### Ecological Modelling with Data

Rebecca Tyson
In order for models to make relevant predictions about real ecological systems, it is helpful to have data to guide the selection of, for example, parameter values, interaction functions, and dispersal kernels. For many ecological systems, however, data is sparse. Nonetheless, these data can still lead to the development of models that give rise to theoretical predictions with real relevance. Several examples will be presented and discussed in this talk.

### Correspondence and Rigidity Results on Asymptotically Anti-de Sitter Spacetimes

Arick Shao
In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Anti-de Sitter (aAdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate such a correspondence statement as a unique continuation problem for PDEs: Is an aAdS solution of the Einstein equations uniquely determined by its data on its conformal boundary In this talk, we report on...

### Handling uncertain spatial data in monitoring and control problems

Natalia Petrovskaya
In many ecological problems spatial data are collected to satisfy the requirement that the population spatial distributions can be reconstructed with high accuracy. The situation, however, may be different when reconstruction of spatial distributions is required in the context of monitoring and control (M&C) protocol. In my talk I will argue that the M&C protocol can be thought of as a data filter as its application transforms the original dataset and it often results in...

### Transient dynamics in equilibrium and non-equilibrium communities

Frithjof Lutscher
Human activities or natural events may perturb locally stable equilibrium communities. One can ask how long the community will take to return to its equilibrium and how "far" from the equilibrium it may get in the process. To answer those questions, we can measure the "resilience" and "reactivity" of a system. These concepts thus quantify one particular form of transient dynamics in ecological models. I will briefly review these measures and give some examples and...

### Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner--NordstrÃ¶m--AdS black holes

Christoph Kehle
I will present a recent result on solutions to the massive linear wave equation $\Box_g \psi - \mu \psi =0$ on the interior of Reissner--NordstrÃ¶m--AdS black holes. This is motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS black holes with negative cosmological constant $\Lambda <0$. Our main result shows that linear waves arising from a spacelike hypersurface with Dirichlet (reflecting) boundary conditions imposed at infinity remain bounded in the interior and can be...

### Vacuum Boundary Problem of the Metric Produced by Perfect Fluid Mass Distributions

Tetu Makino
The mathematical study of the metric produced by compactly supported perfect fluid mass distributions governed by the Einstein-Euler equations is now developing. The main difficulty of the study comes from the situation that the boundary between the mass and the vacuum requires mathematically delicate treatise. This so called `physical vacuum boundary' is a kind of free boundary. The spherically symmetric evolution of the metric near spherically symmetric equilibria, say, solutions of the Tolman-Oppenheimer-Volkoff equation, is...

### A convenient form of complexity in ecology: multiple timescales

Chris Cosner
One of the features that distinguishes biological systems is the wide range of scales in time and space on which processes and interactions occur. This is a form of complexity, but it is one that can sometimes be turned into an advantage. I will describe models for a couple of systems where my collaborators and I have found that to be the case. The first (from long ago) is a system with ladybugs preying on...

### Dynamical relativistic liquid bodies: local-in-time existence and uniqueness

Todd Oliynyk
In this talk, I will discuss a new approach to establishing the well-posedness of the relativistic Euler equations for liquid bodies in vacuum. The approach is based on a wave formulation of the relativistic Euler equations that consists of a system of non-linear wave equations in divergence form together with a combination of acoustic and Dirichlet boundary conditions. The equations and boundary conditions of the wave formulation differs from the standard one by terms proportional...

### Understanding ecological dynamics: Stability metrics and Early warnings

Vasilis Dakos
Understanding stability of ecosystems and communities has always been major challenge for ecologists. Definitions and measures of stability abound and at times are confusing. Nowadays it is in general accepted that stability is multidimensional and it needs to be measured in different ways. Some of the metrics are used to highlight resistance of ecological systems to a specific type of perturbations (like an invasion of an alien). Others have been developed to highlight the approach...

### Global simulation of the non-linear perturbations of a Schwarzschild black hole

Jörg Frauendiener
It is well known that gravitational waves interact in a non-linear way. This makes it difficult to describe them rigorously. The cleanest description is based on a certain conformal invariance of the Einstein equations â a fact which was established by R. Penrose and was used by H. Friedrich to prove several important global results for general relativistic space-times. The so called conformal field equations implement this conformal invariance on the level of partial differential...

David Hilditch

### Persistence and extinction for stochastic ecological difference equations with internal and external variables

Sebastian Schreiber
The dynamics of speciesâ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. I will present recent theorems for stochastic persistence...

### A review of the initial boundary problem in GR and geometric uniqueness

Jacques Smulevici
In the absence of time-like boundary, the classical initial value problem in GR verifies a geometric uniqueness property. In particular, isometric Cauchy data leads to (maximal globally hyperbolic) developments which are isometric. While there exists several well-posed formulation of the initial boundary value problem in GR, no such geometric uniqueness is known. This important issue was put forward by Helmut Friedrich. It is relevant not only for the local initial boundary value problem, but also...

### Implementing higher-order absorbing boundary conditions for Numerical Relativity

Luisa Buchman
The numerical computation of gravitational radiation emitted from binary black hole systems has been pivotal in the detection and characterization of 10 binary black hole astrophysical events since Sept. 14, 2015. However, the drive for more accurate waveforms remains, especially when computing higher-order spherical harmonic modes. The numerical relativity simulations currently used for LIGO / VIRGO detections solve Einsteinâ s field equations on a finite computational domain with an outer boundary. In order to obtain...

Alan Hastings

### Well-posed initial boundary value problem for the Einstein field equations in harmonic coordinates

Olivier Sarbach
A short summary of the well-posed IBVP for the vacuum Einstein field equations in harmonic coordinates formulated in Comm. Math. Phys. 289, 1099-1129 (2009) will be provided.

### Initial boundary value formulation for neutron star magneto- spheres

Federico Carrasco
Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arise on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In those regimes, the electromagnetic field obeys a modified nonlinear version of Maxwell equations, while the plasma only accommodates to locally cancel out the Lorentz force. The aim of the present talk is to discuss the initial/boundary value formulation of FFE at some given astrophysical settings. We start...

### PLOM: Paper (Less) Online Marking

Andrew Rechnitzer
PLOM is open-source online grading software written in Python. It has been used to successfully grade roughly 10,000 exams at UBC. PLOM is designed to easily handle multiple versions of an exam, and allow for higher quality feedback through predefined grading rubrics.

### Sublinear Coherence distillation and a no-broadcasting theorem for coherence and asymmetry

Iman Marvian
In this talk I discuss coherence distillation under Time translation Invariant operations. I show that although for a generic mixed state the distillation rate is zero, it is still possible to distill a sub-linear number of a pure coherent state, with fidelity approaching one, provided that we can consume asymptotically many copies of the mixed state. Furthermore, for a generic mixed input state, there is a tradeoff between the maximum achievable yield and the fidelity...

### Bell inequalities for quantum certification

Antonio Acin
Bell inequalities were derived as conditions satisfied by local hidden-variable models. However, in recent years they have acquired a new status as device-independent certificates of relevant quantum properties. We provide several constructions in which Bell inequalities are constructed from the quantum states and/or measurements to certify, rather than from considerations concerning the geometry of classical correlations. In particular, we present Bell inequalities maximally violated by maximally entangled states or arbitrary dimension and also graph states.

### Asymptotic performance of port-based teleportation

Felix Leditzky
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number N of ports, the error of the optimal protocol is proportional to...

### Resource theory of asymmetric distinguishability

Mark Wilde
We systematically develop the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1006.0302 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of a pair of quantum states, which can be manipulated for free by means of an arbitrary quantum channel. We introduce bits of asymmetric distinguishability as the basic currency in this resource theory, and we prove that it is a reversible resource theory in the...

Michael Wolf

### Embezzlement of Entanglement

Vern Paulsen
Embezzlement of entanglement was studied by van Dam and Hayden who showed that it was imposible to catylyically produce entanglement in the tensor product model, but that one could "nearly" acheive this goal. However, in the commuting operator model one can accomplish this task. We show that there is a parallel between this theory and Tsirelson's problems about the different models for conditional probability densities. In analogy there is a theory of "unitary correlations" that...

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