where the entries of the matrix jump independently from 0 to 1 at rate one. As an application, we show optimal (up to a constant) isotropic delocalisation for bulk eigenvectors of Erdös-Rényi graphs with edge probability p \geq (log N)^2/N. In the same regime, we obtain a local law with optimal (up to a constant) error bounds. Joint work with Antti Knowles.

Ken Brown reviews the history of the question in the title, and describes some recent progress towards answering it, including the identification of a "minimal criminal". The new material is joint work with Jason Bell (Waterloo) and Toby Stafford (Manchester).

Many systems in the natural sciences and beyond exhibit complex relational structure that changes over time. Social networks evolve as relationships change, traffic patterns vary throughout the day, and protein–protein interactions shift with cellular conditions. Learning these dynamics from data is a challenging problem. A recent approach in this area, Graph Neural Controlled Differential Equations, extends Neural CDEs from paths on Euclidean domains to paths on graph domains. In this talk, we discuss an extension of this framework that respects the geometry of the underlying set and is equivariant to permutations of the node ordering. We will discuss empirical advantages of this modification, as well as benefits of the formulation as a continuous-time model. 

Schwinger’s Closed Time Path formalism is the basis of modern treatments of cosmological field theories, hydrodynamics and open quantum systems. Its application to gauge theories at finite temperature is well studied, relying on KMS boundary conditions and complex-time contours. By contrast the discussion of gauge theories such as Yang-Mills out of equilibrium has been less well developed, in large part due to a lack of development of how to treat gauge issues and Faddeev-Popov-DeWitt ghosts on the CTP. I will show how to construct the CTP in the BRST formalism, where a single diagonal copy of BRST symmetry survives, and how to implement the boundary conditions for ghosts for arbitrary initial physical states. As an illustration I will discuss how Hard-thermal-loop EFTs can be viewed as open quantum systems, and how to construct an open EFT for a gauge theory in a Higgs phase. 

The cylindrical snap-fit is a ubiquitous fastening method that is both simple to manufacture and assemble, and yet secure. It consists of a partial cylindrical shell that ‘snaps’ onto a cylindrical object. We build on previous work to describe the mechanics of the cylindrical snap-fit as a naturally curved thin elastic shell placed atop a rigid cylinder; we investigate the shell's behaviour when subject to a point force pushing it onto or pulling it off the cylinder. We classify the possible contact regimes according to whether the shell has a nonzero lifting capacity. We term situations with lifting capacity ‘grip-fits’ and show that this includes both the snap-fit and a ‘stick-fit’ regime, which allows lifting despite not having the characteristic ‘snap’. We show that the different regimes may be characterized entirely by the shell/cylinder geometry and the coefficient of friction. We then consider different metrics for the lifting performance in the grip-fit regime. Our analysis reveals the trade-offs between assembly force, disassembly force, lifting force, and clamping force, providing design principles for secure lifting, easy detachment, and safe handling of fragile objects.

I will discuss some general PDE techniques, for example ``extended substitute kernel'' and ``linearized gluing'', and their application to various gluing constructions in Differential Geometry.

This paper advances the theory of \textit{Collective Finance}, as developed in \cite{BDFFM26}, \cite{DFM25} and \cite{F25}. Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents’ preferences and collective pricing measures. The framework applies to both continuous and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent’s indirect utility.

Fox’s trapezoidal conjecture, proposed in 1962, states that the absolute values of the coefficients of the Alexander polynomial of an alternating knot form a trapezoidal sequence: they strictly increase, possibly plateau, and then strictly decrease. In this talk, I will discuss recent progress on the conjecture, based on joint work with András Juhász and Tamás Kálmán. In particular, we prove the conjecture for diagrammatic plumbings of special alternating links and obtain partial results for alternating three-braid closures

Professor Nicolas Loizou will talk about: 'Extragradient Methods for Modern Machine Learning: New Convergence Guarantees, Step-Size Rules, and Stochastic Variants'

Extragradient methods are a fundamental class of algorithms for solving min-max optimization problems and variational inequalities. While the classical theory is largely developed under smoothness and other relatively restrictive assumptions, many problems arising in modern machine learning call for analysis in weaker regularity regimes and in stochastic large-scale settings. In this talk, we present new convergence results for deterministic and stochastic extragradient methods beyond the classical framework. In particular, we establish convergence guarantees under the (L0, L1)-Lipschitz condition and derive new step-size rules that expand the range of provably convergent regimes. We also introduce Polyak-type step sizes for deterministic and stochastic extragradient methods, leading to adaptive variants with favourable theoretical properties and practical performance. Our results focus primarily on monotone problems, with extensions to selected structured non-monotone settings. We conclude with numerical experiments that illustrate the theory and the empirical behaviour of the proposed methods.

Much recent research has gone into understanding the first order theory of II1 factors. Very recently, Peterson released a preprint which develops deformation rigidity in the ultrapower setting. His techniques give many explicit examples of non-isomorphic ultrapowers for natural families of II1 factors. In this talk, I will introduce some of Peterson's techniques and results, including an analogue of amenability in the ultrapower setting and the interplay between property T and malleable deformations.

I will report on a joint work in progress with Egor Morozov proving that for generic elements in several families of Laplace-type operators invariant under a finite group action, all eigenspaces are irreducible representations. In particular, for the case of Laplace-Beltrami operators, this provides a natural generalization of Uhlenbeck's result on the generic simplicity of the spectrum to the equivariant setting. Moreover, this extends previous work of Zelditch and solves the finite group case of a well-known question raised by Guillemin and Yau. For Schrödinger operators, our results rigorously underpin the notion of accidental degeneracy for certain quantum-mechanical systems with finite symmetry. Our approach involves modern methods of equivariant transversality which we extend to higher dimensions.

For any manifold, we can assign its mapping class group, that is, the group of its diffeomorphisms modulo isotopies. Although such a group can be studied for manifolds of any dimension, the mapping class groups of surfaces draw special attention. They are isomorphic to the outer automorphism groups of $\pi_1(S)$ and have many properties similar to lattices in semisimple Lie groups, as well as connections with the theory of moduli of curves.

One of the most important parts of the research on mapping class groups is the study of their representation. In particular, in the general situation, we still don't know if they have a faithful representation into $\operatorname{GL}_n(\mathbb{C})$.

In my talk, I will show basic facts about mapping class groups and briefly describe a few known methods for constructing their representations and discuss their properties. In particular, I will present recent results classifying low-dimensional representations of the mapping class group.

Many cells exhibit exponential growth not only at the population level but also at the single-cell level. However, single-cell growth rates fluctuate over time. We distinguish between two conceptually distinct sources of growth rate fluctuations: intrinsic continuous fluctuations resulting from intracellular processes, and fluctuations that originate at division events, which we refer to as kicks. We use a simple model to describe single-cell growth and identify the signatures of continuous noise and division kicks. To infer the true biological behavior reliably from experiments, it is crucial to account for measurement noise. We derive analytical expressions for the statistics of meaningful observables, accounting for continuous fluctuations, division kicks, and measurement noise. Importantly, we find that ignoring measurement noise can lead to incorrect biological conclusions. Our results provide insights into how different sources of growth rate variability and measurement errors influence observed cell size dynamics, offering an interpretable framework for analyzing experimental data in cellular biology. 

Professor Luis Nunes Vicente will talk about 'Reducing Sample Complexity in Stochastic Derivative-Free Optimization via Tail Bounds and Hypothesis Testing';

We introduce and analyze new probabilistic strategies for enforcing sufficient decrease conditions in stochastic derivative-free optimization, with the goal of reducing sample complexity and simplifying convergence analysis. First, we develop a new tail bound condition imposed on the estimated reduction in function value, which permits flexible selection of the power used in the sufficient decrease test, q in (1,2]. This approach allows us to reduce the number of samples per iteration from the standard O(delta^{−4}) to O(delta^{-2q}), assuming that the noise moment of order q/(q-1) is bounded. Second, we formulate the sufficient decrease condition as a sequential hypothesis testing problem, in which the algorithm adaptively collects samples until the evidence suffices to accept or reject a candidate step. This test provides statistical guarantees on decision errors and can further reduce the required sample size, particularly in the Gaussian noise setting, where it can approach O(delta^{−2-r}) when the decrease is of the order of delta^r. We incorporate both techniques into stochastic direct-search and trust-region methods for potentially non-smooth, noisy objective functions, and establish their global convergence rates and properties. 

This is joint work with Anjie Ding, Francesco Rinaldi, and Damiano Zeffiro.

Quantum magic quantifies the computational resources needed for quantum operations that cannot be easily performed classically. This requires unitaries, known as "Non-Clifford gates", that map Pauli operators to outside the Pauli group. I will first provide a pedagogical introduction to these concepts following [arXiv:quant-ph/9807006] and then summarise the recent results of [arXiv:2604.14271] constructing non-Clifford gates from path integrals in Chern-Simons theories, whose magic-generating properties are determined by the algebraic data of the topological field theory.

India Marsden will talk about: 'Expanding the definition of a finite element: groups, complexes and software'

The finite element method is a flexible framework to discretise and solve partial differential equations which has been applied to many problems across science and engineering, for example weather modelling and battery design. A core feature of the success of the finite element method, the Ciarlet definition of the components of a finite element has been used for many years. The experience of these decades (and the subsequent implementations) has exposed several key deficiencies. In particular, Ciarlet’s definition is missing information about the global continuity of the mesh and how the degrees of freedom map to each other under the relative orientation of the mesh entities. This information is necessary to implement the finite element method, leaving scope for a new definition.

We propose a new definition to handle these issues and incorporate the constantly growing landscape of new elements. This new definition also aims to encapsulate more information about the elements, such as the symmetries, incorporating ideas from Group Theory. Through this work, we hope to produce a robust, thorough definition that allows processes such as implementation-independent serialisation of finite element data.

Alongside this new definition, we will discuss the new software FUSE, which provides a domain specific language for the definition and enables elements defined in this way to be used in high performance simulation using the finite element package Firedrake. 

Core-annular flows are often proposed to reduce frictional losses in industrial pipeline transport processes. Traditionally, a low-viscosity lubricating film is placed around a more viscous core to reduce the drag on the core. However, maintaining stable pipelining, where the core and the lubricant remain separated has proved challenging.
In this talk we present an alternative approach using three-layer, horizontal core-annular pipe flow, in which two fluids are separated by a deformable elastic solid. In the experiments, an elastic solid created by an in-situ chemical reaction maintains the separation of the core and annular fluids. Corrugations of the elastic interface are observed and stable pipelining, where the elastic shell created separating the two fluids remains intact, is successfully demonstrated even when the core fluid is buoyant. We also develop a theoretical model combining lubrication theory for the fluids with standard shell theory for the elastic solid, to predict the buckling states resulting from radial compression of the shell.
The self-sculpting of the shell by buckling cannot by itself generate hydrodynamic lift owing to symmetry in the direction of flow. Instead, we demonstrate that hydrodynamic lift can be achieved by other elastohydrodynamic effects, when that symmetry becomes broken during the bending of the shell.

Abstract elementary classes (AECs) provide an extension of first order model theory in which we can still attempt a classification theory. The question of when limit models (a kind of surrogate for saturated models for AECs) are isomorphic has connections to important open problems in AECs, such as Shelah's categoricity conjecture. Most work in this area is towards 'positive' results - that is, showing limit models are isomorphic. The question of when limit models are not isomorphic is less explored.

In this talk we give a full characterisation of the spectrum of limit models under reasonable assumptions in a stable AEC - that is, describe completely which limit models are isomorphic and which are not. In particular this applies to the first order stable setting. Given time we will discuss applications, a more general result in the 'positive' direction, and touch on a recent result which says that all high cofinality limit models are disjoint amalgamation bases. Based largely on joint work with Marcos Mazari-Armida.

I will give a short introduction to knotted surfaces in 4-space and discuss some recent developments. First, I will give some motivation, briefly discuss methods for distinguishing knotted surfaces (such as the Khovanov TQFT), and talk about connections with 4-manifolds. Then, I will introduce Artin’s spinning construction, variants of which were defined by Zeeman, Fox, Litherland, and Price-Roseman. Finally, I will specialize to knotted RP^2’s in S^4 and construct a knotted RP^2 in S^4 that cannot be decomposed as the connected sum of an unknotted RP^2 and a knotted S^2. This last result on RP^2’s is joint with Hughes, Kim, and Miller.

Two hundred years ago, Robert Brown observed the statistics of the motion of grains of pollen in water. It took almost one hundred years for Einstein and others to develop an effective theory describing this motion as that of a random walker. In this talk, I will challenge a key implication of this well established theory. When studying systems with very large numbers of particles diffusing together, I will argue that the Einstein random walk theory breaks down when it comes to predicting the statistical behavior of extreme particles—those that move the fastest and furthest in the system. In its place, I will describe a new theory of extreme diffusion which captures the effect of the hidden environment in which particles diffuse together and allows us to interrogate that environment by studying extreme particles. I will highlight one piece of mathematics that led us to develop this theory—a non-commutative binomial theorem—and hint at other connections to integrable probability, quantum integrable systems and stochastic PDEs.

By using the ratios conjecture, we study the asymptotic behaviour of the mean square of long truncations of the Dirichlet series for \(\bigl(\zeta'/\zeta\bigr)^{k}\) near the critical line. We explain the connection between this problem and the variance of the convoluted von Mangoldt function in short intervals. We obtain an explicit leading piecewise polynomial in the length parameter which is consistent with the microscopic-shift results of Fan Ge. We also discuss other RMT results for moments of the logarithmic derivative of characteristic polynomials and their relation to trace-average problems over U(N). 

The Poisson boundary of a probability measure on a countable group is a probability space endowed with a stationary group action that captures the asymptotic behaviour of the associated random walk. Since its introduction by Furstenberg in the 1960s, the study of Poisson boundaries and stationary actions has become a powerful tool for understanding geometric and algebraic properties of groups.

In this talk, I will discuss connections between stabilizers of stationary actions, in particular, those arising from the Poisson boundary, and the C*-simplicity of the associated reduced group C*-algebra. I will also address the (seemingly unrelated) problem of realizing different Poisson boundaries on a common underlying topological model. The talk is based on joint work with Anna Cascioli and Martín Gilabert Vio, and with Josh Frisch.

I will discuss some recent and ongoing works on DT invariants of quivers associated to local Calabi-Yau 3-folds, and on conjectural DT4 invariants of local Calabi-Yau 4-folds, in the spirit of "physical mathematics" --- physics computations leading to potentially interesting mathematics. In the CY3 case, I will explain a recently proposed covering formula for quiver DT invariants [arXiv:2603.15334], wherein the DT invariants of some quiver Q are expressed as a sum of DT invariants of a "larger" Galois-covering quiver. I will aim to explain our partial, physics-based derivation of the covering formula. In the CY4 case, I will look at graded quivers associated to exceptional collections of coherent sheaves on local CY 4-folds and discuss what their "DT4 invariants" should look like according to our current physics intuition. These DT4 invariants are generally rational functions of various equivariant parameters of the local geometry.

A Groethendieck pair consists of a finitely generated residually finite group G, with a finitely generated subgroup N such that the inclusion N -> G induces an isomorphism of profinite completions. I will present a new method to produce Groethendieck pairs with peculiar properties, using iterated group theoretic Dehn filling on hyperbolic virtually special groups. Such pairs witness the profinite non-invariance of quasimorphisms, stable commutator length, and actions on hyperbolic spaces and finite-dimensional CAT(0) cube complexes.

Researchers across disciplines rely on clustering to uncover meaningful patterns in noisy similarity data. Standard two-step pipelines reduce noise before clustering, introducing arbitrary parameters that often produce misleading structure. We unite noise reduction and clustering through Bayesian community detection, using information theory to balance model complexity and fit. This one-step approach automatically determines the number of clusters, avoids detecting patterns in random data, and makes full use of limited samples. Testing on synthetic benchmarks and gene expression data shows the approach yields more reliable and interpretable results than widely used alternatives, improving data-driven discovery across scientific disciplines where samples are limited or expensive.

In recent work with Jef Laga, we adapt a construction of Slodowy to build families of algebraic curves in graded Lie algebras (this generalizes earlier work of Thorne). This required an understanding of nilpotent orbits in Vinberg representations, and it raised some interesting questions about these orbits that we were able to answer. Our motivation comes from proofs in arithmetic statistics in which orbits in certain representations are used to parametrize rational points on curves. In this talk, Beth Romano gives an introduction to these ideas via examples.

An anomaly for a global symmetry G says “no”. It stops us from driving the theory to a trivially gapped phase while preserving G. Relatedly, it also prevents us from constructing boundary conditions that preserve G, without adding additional boundary degrees of freedom.

Does a vanishing anomaly say “yes”? It has been proposed that both of these statements can be upgraded to “if and only if” statements. We probe both of these proposals in the simplest theory in which they are non-trivial: the theory of two Dirac fermions in two dimensions, with G chiral. 

Along the way, we will construct all self-duality defects of two free Weyl fermions that arise from gauging an invertible symmetry. These play a central role then in the construction of symmetric boundaries for two Dirac fermions.

We review recent developments in the theory of weak convergence of pde-constrained sequences. We consider the weak lower semicontinuity problem along weakly convergent A-free sequences, where A is a linear pde system of constant rank, and provide improvements to the A-quasiconvexity theory of Fonseca--Müller and the compensated compactness theory of Murat--Tartar. Special emphasis will be placed on concentration effects of weak convergence, in particular by presenting the resolution of a question due to Coifman--PL Lions--Meyer--Semmes and a recent connection between quasiconcavity and higher integrability, generalizing an old result of Müller. Time permitting, we will present the characterization of Young measures generated by A-free sequences by duality with A-quasiconvex functions and recent advances in the regularity theory for A-quasiconvex variational problems. 

Joint work with Christopher Irving, André Guerra, Jan Kristensen, Zhuolin Li, and Matthew Schrecker.

The Lindelöf hypothesis is known to be weaker than the Riemann hypothesis and one way to assess the difference in their strength is to consider what can be said about the zeroes of the zeta function under the assumption of the Lindelöf hypothesis. Viewing this question in the context of zero density estimates, we prove that $N(\sigma,T) \leq T^{\frac{4(5-6\sigma)}{3(3-2\sigma)} + o(1)}$. This improves the currently known estimate conditional on the Lindelöf hypothesis, $N(\sigma,T) \leq T^{2(1-\sigma)+o(1)}$ based on the mean value theorem, for $\sigma$ near $3/4$.

The talk gives some survey about recent applications of finitely additive measures to Lebesgue integrable functions. After a short introduction to such measures and related integrals, purely finitely additive measures are of particular interest. Special examples are given and, as a first application, an integral representation for the precise representative of Lebesgue integrable functions is provided. Then, based on a general approach to traces, a new version of the Gauss-Green formula is introduced, where neither a pointwise trace nor a pointwise normal is needed on the boundary. This allows e.g. the treatment of inner boundaries and of concentrations on the boundary. A second boundary integral is used to handle singularities that hadnot been accessible before. Finally, weak versions of differentiability for Lebesgue integrable functions are discussed, a mean value formula for a class of Sobolev functions is given, and a new approach to the generalized derivatives in the sense of Clarke is provided.

Weighted flag varieties are generalizations of flag varieties and weighted projective spaces.  Although they are not usually homogeneous varieties, they are orbifolds and admit a torus action with isolated fixed points, and like ordinary flag varieties, their equivariant cohomology admits a Schubert basis.  This talk will be an introduction to weighted flag varieties, and will also discuss positivity.  Abe and Matsumura proved that the equivariant cohomology of weighted Grassmannians has a positivity property analogous to that for ordinary (non-weighted) flag varieties.  We prove a strengthened version of this result for arbitrary weighted flag varieties, along the way providing a geometric interpretation of the weighted roots of Abe and Matsumura.  This is joint work with Scott Larson.

The dynamic nature of first order methods can be interpreted by means of continuous time models. In this survey talk, we explain how physical concepts like acceleration, inertia or momentum have been used to improve the performance of convex optimization algorithms. 

We give special attention to the historical evolution of complexity results, especially in the form of convergence rates, under the light of this connection. We also discuss different ways in which acceleration schemes can be applied when the smoothness or strong convexity parameters are unknown, and how these ideas extend to saddle point and constrained problems. 

Given a cyclic subgroup G of GL(2,C) acting on C^2, it was first noticed by Wunram in the 80s that there is a correspondence between certain special representations of G and the exceptional curves appearing in the minimal resolution Y of the surface singularity C^2/G. In modern terms, this was reformulated by Ishii and Ueda as the existence of a fully faithful functor from the derived category of sheaves of Y to the G-equivariant derived category of C^2. In this talk, I will describe a mirror symmetric interpretation of this which exhibits the fully faithful inclusion in algebraic geometry as a sequence of positive Lefschetz stabilizations in symplectic geometry.

Fersztand, Jacquard, Nanda, and Tilmann ('24) introduced the Skyscraper Invariant, a filtration of the classical rank-invariant, for multiparameter persistence modules. It is defined by considering the Harder-Narasimhan (HN) filtration of the module along a special set of stability conditions.

This talk will begin with a post-hoc motivation for considering stability conditions on persistence modules. To compute an approximation of the Skyscraper Invariant we present a technique which, exploiting the geometry of low-dimensional bifiltrations, lets us perform a brute-force computation. We compare it against Cheng's algorithm [Cheng24] which can compute HN filtrations of arbitrary acyclic quiver representations in polynomial time in the total dimension.

To avoid unnecessary recomputation in our algorithm, we ask for which stability conditions the HN filtrations are equivalent. This partition of the space of stabililty conditions is called the wall-and-chamber structure. We show that for a finitely presented d-parameter module it is given by the lower envelopes of a set of multilinear polynomials of degree d-1. For d=2 it is then easy to compute this, enabling a faster algorithm to compute the Skyscraper Invariant up to arbitrary accuracy. As a proof of concept for data analysis, we use it to compute a filtered version of the Multiparameter Landscape for large modules from real world data.

The Springer correspondence parameterises the irreducible representations of the Weyl group of a complex semisimple Lie algebra by nilpotent orbits. A key ingredient in the construction is the convolution operation, which appears in various forms throughout geometric representation theory. In this talk, we'll introduce the geometry of the Springer resolution, describe the convolution operation, and illustrate how it gives rise to a geometric construction of Weyl group representations.

The characterisation of the physics of the M5-brane remains an important open problem in string theory. While the superconformal field theory that resides on a planar M5-brane in flat space is poorly understood, other configurations involving M5-branes wrapped on certain manifolds have well-known superconformal field theory descriptions, including N=2 class S field theories. In this talk, I will use new methods based on exceptional generalised geometry to describe the gravity duals of class S field theories, compute a universal sector of their light-operator spectrum, and provide, for the first time, a holographic match of their superconformal index.

Heterogeneity is a fundamental feature of biological systems. Oncology is one of the fields in which this feature is most evident, as its key players are characterised by mutability, plasticity, and often “uncontrolled” dynamics. Whether heterogeneity arises from spatial structure, environmental variability, or cellular traits, effective therapeutic strategies must explicitly account for it in order to eradicate or control tumours.

From a modern perspective, this requires balancing the hit-hard / keep-it-sensitive trade-off, while also considering not only medical but also broader patient-related side effects of treatments. Contemporary medicine is increasingly exploring ways to exploit the very characteristics that have historically made cancer so dangerous, turning them into potential advantages for therapy.

The multiscale nature of tumour systems, together with the need to predict the combined effects of multiple, non-parallelisable processes, makes the development of optimised mathematical tools particularly compelling. Such tools can address questions that are both scientifically challenging and highly relevant from a clinical and humanitarian perspective.

In this seminar, we will analyse tumour masses from a structured population perspective, focusing on the role of heterogeneity in shaping therapeutic strategies. We will first discuss how heterogeneity in phenotypic composition and nutrient distribution influences the eco-evolutionary dynamics of tumour growth. We will then consider more specifically its impact on radiotherapy.

In particular, we will highlight the advantages of mathematically rigorous modelling in bridging theory and biology. We will also adopt a more exploratory perspective, using these models to illustrate how mathematics can serve as a potential decision-support tool for the selection and optimisation of treatment protocols, within an image- and model-driven framework.

The final part of the seminar will focus on potential future developments, with the aim of fostering an open and collaborative discussion on novel perspectives to improve understanding, prediction, and therapeutic optimisation.