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, as they become available. The expected publication date is late-2019.

Guest Editors

Algebraic Geometry, Approximation and Optimisation

Enrico Carlini, Jochen Garcke, James Saunderson

On the Frontiers of High Dimensional Computation

Francis 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
P1-nonconforming polyhedral finite elements in high dimensions.

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.

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.

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.