# 2018 MATRIX Annals

The 2018 MATRIX Annals, the third book in the MATRIX Book Series, documents scientific activities at MATRIX in 2018. Pre-publication versions of the articles in the book are posted below.

### Preface

## Guest Editors

#### Algebraic Geometry, Approximation and Optimisation

Enrico Carlini, Jochen Garcke, James Saunderson

#### On the Frontiers of High Dimensional Computation

Frances Kuo

#### Month of Mathematical Biology

Mark Flegg, James Osborne

#### Dynamics, Foliations, and Geometry In Dimension 3

Jonathan Bowden, Andy Hammerlindl

#### Recent Trends on Nonlinear PDEs of Elliptic And Parabolic Type

Daniel Hauer

### Geometric and Categorical Representation Theory

Peter McNamara

## Refereed Articles

### On the Frontiers of High Dimensional Computation

J.C.H. Blake, I. Graham, F. Scheben, A. Spence

The radiative transport equation with heterogeneous cross-sections.

Mahadevan Ganesh, Stuart Hawkins

A reduced-order-model Bayesian obstacle detection algorithm.

Alexander Gilbert, Ivan Graham, Robert Scheichl, Ian Sloan

Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients.

Stefan Heinrich

On the power of restricted Monte Carlo algorithms.

Fred Hickernell, Peter Kritzer, Henryk Wozniakowski

Exponential tractability of linear tensor product problems.

Yoshihito Kazashi, Ian Sloan

Worst-case error for unshifted lattice rules without randomization.

Thomas Kuhn

New preasymptotic estimates for approximation of Sobolev functions.

Hrushikesh Mhaskar, Sergei Pereverzyev, Vasyl Semenov, Evgeniya Semenova

Data based construciton of kernels for classification.

Dongwoo Sheen

P_{1}-nonconforming polyhedral finite elements in high dimensions.

### Month of Mathematical Biology

Stuart T. Johnston, Christopher N. Angstmann, Satya N.V. Arjunan, Casper H.L. Beentjes, Adrien Coulier, Samuel A. Isaacson, Ash A. Khan, Karen Lipkow, Steven S. Andrews

Accurate particle-based reaction algorithms for fixed timestep simulators.

Ana Victoria Ponce Bobadilla, Bartosz Jan Bartmanski, Ramon Grima, Hans G. Othmer

The status of the QSSA approximation in stochastic simulations of reaction networks.

### Recent Trends on Nonlinear PDEs Of Elliptic And Parabolic Type

Elisa Affili, Serena Dipierro, Enrico Valdinoci

Decay estimates in time for classical and anomalous diffusion.

Ben Andrews

Multi-point maximum principles and eigenvalue estimates.

Jérôme Coville

A note on Liouville type results for a fractional obstacle problem.

Serena Dipierro, Pietro Miraglio, Enrico Valdinoci

Symmetry results for the solutions of a partial differential equation arising in water waves.

Francois Hamel, Nikolai Nadirashvili, Yannick Sire

Geometric properties of superlevel sets of semilinear elliptic equations in convex domains.

Michinori Ishiwata, Bernhard Ruf, Federica Sani, Elide Terraneo

A potential well argument for a semilinear parabolic equation with exponential nonlinearity.

Dario Mazzoleni, Benedetta Pellacci, Gianmaria Verzini

Quantitative analysis of a singularly perturbed shape optimization problem in a polygon.

James McCoy, Glen Wheeler

A rigidity theorem for ideal surfaces with flat boundary.

Robin Neumayer

On minimizers and critical points for anisotropic isoperimetric problems.

Philippe Souplet

Liouville-type theorems for nonlinear elliptic and parabolic problems.

## Other Contributed Articles

### Algebraic Geometry, Approximation and Optimisation

Nadezda Sukhorukova, Julien Ugon, David Yost

Schur functions for approximation problems.

### Dynamics, Foliations, and Geometry In Dimension 3

Thomas Barthelmé, Sergio R. Fenley, Steven Frankel, Rafael Potrie

Research announcement: Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds.

Jonathan Bowden, Christian Bonatti, Rafael Potrie

Some remarks on projective Anosov flows in hyperbolic 3-manifolds.

Andy Hammerlindl

Notes on global product structure.

### Geometric and Categorical Representation Theory

Geoff Vooys

The Greenberg functor is site cocontinuous.