Past

Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.

Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.

We study the adaptive finite element approximation of the Dirichlet problem $-\Delta u = f$ with zero boundary values using newest vertex bisection. Our approach is based on the minimization of the corresponding Dirichlet energy. We show that the maximums strategy attains every energy level with a number of degrees of freedom, which is proportional to the optimal number. As a consequence we achieve instance optimality of the error. This is a joint work with Christian Kreuzer (Bochum) and Rob Stevenson (Amsterdam).

Abstract: A diffusion process on a Riemannian manifold whose generator is one half of the Laplacian is called a Brownian motion. The mean local time of Brownian motion on a hypersurface will be considered, as will the situation in which a Brownian motion is conditioned to arrive in a fixed submanifold at a fixed positive time. Doing so provides motivation for the remainder of the talk, in which a probabilistic formula for the integral of the heat kernel over a submanifold is proved and used to deduce lower bounds, an asymptotic relation and derivative estimates applicable to the conditioned process.

We study symplectic invariants of the open symplectic manifolds X
obtained by plumbing cotangent bundles of spheres according to a
plumbing tree. We prove that certain models for the Fukaya category F(X)
of closed exact Lagrangians in X and the wrapped Fukaya category W(X)
are related by Koszul duality. As an application, we give explicit
computations of symplectic cohomology essentially for all trees. This is
joint work with Tolga Etg\"u.

Abstract: The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S-topology and the dynamic programming principle. This is a joint work with Gaoyue Guo and Nizar Touzi.

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincare. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,NL =1)and(3+0,NR =0). 

Across much of the ablation region of the western Greenland Ice Sheet, hydro-fracture events related to supraglacial lake drainages rapidly deliver large volumes of meltwater to the bed of the ice sheet. We investigate what triggers the rapid drainage of a large supraglacial lake using a Network Inversion Filter (NIF) to invert a dense local network of GPS observations over three summers (2011-2013). The NIF is used to determine the spatiotemporal variability in ice sheet behavior (1) prior to lake drainage, and in response to (2) vertical hydro-fracture crack propagation and closure, (3) the opening of a horizontal cavity at the ice-sheet bed that accommodates the rapid injection of melt-water, and (4) extra basal slip due to enhanced lubrication. We find that the opening and propagation of each summer’s lake-draining hydro-fracture is preceded by a local stress perturbation associated with ice sheet uplift and enhanced slip above pre-drainage background velocities. We hypothesize that these precursors are associated with the introduction of meltwater to the bed through neighboring moulin systems.

The first half of the lecture will begin by reviewing what is known about the
neural representation of faces in the primate visual system. How does the
visual system represent the spatial structure of faces, facial identity and
expression? We then discuss how depression is associated with negative
cognitive biases in the recognition of facial expression, whereby depressed
people interpret facial expressions more negatively. The second half of the
lecture presents computer simulations aimed at understanding how these facial
representations may develop through visual experience. We show how neural
representations of expression are linked to particular spatial relationships
between facial features. Building on this, we show how the synaptic connections
in the model may be rewired by visual training to eliminate the negative
cognitive biases seen in depression.

Pengyu Wei's title: Ranking ForexMaster Players

Abstract:

In this talk I will introduce ForexMaster, a simulated foreign exchange trading platform, and how I rank players on this platform. Different methods are compared. In particular, I use random forest and a carefully chosen feature set, which includes not only traditional performance measures like Sharp ratio, but also estimates from the Plackett-Luce ranking model, which has not been used in the financial modelling yet. I show players selected by this method have satisfactory out-of-sample performance, and the Plackett-Luce model plays an important role.

Alissa Kleinnijenhuis title: Stress Testing the European Banking System: Exposure Risk & Overlapping Portfolio Risk
Abstract:
Current regulatory stress testing, as for example done by the EBA, BoE and the FED, is microprudential, non-systemic. These stress tests do not take into account systemic risk, even though the official aim of the stress test is the "test the resilience of the financial system as a whole, and the individual banks therein, to another crisis".
 Two papers are being developed that look at the interconnections between banks. One paper investigates the systemic risk in the European banking system due to interbank exposures, using EBA data. The other paper, looks at the trade-off between individual and systemic risk with overlapping portfolios. The above two "channels of contagion" for systemic risk can be incorporated in stress tests to include systemic components to the traditional non-systemic stress tests.

Blenders and food processors have been around for years.  However, detailed understanding of the fluid and particle dynamics going on with in the multi-phase flow of the processing chamber as well as the influence of variables such as the vessel geometry, blade geometry, speeds, surface properties etc., are not well understood.  SharkNinja would like Oxford Universities help in developing a model that can be used to gain insight into fluid dynamics within the food processing chamber with the goal being to develop a system that will produce better food processing performance as well as predict loading on food processing elements to enable data driven product design.

Many vacuum cleaners sold claim “no loss of suction” which is defined as having only a very small reduction in peak air power output over the life of the unit under normal operating conditions.  This is commonly achieved by having a high efficiency cyclonic separator combined with a filter which the user washes at regular intervals (typically every 3 months).  It has been observed that some vacuum cleaners show an increase in peak air watts output after a small amount of dust is deposited on the filter.  This effect is beneficial since it prolongs the time between filter washing.  SharkNinja are currently working on validating their theory as to why this occurs.  SharkNinja would like Oxford University’s help in developing a model that can be used to better understand this effect and provide insight towards optimizing future designs.

Although a very simple system from a construction standpoint, creating a drip coffee maker that can be produce a range of coffee sizes from a single cup to a multi-cup carafe presents unique problems.  Challenges within this system result from varying pressure heads on the inlet side, accurate measurement of relatively low flow rates, fluid motive force generated by boilers, and head above the boiler on the outlet side.  Getting all of these parameters right to deliver the proper strength, proper temp, and proper volume of coffee requires in depth understanding of the fluid dynamics involved in the system.  An ideal outcome from this work would be an adaptive model that enables a fluid system model to be created from building blocks.  This system model would include component models for tubing, boilers, flow meters, filters, pumps, check valves, and the like.

We consider the decision problem of determining whether an exponential
polynomial has a real zero.  This is motivated by reachability questions
for continuous-time linear dynamical systems, where exponential
polynomials naturally arise as solutions of linear differential equations.

The decidability of the Zero Problem is open in general and our results
concern restricted versions.  We show decidability of a bounded
variant---asking for a zero in a given bounded interval---subject to
Schanuel's conjecture.  In the unbounded case, we obtain partial
decidability results, using Baker's Theorem on linear forms in logarithms
as a key tool.  We show also that decidability of the Zero Problem in full
generality would entail powerful new effectiveness results concerning
Diophantine approximation of algebraic numbers.

This is joint work with Ventsislav Chonev and Joel Ouaknine.

Deformation K-theory was introduced by G. Carlsson and gives an interesting invariant of a group G encoding higher homotopy information about its representation spaces. Lawson proved a relation between this object and a homotopy theoretic analogue of the representation ring. This talk will not contain many details, instead I will outline some basic constructions and hopefully communicate the main ideas.
 

A well-known result of Landsberger and Meilijson says that efficient risk-sharing rules for univariate risks are characterized by a so-called comonotonicity condition. In this talk, I'll first discuss a multivariate extension of this result (joint work with R.-A. Dana and A. Galichon). Then I will discuss the restrictions (in the form of systems of nonlinear PDEs) efficient risk sharing imposes on individual consumption as a function of aggregate consumption. I'll finally give an identification result on how to recover preferences from the knowledge of the risk sharing (joint work with M. Aloqeili and I. Ekeland).

The Möbius function plays a central role in number theory; both the prime number theorem and the Riemann Hypothesis are naturally formulated in terms of the amount of cancellations one gets when summing the Möbius function. In a recent joint work with Maksym Radziwill we have shown that the sum of the Möbius function exhibits cancellation in "almost all intervals" of arbitrarily slowly increasing length. This goes beyond what was previously known conditionally on the Riemann Hypothesis. Our result holds in fact in much greater generality, and has several further applications, some of which I will discuss in the talk. For instance the general result implies that between a fixed number of consecutive squares there is always an integer composed of only "small" prime factors. This settles a conjecture on "smooth" or "friable" numbers and is related to the running time of Lenstra's factoring algorithm.

Noise limits are one of the major constraints when designing
aircraft engines.  Acoustic liners are fitted in almost all civilian
turbofan engine intakes, and are being considered for use elsewhere in a
bid to further reduce noise.  Despite this, models for acoustic liners
in flow have been rather poor until recently, with discrepancies of 10dB
or more.  This talk will show why, and what is being done to model them
better.  In the process, as well as mathematical modelling using
asymptotics, we will show that state of the art Computational
AeroAcoustics simulations leave a lot to be desired, particularly when
using optimized finite difference stencils.

The relationship between the so-called ancient (backwards) solutions to the Navier-Stokes equations in the space or in a half space and the global well-posedness of initial boundary value problems for these equations will be explained. If time permits I will sketch details of an equivalence theorem and a proof of smoothness properties of mild bounded ancient solutions in the half space, which is a joint work with Gregory Seregin

This talk will be an easy introduction to some CAT(0) geometry. Among other things, we'll see why centralizers in groups acting geometrically on CAT(0) spaces split (at least virtually). Time permitting, we'll see why having a geometric action on a CAT(0) space is not a quasi-isometry invariant.

The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. We will discuss hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for several methods of solving LWE we require a lattice reduction step, we also review lattice reduction algorithms and propose a refined model for estimating their running times. We also give concrete estimates for various families of LWE instances, provide a Sage module for computing these estimates and highlight gaps in the knowledge about algorithms for solving the Learning with Errors problem.

We investigate equivalence relations for quadratic forms that can be expressed in terms of algebro-geometric properties of their associated quadrics, more precisely, birational, stably birational and motivic equivalence, and isomorphism of quadrics. We provide some examples and counterexamples and highlight some important open problems.

Igusa's p-adic zeta function $Z(s)$ attached to a polynomial $f$ in $N$ variables is a meromorphic function on the complex plane that encodes the numbers of solutions of the equation $f=0$ modulo powers of a prime $p$. It is expressed as a $p$-adic integral, and Igusa proved that it is rational in $p^{-s}$ using resolution of singularities and the change of variables formula. From this computation it is immediately clear that the order of a pole of $Z(s)$ is at most $N$, the number of variables in $f$. In 1999, Wim Veys conjectured that the only possible pole of order $N$ of the so-called topological zeta function of $f$ is minus the log canonical threshold of $f$. I will explain a proof of this conjecture, which also applies to the $p$-adic and motivic zeta functions. The proof is inspired by non-archimedean geometry and Mirror Symmetry, but the main technique that is used is the Minimal Model program in birational geometry. This talk is based on joint work with Chenyang Xu.

Modelling two-phase, incompressible flow with level set or volume-of-fluid formulations results in a variable coefficient Navier-Stokes system that is challenging to solve computationally. In this talk I will present work from a recent InFoMM CDT mini-project which looked to adapt current preconditioners for one-phase Navier-Stokes flows. In particular we consider systems arising from the application of finite element methodology and preconditioners which are based on approximate block factorisations. A crucial ingredient is a good approximation of the Schur complement arising in the factorisation which can be computed efficiently.

The Erdős–Ko–Rado theorem is a central result in extremal set theory which tells us how large uniform intersecting families can be. In this talk, I shall discuss some recent results concerning the 'stability' of this result. One possible formulation of the Erdős–Ko–Rado theorem is the following: if $n \ge 2r$, then the size of the largest independent set of the Kneser graph $K(n,r)$ is $\binom{n-1}{r-1}$, where $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\dots,n\}$ in which two sets are adjacent if and only if they are disjoint. The following will be the question of interest. Delete the edges of the Kneser graph with some probability, independently of each other: is the independence number of this random graph equal to the independence number of the Kneser graph itself? I shall discuss an affirmative answer to this question in a few different regimes. Joint work with Bollobás and Raigorodskii, and Balogh and Bollobás.

The question that the Crepant Resolution Conjecture (CRC) wants to address is: given an orbifold X that admits a repant resolution Y, can we systematically compare the Gromov-Witten theories of the two spaces? That this should happen was first observed by physicists and the question was imported into mathematics by Y.Ruan, who posited it as the search for an isomorphism in the quantum cohomologies of the two spaces. In the last fifteen years this question has evolved and found different formulations which various degree of generality and validity. Perhaps the most powerful approach to the CRC is through Givental's formalism. In this case, Coates, Corti, Iritani and Tseng propose that the CRC should consist of the natural comparison of geometric objects constructed from the GW potential fo the space. We explore this approach in the setting of open GW invariants. We formulate an open version of the CRC using this formalism, and make some verifications. Our approach is well tuned with Iritani's approach to the CRC via integral structures, and it seems to suggest that open invariants should play a prominent role in mirror symmetry. 

Wave scattering problems arise in numerous applications in acoustics, electromagnetics and linear elasticity. In the boundary element method (BEM) one reformulates the scattering problem as an integral equation on the scatterer boundary, e.g. using Green’s identities, and then seeks an approximate solution of the boundary integral equation (BIE) from some finite-dimensional approximation space. The conventional choice is a space of piecewise polynomials; however, in the “high frequency” regime when the wavelength is small compared to the size of the scatterer, it is computationally expensive to resolve the highly oscillatory wave solution in this way. The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost by enriching the BEM approximation space with oscillatory functions, carefully chosen to capture the high frequency asymptotic solution behaviour. To date, the HNA methodology has been implemented almost exclusively in a Galerkin variational framework. This has many attractive features, not least the possibility of proving rigorous convergence results, but has the disadvantage of requiring numerical evaluation of high dimensional oscillatory integrals. In this talk I will present the results of some investigations carried out with my MSc student Emile Parolin into collocation-based implementations, which involve lower-dimensional integrals, but appear harder to analyse in terms of convergence and stability.

I want to give an introduction into non-Archimedean Geometry, and show how Model Theory was used to prove the recent results of Hrushovski-Loeser on topological properties of analytic spaces. This may also be of interest with view towards Zilber's programme for syntax-semantics dualities.

The study of rational points on K3 surfaces has recently seen a lot of activity. We discuss how to compute the Picard rank of a K3 surface over a number field, and the implications for the Brauer-Manin obstruction.

We establish sharp Sobolev inequalities of order four on Euclidean $d$-balls for $d$ greater than or equal to four. When $d=4$, our inequality generalizes the classical second order Lebedev-Milin inequality on Euclidean $2$-balls. Our method relies on the use of scattering theory on hyperbolic $d$-balls. As an application, we charcaterize the extremals of the main term in the log-determinant formula corresponding to the conformal Laplacian coupled with the boundary Robin operator on Euclidean $4$-balls. This is joint work with Alice Chang. 

Abstract: Joint work with Oleg Zaboronsky (Warwick).

Some one dimensional nearest neighbour particle systems are examples of Pfaffian point processes - where all intensities are determined by a single kernel.In some cases these kernels have appeared in the random matrix literature (where the points are the positions of eigenvalues). We are attempting to use random matrix tools on the particle sytems, and particle tools on the random matrices.

Recent developments in 3-dimensional topological quantum field theory allow us to understand the vector spaces assigned to surfaces as spaces of string diagrams. In the Reshetikhin-Turaev model, these string diagrams live inside a handlebody bounding the surface, while in the Turaev-Viro model, they live on the surface itself. There is a "lifting map" from the former to the latter, which sheds new light on a number of constructions. Joint with Gerrit Goosen.

Abstract:   Consider the square $[0,n]^2$ with points from a Poisson point process of intensity 1 distributed within it. In a seminal work, Baik, Deift and Johansson proved that the number of points $L_n$ (length) on a maximal increasing path (an increasing path that contains the most number of points), when properly centered and scaled, converges to the Tracy-Widom distribution. Later Johansson showed that all maximal paths lie within the strip of width $n^{\frac{2}{3} +\epsilon}$ around the diagonal with probability tending to 1 as $n \to \infty$. We shall discuss recent work on the Gaussian behaviour of the length $L_n^{(\gamma)}$ of a maximal increasing path restricted to lie within a strip of width $n^{\gamma}, \gamma< \frac{2}{3}$.

 

Milnor has shown that three-dimensional Lie groups with left invariant Riemannian metrics furnish examples of 3-manifolds with principal Ricci curvatures of fixed signature --- except for the signatures (-,+,+), (0,+,-), and (0,+,+).  We examine these three cases on a Riemannian 3-manifold, and prove global obstructions in certain cases.  For example, if the manifold is closed, then the signature (-,+,+) is not globally possible if it is of the form -µ,f,f, with µ a positive constant and f a smooth function that never takes the values 0,-µ (this generalizes a result by Yamato '91).  Similar obstructions for the other cases will also be discussed.  Our methods of proof rely upon frame techniques inspired by the Newman-Penrose formalism.  Thus, we will close by turning our attention to four dimensions and Lorentzian geometry, to uncover a relation between null vector fields and exact symplectic forms, with relations to Weinstein structures. 

We review some recent progress in computing massless spectra 

and moduli in heterotic string compactifications. In particular, it was   

recently shown that the heterotic Bianchi Identity can be accounted 

for by the construction of a holomorphic operator. Mathematically,

this corresponds to a holomorphic double extension. Moduli can 

then be computed in terms of cohomologies of this operator. We 

will see how the same structure can be derived form a 

Gukov-Vafa-Witten type superpotential. We note a relation between 

the lifted complex structure and bundle moduli, and cover some 

examples, and briefly consider obstructions and Yukawa 

couplings arising from these structures.

Derived geometry and approximations - Pavel Safronov

Derived geometry has been developed to address issues arising in geometry from a consideration of spaces with intrinsic symmetry or some singular spaces arising as complicated intersections.  It has been successful both in pure mathematics and theoretical physics where derived geometric structures appear in quantum gauge field theories such as the theory of quantum electrodynamics.  Recently Lurie has developed a transparent approach to deformation theory, i.e. the theory of approximations of algebraic structures, using the language of derived algebraic geometry.  I will motivate the theory on a basic example and explain one of the theorems in the subject.

_______________________________

How magnets and mathematics can help solve the current water crisis - Ian Griffiths

Although water was once considered an almost unlimited resource, population growth, drought and contamination are straining our water supplies.  Up to 70% of deaths in Bangladesh are currently attributed to arsenic contamination, highlighting the essential need to develop new and effective ways of purifying water.

Since arsenic binds to iron oxide, magnets offer one such way of removing arsenic by simply pulling it from the water.  For larger contaminants, filters with a spatially varying porosity can remove particles through selective sieving mechanisms.

Here we develop mathematical models that describe each of these scenarios, show how the resulting models give insight into the design requirements for new purification methods, and present methods for implementing these ideas with industry.

It is well known that stochasticity can play a fundamental role in 
various biochemical processes, such as cell regulatory networks and 
enzyme cascades. Isothermal, well-mixed systems can be adequately 
modeled by Markov processes and, for such systems, methods such as 
Gillespie's algorithm are typically employed. While such schemes are 
easy to implement and are exact, the computational cost of simulating 
such systems can become prohibitive as the frequency of the reaction 
events increases. This has motivated numerous coarse grained schemes, 
where the ``fast'' reactions are approximated either using Langevin 
dynamics or deterministically.  While such approaches provide a good 
approximation for systems where all reactants are present in large 
concentrations,  the approximation breaks down when the fast chemical 
species exist in small concentrations,  giving rise to significant 
errors in the simulation.  This is particularly problematic when using 
such methods to compute statistics of extinction times for chemical 
species, as well as computing observables of cell cycle models.  In this 
talk, we present a hybrid scheme for simulating well-mixed stochastic 
kinetics, using Gillepsie--type dynamics to simulate the network in 
regions of low reactant concentration, and chemical langevin dynamics 
when the concentrations of all species is large.  These two regimes are 
coupled via an intermediate region in which a ``blended'' jump-diffusion 
model is introduced.  Examples of gene regulatory networks involving 
reactions occurring at multiple scales, as well as a cell-cycle model 
are simulated, using the exact and hybrid scheme, and compared, both in 
terms weak error, as well as computational cost.

This is joint work with A. Duncan (Imperial) and R. Erban (Oxford)

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland [03], we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model--independent and model--specific settings and allows to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices is equal to supremum over calibrated martingale measures. In presence of non-trivial beliefs, the equality is between limiting values of perturbed problems. In particular, our results include the martingale optimal transport duality of Dolinsky and Soner [13] and extend it to multiple dimensions and multiple maturities.

In contrast to the Artin-Schreier Theorem, its $p$-adic analog(s) involve infinite Galois theory, e.g., the absolute Galois group of $p$-adic fields.  We plan to give a characterization of $p$-adic $p$-Henselian valuations in an essentially finite way. This relates to the $Z/p$ metabelian form of the birational $p$-adic Grothendieck section conjecture.

In contrast to the Artin-Schreier Theorem, its p-adic analog(s) involve infinite Galois theory, e.g., the absolute Galois group of p-adic fields.  We plan to give a characterization of p-adic p-Henselian valuations in an essentially finite way. This relates to the Z/p metabelian form of the birational p-adic Grothendieck section conjecture.

The talk is concerned with adapted solution of a multi-dimensional BSDE with a "diagonally" quadratic generator, the quadratic part of whose iith component only depends on the iith row of the second unknown variable. Local and global solutions are given. In our proofs, it is natural and crucial to apply both John-Nirenberg and reverse Holder inequalities for BMO martingales. 

I will explain the formulation and proof of Arthur's multiplicity formula for automorphic representations of special orthogonal groups and certain inner forms of symplectic groups $G$ over a number field $F$. I work under an assumption that substantially simplifies the use of the stabilisation of the trace formula, namely that there exists a non-empty set $S$ of real places of $F$ such that $G$ has discrete series at places in $S$ and is quasi-split at places outside $S$, and restricting to automorphic representations of $G(A_{F})$ which have algebraic regular infinitesimal character at the places in $S$. In particular, this proves the general multiplicity formula for groups $G$ such that $F$ is totally real, $G$ is compact at all real places of $F$ and quasi-split at all finite places of $F$. Crucially, the formulation of Arthur's multiplicity formula is made possible by Kaletha's recent work on local and global Galois
gerbes and their application to the normalisation of Kottwitz-Langlands-Shelstad transfer factors.

Michael Gomez:

Title: The role of ghosts in elastic snap-through
Abstract: Elastic `snap-through' buckling is a striking instability of many elastic systems with natural curvature and bistable states. The conditions under which bistability exists have been reasonably well studied, not least because a number of engineering applications make use of the rapid transitions between states. However, the dynamics of the transition itself remains much less well understood. Several examples have been studied that show slower dynamics than would be expected based on purely elastic timescales of motion, with the natural conclusion drawn that some other effect, such as viscoelasticity, must play a role. I will present analysis (and hopefully experiments) of a purely elastic system that shows similar `anomalous dynamics'; however, we show that here this dynamics is a consequence of the ‘ghost’ of the snap-through bifurcation.

Andrew Krause:

Title: Fluid-Growth Interactions in Bioactive Porous Media   
Abstract: Recent models in Tissue Engineering have considered pore blocking by cells in a porous tissue scaffold, as well as fluid shear effects on cell growth. We implement a suite of models to better understand these interactions between cell growth and fluid flow in an active porous medium. We modify some existing models in the literature that are spatially continuous (e.g. Darcy's law with a cell density dependent porosity). However, this type of model is based on assumptions that we argue are not good at describing geometric and topological properties of a heterogeneous pore network, and show how such a network can emerge in this system. Therefore we propose a different modelling paradigm to directly describe the mesoscopic pore networks of a tissue scaffold. We investigate a deterministic network model that can reproduce behaviour of the continuum models found in the literature, but can also exhibit finite-scale effects of the pore network. We also consider simpler stochastic models which compare well with near-critical Percolation behaviour, and show how this kind of behaviour can arise from our deterministic network model.