Past

In this presentation, we investigate the spectrum of the Neumann-Poincaré operator associated to a periodic distribution of small inclusions with size ε, and its asymptotic behavior as the parameter ε vanishes. Combining techniques pertaining to the fields of homogenization and potential theory, we prove that the limit spectrum is composed of the `trivial' eigenvalues 0 and 1, and of a subset which stays bounded away from 0 and 1 uniformly with respect to ε. This non trivial part is the reunion of the Bloch spectrum, accounting for the collective resonances between collections of inclusions, and of the boundary layer spectrum, associated to eigenfunctions which spend a not too small part of their energies near the boundary of the macroscopic device. These results shed new light about the homogenization of the voltage potential uε caused by a given source in a medium composed of a periodic distribution of small inclusions with an arbitrary (possibly negative) conductivity a surrounded by a dielectric medium, with unit conductivity.

The cyclic surgery theorem of Culler, Gordon, Luecke, and Shalen implies that any knot in S^3 other than a torus knot has at most two nontrivial cyclic surgeries. In this talk, we investigate the weaker notion of SU(2)-cyclic surgeries on a knot, meaning surgeries whose fundamental groups only admit SU(2) representations with cyclic image. By studying the image of the SU(2) character variety of a knot in the “pillowcase”, we will show that if it has infinitely many SU(2)-cyclic surgeries, then the corresponding slopes (viewed as a subset of RP^1) have a unique limit point, which is a finite, rational number, and that this limit is a boundary slope for the knot. As a corollary, it follows that for any nontrivial knot, the set of SU(2)-cyclic surgery slopes is bounded. This is joint work with Raphael Zentner.

Abstract: In this talk we describe an invariance principle for a class of non-homogeneous martingale random walks in $\RR^d$ that can be recurrent or transient for any dimension $d$. The scaling limit, which we construct, is a martingale diffusions with law determined uniquely by an SDE with discontinuous coefficients at the origin whose pathwise uniqueness may fail. The radial component of the diffusion is a Bessel process of dimension greater than 1. We characterize the law of the diffusion, which must start at the origin, via its excursions built around the Bessel process: each excursion has a generalized skew-product-type structure, in which the angular component spins at infinite speed at the start and finish of each excursion. Defining a Riemannian metric $g$ on the sphere $S^{d−1}$, different from the one induced by the ambient Euclidean space, allows us to give an explicit construction of the angular component (and hence of the entire skew-product decomposition) as a time-changed Browninan motion with drift on the Riemannian manifold $(S^{d−1}, g)$. In particular, this provides a multidimensional generalisation of the Pitman–Yor representation of the excursions of Bessel process with dimension between one and two. Furthermore, the density of the stationary law of the angular component with respect to the volume element of $g$ can be characterised by a linear PDE involving the Laplace–Beltrami operator and the divergence under the metric $g$. This is joint work with Nicholas Georgiou and Andrew Wade.

The interplay of minimum degree and 'structural properties' of large graphs with a given forbidden subgraph is a central topic in extremal graph theory. For a given graph $F$ we define the homomorphism threshold as the infimum $\alpha$ such that every $n$-vertex $F$-free graph $G$ with minimum degree $>\alpha n$ has a homomorphic image $H$ of bounded size (independent of $n$), which is $F$-free as well. Without the restriction of $H$ being $F$-free we recover the definition of the chromatic threshold, which was determined for every graph $F$ by Allen et al. The homomorphism threshold is less understood and we present recent joint work with O. Ebsen on the homomorphism threshold for odd cycles.

We propose a new splitting algorithm to solve a class of quasilinear PDEs with convex and quadratic growth gradients. 

By splitting the original equation into a linear parabolic equation and a Hamilton-Jacobi equation, we are able to solve both equations explicitly. 

In particular, we solve the associated Hamilton-Jacobi equation by the Hopf-Lax formula, 

and interpret the splitting algorithm as a stochastic Hopf-Lax approximation of the quasilinear PDE.  

We show that the numerical solution will converge to the viscosity solution of the equation.  

The upper bound of the convergence rate is proved based on Krylov's shaking coefficients technique, 

while the lower bound is proved based on Barles-Jakobsen's optimal switching approximation technique. 

Based on joint work with Shuo Huang and Thaleia Zariphopoulou.

In this talk two different methods for constructing complete steady and expanding Ricci solitons of cohomogeneity one will be discussed. The first is based on an estimate on the growth of the soliton potential and holds for large classes of cohomogeneity one manifolds. The second approach is specific to the two summands case and uses a Lyapunov function. This method also carries over to the Einstein case and as an application, a simplified construction of B\"ohm's Einstein metrics of positive scalar curvature on spheres will be explained.

We consider the one parameter mirror families W of the Calabi-Yau 3-folds with Picard-Fuchs  equations of hypergeometric type. By mirror symmetry the  even D-brane masses of orginial Calabi-Yau manifolds M can be identified with four periods with respect to an integral symplectic basis of $H_3(W,\mathbb{Z})$ at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of $\Gamma_0(N)$. For the quintic in  $\mathbb{P}^4$ it this Hecke eigenform of $\Gamma_0(25)$ was as found by Chad Schoen.  It was discovered  by de la Ossa, Candelas and Villegas that  its  coefficients $a_p$ count the number of  solutions of  the mirror quinitic at the conifold over the finite number field $\mathbb{F}_p$ . Using the theory of periods and quasi-periods of $\Gamma_0(N)$ and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.  

Richard Wade:   Classifying spaces, automorphisms, and right-angled Artin groups 

Right-angled Artin groups (otherwise known as partially commutative groups, or graph groups), interpolate between free abelian groups and free groups. These groups have seen a lot of attention recently, much of this due to some surprising links to the world of hyperbolic 3-manifolds.We will look at classifying spaces for such groups and their associated automorphism groups. These spaces are useful as they give a topological way to understand algebraic invariants of groups. This leads us to study some beautiful mathematical objects: deformation spaces of tori and trees. We will look at some recent results that aim to bridge the gap between these two families of spaces.
 
Andrey Kormilitzin:   Learning from electronic health records using the theory of rough paths

In this talk, we bring the theory of rough paths to the study of non-parametric statistics on streamed data and particularly to the problem of regression and classification, where the input variable is a stream of information, and the dependent response is also (potentially) a path or a stream.  We informally explain how a certain graded feature set of a stream, known in the rough path literature as the signature of the path, has a universality that allows one to characterise the functional relationship summarising the conditional distribution of the dependent response. At the same time this feature set allows explicit computational approaches through machine learning algorithms.

Finally, the signature-based modelling can be applied to some real-world problems in medicine, in particular in mental health and gastro-enterology.

This will be a whistle-stop tour of a few topics on infectious disease modelling, mainly influenza. Topics to include:

• challenges in capturing dynamics of pathogens with multiple co-circulating strains
• untangling the 2009 influenza pandemic from medical insurance claims data from the US
• bioinformatic methods to detect viral packaging signals
• and a big science project (top secret until the talk!)

Julia will be visiting the Mathematical Institute on sabbatical this term, and hopes this talk will help us find areas of overlapping interests.

It is thought that the hairy legs of water walking arthropods are able to remain clean and dry because the flexibility of the hairs spontaneously moves drops off the hairs. We present a mathematical model of this bending-induced motion, or bendotaxis, and study how it performs for wetting and non-wetting drops. Crucially, we show that both wetting and non-wetting droplets move in the same direction (using physical arguments and numerical solutions). This suggests that a surface covered in elastic filaments (such as the hairy leg of insects) may be able to universally self-clean. To quantify the efficiency of this effect, we explore the conditions under which drops leave the structure by ‘spreading’ rather than translating and also how long it takes to do so.

In a recent preprint, Basterra, Bobkova, Ponto, Tillmann and Yeakel
defined operads with homological stability (OHS) and showed that after
group-completion, algebras over an OHS group-complete to infinite loop
spaces. This can in particular be used to put a new infinite loop space
structure on stable moduli spaces of high-dimensional manifolds in the
sense of Galatius and Randal-Williams, which are known to be infinite
loop spaces by a different method.

To complicate matters further, I shall introduce a mild strengthening of
the OHS condition and construct yet another infinite loop space
structure on these stable moduli spaces. This structure turns out to be
equivalent to that constructed by Basterra et al. It is believed that
the infinite loop space structure due to Galatius--Randal-Williams is
also equivalent to these two structures.

l-adic cohomology was built to provide an etale cohomology with coefficients in a field of characteristic 0. This, via the Grothendieck trace formula, gives  a cohomological interpretation of L-functions - a fundamental tool in Deligne's theory of weights developed in Weil II. Instead of l-adic coefficients one can consider coefficients in ultra products of finite fields. I will state the fundamental theorem of Weil II for curves in this setting and explain briefly what are the difficulties to overcome to adjust Deligne's proof. I will then discuss how this ultra product variant of Weil II allows to extend to arbitrary coefficients  previous results of Gabber and Hui, Tamagawa and myself for constant $\mathbb{Z}_\ell$-coefficients.  For instance,  it implies that, in an $E$-rational compatible system of smooth $\overline{\mathbb{Q}}_\ell$-sheaves all what is true for $\overline{\mathbb{Q}}_\ell$-coefficients (semi simplicity, irreducibility, invariant dimensions etc) is true for $\overline{\mathbb{F}}_\ell$-coefficients provided $\ell$ is large enough or that the $\overline{\mathbb{Z}}_\ell$-models are unique with torsion-free cohomology provided $\ell$ is large enough.

Many species of insects adhere to vertical and inverted surfaces using footpads that secrete thin films of a mediating fluid. The fluid bridges the gap between the foot and the target surface. The precise role of this liquid is still subject to debate, but it is thought that the contribution of surface tension to the adhesive force may be significant. It is also known that the footpad is soft, suggesting that capillary forces might deform its surface. Inspired by these physical ingredients, we study a model problem in which a thin, deformable membrane under tension is adhered to a flat, rigid surface by a liquid droplet. We find that there can be multiple possible equilibrium states, with the number depending on the applied tension and aspect ratio of the system. The presence of elastic deformation  ignificantly enhances the adhesion force compared to a rigid footpad. A mathematical model shows that the equilibria of the system can be controlled via two key parameters depending on the imposed separation of the foot and target surface, and the tension applied to the membrane. We confirm this finding experimentally and show that the system may transition rapidly between two states as the two parameters are varied. This suggests that different strategies may be used to adhere strongly and then detach quickly.

In this talk, I consider  the problem of
hedging European and Bermudan option with a given probability. This 
question is
more generally linked to portfolio optimisation problems under weak
stochastic target constraints.
I will recall, in a Markovian framework, the characterisation of the 
solution by
non-linear PDEs. I will then discuss various numerical algorithms
to compute in practice the quantile hedging price.

This presentation is based on joint works with B. Bouchard (Université 
Paris Dauphine), G. Bouveret (University of Oxford) and ongoing work 
with C. Benezet (Université Paris Diderot).

Spline curves represent a simple and efficient tool for data interpolation in Euclidean space. During the past decades, however, more and more applications have emerged that require interpolation in (often high-dimensional) nonlinear spaces such as Riemannian manifolds. An example is the generation of motion sequences in computer graphics, where the animated figure represents a curve in a Riemannian space of shapes. Two particularly useful spline interpolation methods derive from a variational principle: linear splines minimize the average squared velocity and cubic splines minimize the average squared acceleration among all interpolating curves. Those variational principles and their discrete analogues can be used to define continuous and discretized spline curves on (possibly infinite-dimensional) Riemannian manifolds. However, it turns out that well-posedness of cubic splines is much more intricate on nonlinear and high-dimensional spaces and requires quite strong conditions on the underlying manifold. We will analyse and discuss linear and cubic splines as well as their discrete counterparts on Riemannian manifolds and show a few applications.

In the study of variational models for non-linear elasticity in the context of proving regularity we are led to the challenging so-called Ball-Evan's problem of approximating a Sobolev homeomorphism with diffeomorphisms in its Sobolev space. In some cases however we are not able to guarantee that the limit of a minimizing sequence is a homeomorphism and so the closure of Sobolev homeomorphisms comes into the game. For $p\geq 2$ they are exactly Sobolev monotone maps and for $1\leq p<2$ the monotone maps are intricately related to these limits. In our paper we prove that monotone maps can be approximated by diffeomorphisms in their Sobolev (or Orlicz-Sobolev) space including the case $p=1$ not proven by Iwaniec and Onninen.
 

Warped cones are infinite metric spaces that are associated with actions by homeomorphisms on metric spaces. In this talk I will try to explain why the coarse geometry of warped cones can be seen as an invariant of the action and what it can tell us about the acting group.

Broken cryptographic algorithms and hardness assumptions are a constant
threat to real-world protocols. Prominent examples are
hash functions for which collisions become known, or number-theoretic
assumptions which are threatened by advances in quantum computing.
Especially when it comes to key exchange protocols, the switch to
quantum-resistant primitives has begun and aims to protect today’s
secrets against future developments, moving from common Diffie–Hellman
based solutions to Learning-With-Errors-based approaches. Remarkably,
the authentication step in such protocols is usually still carried out
with quantum-vulnerable signature schemes. The intuition here is that
the adversary would need to break this protocol primitive today, without
having quantum power yet. The question we address here is if this
intuition is justified, and if so, if we can show this rigorously. We
particularly consider the authenticated variant of the recently
introduced post-quantum secure key exchange protocol NewHope (Alkim et
al., USENIX Security 2016), as well as by TLS 1.3, which is currently
being developed by the Internet Engineering Task Force.

I was speak on the way Newton carries out his calculus in the Principia in the framework of classical geometry rather than with fluxions, his deficiencies, and the relation of this work to inverse-square laws.

Understanding the distribution of subgraph counts has long been a central question in the study of random graphs. In this talk, we consider the distribution of Sn, the number of K4 subgraphs, in the Erdös Rényi random graph G(n, p). When the edge probability p \in (0, 1) is constant, a classical central limit theorem for Sn states that (Sn−µn)/σn converges in distribution. We establish a stronger form of convergence, namely the corresponding local limit theorem, which is joint work with O. Riordan.
 

(Joint with Gareth Boxall) In this talk I will introduce some properties of distal theories. I will remark that distality is preserved neither under reducts nor expansions of the language. I will then go on to discuss a recent result that the Shelah expansion of a theory is distal if and only if the theory itself is distal. 

In mirror symmetry, the prepotential on the Kahler side has an expansion, the constant term of which is a rational multiple of zeta(3)/(2 pi i)^3 after an integral symplectic transformation. In this talk I will explain the connection between this constant term and the period of a mixed Hodge-Tate structure constructed from the limit MHS at large complex structure limit on the complex side. From Ayoub’s works on nearby cycle functor, there exists an object of Voevodsky’s category of mixed motives such that the mixed Hodge-Tate structure is expected to be a direct summand of the third cohomology of its Hodge realisation. I will present the connections between this constant term and conjecture about how mixed Tate motives sit inside Voevodsky’s category, which will also provide a motivic interpretation to the occurrence of zeta(3) in prepotential. 

I will describe a novel algorithm for computing the Walsh Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. The algorithm shares precisely the same serial complexity as the popular divide-and-conquer algorithm for the WHT. There is also a natural way to parallelize the algorithm which appears to have a number of attractive features.

A class C of graphs has polynomial expansion if there exists a polynomial p such that for every graph G from C and for every integer r, each minor of G obtained by contracting disjoint subgraphs of radius at most r is p(r)-degenerate. Classes with polynomial expansion exhibit interesting structural, combinatorial, and algorithmic properties. In the talk, I will survey these properties and propose further research directions.

Medical imaging is a key diagnostic tool, and is paramount for disease detection and for patient monitoring during ongoing care. Often, to reduce the amount of radiation that a patient is subjected to, there is a strong incentive to consider image reconstruction from incomplete sets of measurements, and so the imaging process is formulated as a compressed sensing problem.

In this talk, we will focus on compressed sensing for digital tomosynthesis (DTS), in which three-dimensional images are reconstructed from a set of two-dimensional X-ray projections. We first discuss a reconstruction approach for static bodies, with a particular interest in the choice of basis for the image representation. We will then focus on the need for accurate image reconstructions when the body of interest is not stationary, but is undergoing simple motion, discussing two different approaches for tackling this dynamic problem.

This will be a discussion of the paper https://arxiv.org/abs/1604.02618

A great deal of effort has gone into trying to model social influence --- including the spread of behavior, norms, and ideas --- on networks. Most models of social influence tend to assume that individuals react to changes in the states of their neighbors without any time delay, but this is often not true in social contexts, where (for various reasons) different agents can have different response times. To examine such situations, we introduce the idea of a timer into threshold models of social influence. The presence of timers on nodes delays the adoption --- i.e., change of state --- of each agent, which in turn delays the adoptions of its neighbors. With a homogeneous-distributed timer, in which all nodes exhibit the same amount of delay, adoption delays are also homogeneous, so the adoption order of nodes remains the same. However, heterogeneously-distributed timers can change the adoption order of nodes and hence the "adoption paths" through which state changes spread in a network. Using a threshold model of social contagions, we illustrate that heterogeneous timers can either accelerate or decelerate the spread of adoptions compared to an analogous situation with homogeneous timers, and we investigate the relationship of such acceleration or deceleration with respect to timer distribution and network structure. We derive an analytical approximation for the temporal evolution of the fraction of adopters by modifying a pair approximation of the Watts threshold model, and we find good agreement with numerical computations. We also examine our new timer model on networks constructed from empirical data.

Link to arxiv paper: https://arxiv.org/abs/1706.04252

I will review some classical results on geometric scattering
theory for linear hyperbolic evolution equations
on globally hyperbolic spacetimes and its relation to particle and charge
creation in QFT. I will then show that some index formulae for the
scattering matrix can be interpreted as a special case of the  Lorentzian
analog of the Atyiah-Patodi-Singer index theorem. I will also discuss a
local version of this theorem and its relation to anomalies in QFT.
(Joint work with C. Baer)

Many industrial optimisation problems involve the challenging task of efficiently searching for optimal decisions from a huge set of possible combinations. The optimal solution is the one that best optimises a set of objectives or goals, such as maximising productivity while minimising costs. If we have a nice mathematical equation for how each objective depends on the decisions we make, then we can usually employ standard mathematical approaches, such as calculus, to find the optimal solution. But what do we do when we have no idea how our decisions affect the objectives, and thus no equations? What if all we have is a small set of experiments, where we have tried to measure the effect of some decisions? How do we make use of this limited information to try to find the best decisions?

This talk will present a common industrial optimisation problem, known as expensive black box optimisation, through a case study from the manufacturing sector. For problems like this, calculus can’t help, and trial and error is not an option! We will introduce some methods and tools for tackling expensive black-box optimisation. Finally, we will discuss new methodologies for assessing the strengths and weaknesses of optimisation methods, to ensure the right method is selected for the right problem.

I will talk about the diffeomorphism classification of 4-manifolds up to 
connected sums with the complex projective plane, and how the resulting 
equivalence class of a manifold can be detected by algebraic topological 
invariants of the manifold.  I may also discuss related results when one 
takes connected sums with another favourite 4-manifold, S^2 x S^2, instead.

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. The signature method is derived from stochastic analysis (rough paths theory) and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.

In this joint work with Amandine Aftalion we study the minimisers of an energy functional in two-dimensions describing a rotating two-component condensate. This involves in particular separating a line-energy term and a vortex term which have different orders of magnitude, and requires new estimates for functionals of the Cahn-Hilliard (or Modica-Mortola) type.

In this talk, I am going to report on some on-going research at the interface between Rough Paths Theory and Schramm-Loewner evolutions (SLE). In this project, we try to adapt techniques from Rough Differential Equations to the study of the Loewner Differential Equation. The main ideas concern the restart of the backward Loewner differential equation from the singularity in the upper half plane. I am going to describe some general tools that we developed in the last months that lead to a better understanding of the dynamics in the closed upper half plane under the backward Loewner flow.
Joint work with Prof. Dmitry Belyaev and Prof. Terry Lyons

Associated to a finite graph without loops is the Kac-Moody Lie algebra for the Cartan matrix whose off diagonal entries are (minus) the adjacency matrix for the graph.  Two famous conjectures of Kac, proved by Hausel, Letellier and Villegas, hint that there may be some larger cohomologically graded algebra associated to the graph (even if there are loops), providing "higher" Kac moody Lie algebras, or at least their positive halves.  Using work with Sven Meinhardt, I will give a geometric construction of the (full) Kac-Moody algebra for a general finite graph, using cohomological DT theory.  Along the way we'll see a proof of the positivity conjecture for the modified Kac polynomials of Bozec, Schiffmann and Vasserot counting various types of representations of quivers.

The existence of planetary and stellar magnetic fields is attributed to the dynamo instability, the mechanism by which a background turbulent flow spontaneously generates a magnetic field by the constructive refolding of magnetic field lines. Many efforts have been made by several experimental groups to reproduce the dynamo instability in the laboratory using liquid metals. However, so far, unconstrained dynamos driven by turbulent flows have not been achieved in the intrinsically low magnetic Prandtl number $P_m$ (i.e. $Pm = Rm/Re << 1$) laboratory experiments. In this seminar I will demonstrate that the critical magnetic Reynolds number $Rm_c$ for turbulent non-helical dynamos in the low $P_m$ limit can be significantly reduced if the flow is submitted to global rotation. Even for moderate rotation rates the required energy injection rate can be reduced by a factor more than 1000. Our finding thus points into a new paradigm for the design of new liquid metal dynamo experiments.

Image use continues to increase in both biomedical sciences and clinical practice. State of the art acquisition techniques allow characterisation from subcellular to whole organ scale, providing quantitative information of structure and function. In the heart, for example, images acquired from a single modality (cardiac MRI) can characterise micro- and macrostructure, describe mechanical function and measure blood flow. In the lungs, new contrast agents can be used to visualise the flow of gas in free breathing subjects. This provides rich new sources of information as well as new challenges to extract data in a way that is useful to clinicians as well as computer modellers.
I will describe efforts in my group to use the latest advances in machine learning to analyse images, and explain how we are applying these to the development of accurate computer models of the heart.
 

We discuss pathwise pricing-hedging dualities in continuous time and on a frictionless market consisting of finitely many risky assets with continuous price trajectories.

The costs to Vodafone of calls terminating on other networks – especially fixed networks – are largely determined by the termination charges levied by other telecoms operators.  We interconnect to several other telecoms operators, who charge differently; within one interconnect operator, costs vary depending on which of their switching centres we deliver calls to, and what the terminating phone number is.  So, while these termination costs depend partly on factors that we cannot control (such as the number called, the call duration and the time of day), they are also influenced by some factors that we can control.  In particular, we can route calls within our network before handing them over from our network to the other telecoms operator; where this “handover” occurs has an impact on termination cost.  
Vodafone would like to develop a repeatable capability to determine call delivery cost efficiency and identify where network routing changes can be made to improve matters, and determine traffic growth forecasts.

In this talk I will discuss the problem of finding Einstein metrics in the homogeneous and cohomogeneity one setting. 
In particular, I will describe a recent result concerning existence of solutions to the Dirichlet problem for cohomogeneity one Einstein metrics.

We present a framework for the design, analysis and application of computational multiscale methods for slow-fast high-dimensional stochastic processes. We call these processes "microscopic'', and assume existence of an approximate "macroscopic'' model that captures the slow behaviour of a selected set of macroscopic state variables. The methodology combines short bursts of microscopic simulation with extrapolation at the macroscopic level. The methodology requires the careful study of a few key algorithmic ingredients. First, we need to properly initialise the microscopic system, based on a given macroscopic state and (possibly) a prior microscopic state that contains additional information about the system. Second, we need to control the variance of the noise that originates from the microscopic Monte Carlo simulation. Third, we need to analyse stability of the extrapolation step. We will discuss these aspects on two types of model problems -- scale-separated SDEs and kinetic equations -- and show the efficacity of the resulting methods in diverse applications, ranging from tumor growth to fusion energy.

We formulate and solve a class of Backward Stochastic Differential Equations (BSDEs) driven by the compensated random measure associated to a given marked point process on a general state space. We present basic well-posedness results in L 2 and in L 1 . We show that in the setting of point processes it is possible to solve the equation recursively, by replacing the BSDE by an ordinary differential equation in between jumps. Finally we address applications to optimal control of marked point processes, where the solution of a suitable BSDE allows to identify the value function and the optimal control. The talk is based on joint works with Marco Fuhrman and Jean Jacod. 

Maintenance activities help prevent costly power generator breakdowns but because generators under maintenance are typically unavailable, the impact of maintenance schedules is significant and their cost must be accounted for when planning maintenance. In this paper we address the generator maintenance scheduling problem in hydropower systems. While this problem has been widely studied, specific operating conditions of hydroelectric systems have received less attention. We present a mixed-integer linear programming model that considers the time windows of the maintenance activities, as well as the nonlinearities and disjunctions of the hydroelectric production functions. Because the resulting model is hard to solve, we also propose an extended formulation, a set reduction approach that uses logical conditions for excluding unnecessary set elements from the model, and valid inequalities. Computational experiments using a variety of instances adapted from a real hydropower system in Canada support the conclusion that the extended formulation with set reduction achieves the best results in terms of computational time and optimality gap. This is joint work with Jesus Rodriguez, Pascal Cote and Guy Desaulniers.

Outer Space is an important object in Geometric Group Theory and can be described from two viewpoints: as a space of marked graphs and a space of actions on trees. The latter viewpoint can be used to prove that Outer Space is contractible; and this fact together with some arguments using the first viewpoint enables us to say something about the Outer Automorphism group of a free group - I will sketch both these proofs.

We discuss the connections and differences between the ZFC set theory and univalent foundations and answer the above question in the negative.
 

The birth of fixed-wing, powered flight in the first decade of the twentieth century brought with it significant potential for pilots to return to Earth by unintended, often fatal, means. I will discuss the nature of the contemporary mathematical and engineering debates associated with these facets of flight, and the practical steps taken to facilitate safer aircraft and more robust operating procedures.