Workshop on Analysis, Geometry and Mathematical
Relativity: a celebration of Robert Bartnik’s 60th birthday
Monash University, 22-26 February 2016
Held at the Clayton campus
Science Lecture Theatre S14, 11 Rainforest Walk
Organised and funded by the
School of Mathematical Sciences at Monash University
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Organizing Committee
• Yann Bernard
School of Mathematical Sciences
Monash University
yann.bernard@monash.edu
• Julie Clutterbuck
School of Mathematical Sciences
Monash University
julie.clutterbuck@monash.edu
• Todd Oliynyk
School of Mathematical Sciences
Monash University
todd.oliynyk@monash.edu
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Monday 22 February 2016
8:00 –
8:50 Registration
S14
8:50 –
9:00 Opening Remarks
S14
9:00 –
9:30 Gerhard Huisken
S14
Robert Bartnik and geometric structures in space-time
9:30 – 10:30 Richard Schoen
(Abstract p18)
S14
(Abstract p10)
S14
(Abstract p10)
S14
A report on the Bartnik quasi-local mass
10:30 – 11:00 Jörg Frauendiener
Numerically gluing initial data sets
11:00 – 11:30 Coffee Break
11:30 – 12:30 Zihua Guo
Non-existence of solution to the 1D periodic cubic nonlinear
Schrödinger equation below L2
12:30 – 14:00 Lunch
14:00 – 15:00 Andrew Hassell
(Abstract p12)
S14
Distribution of eigenvalues of families of unitary operators
15:00 – 16:00 Nalini Joshi
(Abstract p14)
S14
(Abstract p16)
S14
Geometry and analysis of the Painlevé Equations
16:00 – 16:30 Coffee Break
16:30 – 17:00 Chao Liu
Global existence of Newtonian limits for the Einstein-Euler system
with a positive cosmological constant.
17:00 – 17:30 Paul Lasky
(Abstract p18)
S14
The dawn of gravitational-wave astronomy
17:30 – 18:30 Welcome Reception
All lectures take place in the Science Lecture Theatre S14, 11 Rainforest Walk.
1
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Tuesday 23 February 2016
9:30 – 10:30 Gerhard Huisken
(Abstract p13)
S14
Mean curvature flow with surgery for embedded mean-convex surfaces
10:30 – 11:00 James McCoy
(Abstract p17)
S14
Curvature contraction of convex surfaces by nonsmooth speeds
11:00 – 11:30 Coffee Break
11:30 – 12:30 Lydia Bieri
(Abstract p7)
S14
(Abstract p11)
S14
The Shape of the Universe
12:30 – 14:00 Lunch
14:00 – 15:00 Xiaolong Han
Quantum ergodicity: hyperbolic dynamics and randomization
15:00 – 15:30 Pierre Portal
(Abstract p20)
S14
(Abstract p9)
S14
Harmonic analysis of Hodge-Dirac operators
15:30 – 16:00 Coffee Break
16:00 – 16:30 Owen Dearricott
An algebraic closed form for a self-dual Einstein orbifold metric
16:30 – 17:00 Leo Brewin
(Abstract p8)
S14
Some applications of smooth lattice methods to Ricci flow and
numerical relativity
All lectures take place in the Science Lecture Theatre S14, 11 Rainforest Walk.
2
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Wednesday 24 February 2016
9:30 – 10:30 Piotr Chruściel
(Abstract p9)
S14
(Abstract p19)
S14
Mass of characteristic surfaces
10:30 – 11:30 Gilbert Weinstein
The positive mass theorem for multiple rotating charged black holes
11:30 – 12:00 Coffee Break
12:00 – 13:00 Thomas Leistner
(Abstract p15)
S14
Cauchy problems for Lorentzian manifolds with special holonomy
13:00
Free Afternoon
All lectures take place in the Science Lecture Theatre S14, 11 Rainforest Walk.
3
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Thursday 24 February 2016
9:30 – 10:30 James Isenberg
(Abstract p14)
S14
What We Know and Dont Know about the Space of Solutions of the Einstein Constraint Equations
10:30 – 11:00 David Hartley
(Abstract p11)
S14
Eigenfunctions of the Hydrogen Atom with Prescribed Knotted Zeros
11:00 – 11:30 Coffee Break
11:30 – 12:30 Michel Chipot
(Abstract p8)
S14
Nonhomogeneous boundary value problems for the stationary
Navier-Stokes equations in two-dimensional domains with semi-infinite outlets
12:30 – 14:00 Lunch
14:00 – 15:00 Valentina Wheeler
(Abstract p19)
S14
Mean curvature flow with free boundary and uniqueness of
minimal hypersurfaces
15:00 – 15:30 Seungsu Hwang
(Abstract p13)
S14
Linearization of scalar curvature and blackhole uniqueness
15:30 – 16:00 Kuo-Wei Lee
(Abstract p15)
S14
Dirichlet problem for constant mean curvature equation and CMC
foliation in the extended Schwarzschild spacetimes
16:00 – 16:30 Coffee Break
16:30 – 17:00 Binaya Kumar Bishi
(Abstract p7)
S14
Dark energy models in f (R, T ) modify gravity with variable
deceleration parameter
17:00 – 17:30 Stephen McCormick
(Abstract p16)
S14
Killing vectors as Lagrange multipliers
17:30 – 18:30 Break
18:30
Workshop Dinner
All lectures take place in the Science Lecture Theatre S14, 11 Rainforest Walk.
4
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Friday 26 February 2016
9:30 – 10:30 Tristan Rivière
(Abstract p18)
S14
Willmore Minmax Surfaces and the Cost of the Sphere Eversion
10:30 – 11:00 Daniel Hauer
(Abstract p12)
S14
A nonlinear interpolation result with application to nonlinear semigroups
11:00 – 11:30 Coffee Break
11:30 – 12:30 Pengzi Miao
(Abstract p17)
S14
On a variational analogue of the Brown-York mass
12:30 – 12:40 Closing Remarks
S14
All lectures take place in the Science Lecture Theatre S14, 11 Rainforest Walk.
5
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
Location
• The meeting will be held at the Clayton campus and all lectures will take place in the Science
Lecture Theatre S14, 11 Rainforest Walk.
• All coffee breaks will be held in the lobby on the ground floor of the Mathematics & Earth,
Atmosphere and Environment building, 9 Rainforest Walk.
Welcome Reception
A welcome reception will be held in the lobby on the ground floor of the Green Chemical Futures
building, 13 Rainforest Walk, on Monday at 5:30 pm.
Workshop dinner
The workshop dinner will be held at the Monash Club, 32 Exhibition Walk, at 6:30 pm on Thursday.
6
Lydia Bieri
The Shape of the Universe
Tue 11:30 – 12:30
S14
Some of the most interesting solutions of the Einstein equations are space-times exhibiting
gravitational radiation. So far, most studies have been devoted to asymptotically flat systems,
which applies perfectly to gravitational wave sources whose distance to the detector is small
compared to the Hubble radius. However, some of the most powerful sources are at cosmological
distances, and we have to study what happens in an expanding universe. In this talk, we
investigate the geometric-analytic properties of various spacetimes with gravitational radiation,
in particular of cosmological spacetimes. This is joint work with D. Garfinkle.
Binaya Kumar Bishi
Dark energy models in f (R, T ) modify gravity with variable
deceleration parameter
Thu 16:30 – 17:00
S14
This article deals with the Bianchi type-III dark energy model and equation of state parameter
in a first class of f (R, T ) modify gravity. The exact solutions of the modified field equations are
obtained by using (i) linear relation between expansion scalar and shear scalar (ii) linear relation
between state parameter and skewness parameter and (iii) variable deceleration parameter. It
is observed that our models are accelerating for 0 < n < 1 and for n > 1, models show phase
transition from deceleration to acceleration. Further, we have discussed physical properties of
the models.
7
Leo Brewin
Some applications of smooth lattice methods to Ricci flow and
numerical relativity
Tue 17:00 – 17:30
S14
Numerical studies of Ricci flow and general relativity usually employ either finite difference or
spectral methods. Here we will present a different approach that uses a smooth lattice. The
smooth lattice is a collection of vertices and legs with a piecewise local C 2 metric. It can be
considered an extension of the more familiar piecewise-flat lattices used in the Regge Calculus.
The dynamics of the lattice are usually described by evolution equations for the legs and the
curvatures. An outline of the basic mathematics behind the method will be presented as well
some simple examples including axisymmetric Ricci flow in 2 dimensions and the evolution of
Teukolsky waves in 3+1 numerical relativity.
Michel Chipot
Nonhomogeneous boundary value problems for the stationary
Navier-Stokes equations in two-dimensional domains with semi-infinite outlets
Thu 11:30 – 12:30
S14
We would like to present existence results for the stationary nonhomogeneous Navier-Stokes
system



−ν∆u
+
u
·
∇
u + ∇p = f



div u = 0 in Ω,




u = a on ∂Ω.
in Ω,
In this system u is the velocity of a fluid, a its boundary value assumed to have compact
support, ν its viscosity and p its pressure. Ω is the domain occupied by the fluid which is
supposed to be unbounded and having outlets to infinity. The core of the technique is the
construction of solenoidal extensions of a satisfying the so-called Leray-Hopf condition.
8
Piotr Chruściel
Mass of characteristic surfaces
Wed 9:30 – 10:30
S14
Given Robert Bartnik’s studies of the notion of mass in general relativity and of the characteristic Cauchy problem, it appears appropriate to talk about the mass of characteristic surfaces
in this meeting. After a brief review of the general relativistic characteristic Cauchy problem, I
will show how to define the mass of characteristic surfaces. I will present a new identity, valid
for any value of cosmological constant Lambda and derived in collaboration with Lukas Ifsits,
involving the characteristic mass and the “renormalised volume” of the characteristic surface.
When Lambda vanishes, the identity reduces to one established previously by myself and Tim
Paetz, and which gives an elementary proof of positivity of the Trautman-Bondi mass.
Owen Dearricott
An algebraic closed form for a self-dual Einstein orbifold metric
Tue 16:30 – 17:00
S14
In the 90s Hitchin found a number of algebraic solutions to the Painleve VI equation through
the study of triaxial Bianchi IX self-dual Einstein metrics via the theory of isomonodromic
deformations. In this talk we discuss an algebraic solution of Painleve VI and how it gives rise
to an algebraic parametrisation of an SDE metric on a certain space with a locus of conical
singularities and applications to the study of positive sectional curvature in dimension seven.
9
Jörg Frauendiener
Numerically gluing initial data sets
Mon 10:30 – 11:00
S14
About 15 years ago Corvino and Schoen gave a new analytical method for solving the constraint
equations of general relativity. This has been used in several applications in particular to
prove the existence of non-trivial asymptotically simple vacuum space-times. In this talk I
will describe a method to implement the Corvinno-Schoen approach numerically and give some
preliminary examples
Zihua Guo
Non-existence of solution to the 1D periodic cubic nonlinear
Schrödinger equation below L2
Mon 11:30 – 12:30
S14
We prove non-existence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the
circle if initial data belong to H s \ L2 for s < 0. The proof is based on establishing an a priori
bound on solutions to a renormalized cubic NLS in negative Sobolev spaces via the short time
Fourier restriction norm method.
10
Xiaolong Han
Quantum ergodicity: hyperbolic dynamics and randomization
Tue 14:00 – 15:00
S14
We survey some recent advances in quantum ergodicity. On negatively curved manifolds, the
geodesic flows are chaotic (i.e. with exponential instability), we show that any Laplacian eigenbasis contains a full density subsequence that is equidistributed at logarithmic scales; on the
spheres and tori, the space of Laplacian eigenbases is infinite-dimensional and therefore is endowed with a natural probability measure, we show that a random eigenbasis is equidistributed
at polynomical scales.
David Hartley
Eigenfunctions of the Hydrogen Atom with Prescribed Knotted Zeros
Thu 10:30 – 11:00
S14
In 2001, motivated by finding eigenfunctions of the hydrogen atom whose nodal sets form torus
knots, Michael Berry asked whether any finite link could be realised as the nodal set of an
eigenfunction to some quantum system. In previous work with Alberto Enciso and Daniel
Peralta-Salas we proved this was the case by considering high energy eigenfunctions of the
harmonic oscillator. This talk will discuss recent work where we provide a new proof of the
conjecture using eigenfunctions of the hydrogen atom in order to match Berry’s original setting.
Specifically, we proved that any finite link in R3 can be realised as the union of connected
components of the nodal set of a hydrogen atom eigenfunction, up to a diffeomorphism of R3 .
The high energy asymptotics of the hydrogen atom’s eigenfunctions and the existence of a
Green’s function with certain smoothness properties play key roles in this proof.
11
Andrew Hassell
Distribution of eigenvalues of families of unitary operators
Mon 14:00 – 15:00
S14
Unitary operators arise in many places in geometric analysis. I will consider two cases: the scattering matrix for a perturbation of the Laplacian in Euclidean space, and the Cayley transform
of the semiclassical Dirichlet-to-Neumann operator on a compact Riemannian with boundary.
(It might be thought that the second example is artificial, but I will explain that this is not
so.) In these examples, one has a family of unitary operators U (h), depending on a Planck
constant h → 0. As unitaries, these operators have spectrum on the unit circle. Under suitable
conditions, the spectrum is discrete away from the point 1 on the unit circle, and one can obtain
asymptotics for the number of eigenvalues in any interval of the unit circle away from 1.
I will discuss various settings in which we have been able to obtain such asymptotics.
Daniel Hauer
A nonlinear interpolation result with application to nonlinear semigroups
Fri 10:30 – 11:00
S14
In this talk, I want to present a new nonlinear interpolation theorem, which improves Peetres
(Theorem 3.1 in [Mathematica1970]) and Tartar’s (Théorème 4 in JFA1972) nonlinear interpolation results. In order to highlight the strength of this result I will provide some applications to
nonlinear semigroups. The results present in this talk are obtained in joint work with Thierry
Coulhon (PSL, Paris)
12
Gerhard Huisken
Mean curvature flow with surgery for embedded mean-convex surfaces
Tue 9:30 – 10:30
S14
The lecture presents joint work with Simon Brendle on the deformation of closed embedded
surfaces of positive mean curvature in Riemannian manifolds. The flow develops singularities
that can be overcome with finitely many surgeries. The lecture explains crucial techniques and
an application to asymptotically flat 3-manifolds arising in General Relativity.
Seungsu Hwang
Linearization of scalar curvature and blackhole uniqueness
Thu 15:00 – 15:30
S14
Recent results on the kernel of linearized scalar curvature will be presented. Also its relation
to the blackhole uniqueness or critical points of the total scalar curvature will be discussed.
13
James Isenberg
What We Know and Dont Know about the Space of Solutions of the Einstein Constraint
Thu 9:30 – 10:30
Ten years ago, Robert Bartnick and I wrote a review article summarizing what was known
at the time about the Einstein constraint equations and their solutions. In that article, we
noted that while much was known about solutions of the constraints which have constant mean
curvature (CMC) or are nearly CMC, very little was known about solutions which are far from
CMC. The hope at the time was that the effectiveness of the conformal method for constructing
CMC and near-CMC solutions would (perhaps after much work) extend to far-from-CMC.
In the years since this article appeared, new results have slowly been obtained. While some
have been consistent with this optimistic view, many others have shown that the picture for
far-from CMC solutions is likely to be much more complicated. After a brief survey of what
the conformal method is and what it has shown us for CMC and for near-CMC solutions, we
survey a variety of new results which show how complicated things can become for far-fromCMC solutions, and for solutions which include a cosmological constant (of the DeSitter type).
We also note some very recent results which fill in some holes in our understanding of CMC
and near-CMC solutions.
Nalini Joshi
Geometry and analysis of the Painlevé Equations
Mon 15:00 – 16:00
S14
TBA
14
Kuo-Wei Lee
Dirichlet problem for constant mean curvature equation and CMC
foliation in the extended Schwarzschild spacetimes
Thu 15:30 – 16:00
S14
In this talk, we will show the existence and uniqueness of the Dirichlet problem for the constant mean curvature equation with spherical symmetry and symmetric boundary data in the
extended Schwarzschild spacetime. As an application, we will prove the existence of the CMC
foliation in the extended Schwarzschild spacetime, which is conjectured by Melac and O Murchadha.
Thomas Leistner
Cauchy problems for Lorentzian manifolds with special holonomy
Wed 12:00 – 13:00
S14
Lorentzian manifolds with parallel null spinor or, more generally, parallel null vector arise
naturally in general relativity, as supersymmetric supergravity backgrounds, but also in the
theory of Lorentzian manifolds with special holonomy. In analogy to the Cauchy problem in
general relativity, we study the corresponding Cauchy problems for these manifolds: Can a
given Riemannian manifold (M,g) be embedded (as a Cauchy hypersurface) in a Lorentzian
manifold with parallel null vector/ spinor field? We derive the constraint and the evolution
equations for this problem. By reducing them to a system in Cauchy-Kowalevski form and
moreover to a quasilinear symmetric hyperbolic system, we show that the evolution equations
have a unique (analytic/smooth) solution provided the initial data are analytic/smooth and
satisfy the constraints. Moreover, for Riemannian manifolds obeying the constraint conditions,
we derive a local normal form and use the classification of Lorentzian holonomy groups to
describe their special geometry. As an application of our results to Riemannian geometry we
obtain a classification of the local geometry of Riemannian manifolds with generalised imaginary
Killing spinors. This is joint work with H. Baum and A. Lischewski (both Humboldt University
Berlin).
15
Chao Liu
Global existence of Newtonian limits for the Einstein-Euler system
with a positive cosmological constant.
Mon 16:30 – 17:00
S14
We have known FLRW background solutions to Einstein-Euler system with positive cosmological constant are future-stable globally. In this talk, we will briefly prove all these small
perturbation solutions around above FLRW background also have Newtonian limits globally
under some specific conditions.
Stephen McCormick
Killing vectors as Lagrange multipliers
Thu 17:00 – 17:30
S14
We review a result of Bartnik equating stationary initial data with critical points of the ADM
mass; a result that ultimately boils down to a Lagrange multipliers argument. The Lagrange
multiplier in this case is the Killing vector. By imposing different boundary conditions, both at
infinity and on an interior boundary, one obtains a variety of analogous conditions for initial data
to be Killing. One also has analogous results in coupled systems, such as Einstein-Maxwell and
Einstein-Yang-Mills. We discuss some consequences of this argument under different boundary
conditions on the initial data and Lagrange multiplier, including connections to the first law of
black hole mechanics and quasilocal mass.
16
James McCoy
Curvature contraction of convex surfaces by nonsmooth speeds
Tue 10:30 – 11:00
S14
We consider the motion of convex surfaces and hypersurfaces with normal speeds given by
arbitrary strictly monotone, homogeneous degree one functions of the principal curvatures that
are not necessarily smooth. We prove that such processes deform arbitrary uniformly convex
initial surfaces to points in finite time, with spherical limiting shape. Two crucial ingredients in
the proof are a suitable regularisation procedure for the speed and an exponentially decreasing
curvature quantity for the rescaled flows that survives to remain monotone for the ‘limit flow’
by the nonsmooth speed.
Pengzi Miao
On a variational analogue of the Brown-York mass
Fri 11:30 – 12:30
S14
Let (Ω, g) be a compact 3-Riemannian manifold with nonnegative scalar curvature, with boundary Σ. If Σ is topologically a 2-sphere with positive Gaussian curvature and positive mean
curvature, the Brown-York mass of Σ in (Ω, g) is given by
Z
1
(H0 − H)dσ
8π Σ
where H0 is the mean curvature of the isometric embedding of Σ in R3 , H is the mean curvature
of Σ in (Ω, g) and dσ is the area element on Σ. In this talk, we discuss a variational analogue
of the Brown-York mass which does not require Σ to have positive Gaussian curvature. This
is a joint work with Christos Mantoulidis.
17
Tristan Rivière
Willmore Minmax Surfaces and the Cost of the Sphere Eversion
Fri 9:30 – 10:30
S14
We develop a general Minmax procedure in Euclidian spaces for constructing Willmore surfaces
of non zero indices. We implement this procedure to the Willmore Minmax Sphere Eversion in
the 3 dimensional euclidian space in order to compute the cost of this famous eversion.
Richard Schoen
A report on the Bartnik quasi-local mass
Mon 9:30 – 10:30
S14
We will introduce the Bartnik quasi-local mass and discuss some of its properties. The definition
postulates a difficult variational problem for exterior metrics about which we still know very
little. In the very special case that the inner boundary is an an apparent horizon (or nearly
one) it turns out to be possible to compute the Bartnik mass rather precisely and to describe
what happens to a minimizing sequence. This ties in with geometric properties of apparent
horizons and a conjecture of Gibbons in the spirit of the hoop conjecture of Thorne. The latter
part of this talk will describe joint work with C. Mantoulidis.
Paul Lasky
The dawn of gravitational-wave astronomy
Mon 17:00 – 17:30
S14
LIGO has directly detected gravitational waves. The inspiral, merger and ringdown of a binary
black hole was measured on the 14th of September 2015. I will describe in detail the experiment,
the observations, and the future of gravitational-wave astronomy.
18
Gilbert Weinstein
The positive mass theorem for multiple rotating charged black holes
Wed 10:30 – 11:30
S14
In this talk, I will present a lower bound for the ADM mass given in terms of the angular
momenta and charges of black holes present in axisymmetric initial data sets for the EinsteinMaxwell equations. This generalizes the mass-angular momentum-charge inequality obtained
by Chruściel and Costa to the case of multiple black holes. The hypotheses used in the proof
of this result for single black holes are also weakened and we establish the associated rigidity
statement. This is joint work with Marcus Khuri.
Valentina Wheeler
Mean curvature flow with free boundary and uniqueness of
minimal hypersurfaces
Thu 14:00 – 15:00
S14
A mean curvature flow with free boundary is a family of hypersurfaces evolving by mean
curvature flow that meet another hypersurface perpendicularly. The boundary is ‘free’ in the
sense that, as points move in the normal direction only, no compatibility conditions are required.
In this talk, we survey recent progress on questions of global existence for the flow and possible
asymptotic shapes; these include minimal hypersurfaces as well as translating solutions. We
shall also demonstrate how the flow can provide an intuitive method to establish uniqueness
theorems for minimal hypersurfaces in special situations for a class of support hypersurfaces.
These uniqueness theorems allow, in some cases, support hypersurfaces and topologies of the
minimal hypersurface more general than previously considered in the literature. Some results
mentioned in this talk are joint work with Glen Wheeler and Hojoo Lee.
19
Pierre Portal
Harmonic analysis of Hodge-Dirac operators
Tue 15:30 – 16:00
S14
When the metric on a Riemannian manifold is perturbed in a rough (merely bounded and
measurable) manner, do basic estimates involving the Hodge Dirac operator D = d + d∗ remain
valid? Even in the model case of a perturbation of the euclidean metric on Rn , this is a difficult
√
question. For instance, the fact that the L2 estimate kDuk2 ∼ k D2 uk2 remains valid for
perturbed versions of D was a famous conjecture made by Kato in 1961 and solved, positively,
in a ground breaking paper of Auscher, Hofmann, Lacey, McIntosh and Tchamitchian in 2002.
In the past fifteen years, a theory has emerged from the solution of this conjecture, making rough
perturbation problems much more tractable. In this talk, I will give a general introduction to
this theory, and present one of its latest results: a flexible approach to Lp estimates for the
holomorphic functional calculus of D. This is joint work with D. Frey (Delft) and A. McIntosh
(ANU).
20
Workshop on Analysis, Geometry and Mathematical Relativity:
a celebration of Robert Bartnik’s 60th birthday
List of Participants
• Chris van der Heide [University of Queensland]
• Kishor Adhav [Sant Gadge Baba Amravati University]
chris.vdh@gmail.com
ati_ksadhav@yahoo.co.in
• Subash Adhikari [Tribhuvan University]
subash1e@hotmail.com
• Robert Bartnik [Monash University]
robert.bartnik@monash.edu
• Dipanjali Behera [Sambalpur University]
dipadolly@rediffmail.com
• Yann Bernard [Monash University]
yann.bernard@monash.edu
• Lydia Bieri [University of Michigan]
lbieri@umich.edu
• Binaya Kumar Bishi [Visvesvaraya National Institute of Technology]
• Leo Brewin [Monash University]
binaybc@gmail.com
leo.brewin@monash.edu
• Anthony Carapetis [Australian National University]
• Michel Chipot [Universität Zürich ]
anthony.carapetis@gmail.com
m.m.chipot@math.uzh.ch
• Piotr Chruściel [Universität Wien]
piotr.chrusciel@univie.ac.at
• Julie Clutterbuck [Monash University]
julie.clutterbuck@monash.edu
• Matthew Cooper [University of New England]
• Owen Dearricott [University of Melbourne]
• Friederike Dittberner [ Freie Universität Berlin]
mcoope42@une.edu.au
odearricott@ms.unimelb.edu.au
dittberner@math.fu-berlin.de
• Jerome Droniou [Monash University]
jerome.droniou@monash.edu
• Mark Fisher [Monash University]
markfisher.mail@gmail.com
• Justin Forlano [Monash University]
justin.forlano@monash.edu
• Jörg Frauendiener [University of Otago]
joergf@maths.otago.ac.nz
• Hamed Ghaemidizicheh [Koç University]
hghaemidizicheh@ku.edu.tr
• Wolfgang Globke [University of Adelaide]
wolfgang.globke@adelaide.edu.au
• Zihua Guo [Monash University]
zihua.guo@monash.edu
• Andy Hammerlindl [Monash University]
andy.hammerlindl@monash.edu
• Xiaolong Han [Australian National University]
• David Hartley [Instituto de Ciencias Matemáticas]
• Andrew Hassell [Australian National University]
• Daniel Hauer [University of Sydney]
Xiaolong.Han@anu.edu.au
david.hartley@icmat.es
Andrew.Hassell@anu.edu.au
daniel.hauer@sydney.edu.au
• Shuhui He [University of Wollongong]
sh807@uowmail.edu.au
• John Head [Monash University]
john.head@monash.edu
• Peter Huf [Deakin University]
peterhuf@deakin.edu.au
• Gerhard Huisken [Universität Tübingen]
gerhard.huisken@uni-tuebingen.de
• Seungsu Hwang [Chung-Ang University]
seungsu@cau.ac.kr
21
• James Isenberg [University of Oregon]
isenberg@uoregon.edu
• Daniel Jackson [Monash University]
daniel.jackson@monash.edu
• Nalini Joshi [University of Sydney]
nalini.joshi@sydney.edu.au
• Nikos Kalogeropoulos [Weill Cornell Medicine - Qatar]
nik2011@qatar-med.cornell.edu
• Goverdhan Khadekar [RTM Nagpur Unversity]
gkhadekar@yahoo.com
• Kwok-Kun Kwong [National Cheng Kung University]
kwong@mail.ncku.edu.tw
• Paul Lasky [Monash University]
paul.lasky@monash.edu
• Hojoo Lee [Korea Institute for Advanced Study]
momentmaplee@gmail.com
• Kuo-Wei Lee [National Taiwan University]
• Thomas Leistner [University of Adelaide]
d93221007@gmail.com
thomas.leistner@adelaide.edu.au
• Tyson Liddell [Monash University]
tlid1@student.monash.edu
• Chao Liu [Monash University]
chao.liu@monash.edu
• Gregoire Loeper [Monash University]
gregoire.loeper@monash.edu
• Ali Maalaoui [American University of Ras Al Khaimah]
ali.maalaoui@gmail.com
• Mohamed Mame [Ecole of Teachers in Akjoujt ENI ENI]
OULDEMAME@UNIV-NKC.MR
• Daniel Mathews [Monash University]
Daniel.Mathews@monash.edu
• Stephen McCormick [University of New England]
stephen.mccormick@une.edu.au
• James McCoy [University of Wollongong]
jamesm@uow.edu.au
• Alan McIntosh [Australian National University]
alan.mcintosh@anu.edu.au
• Pengzi Miao [Miami University]
pengzim@math.miami.edu
• Bivudutta Mishra [Birla Institute of Technology and Science]
• Chaitanya Oehmigara [Australian National University]
bivudutta@gmail.com
chaitanya.oehmigara@anu.edu.au
• Todd Oliynyk [Monash University]
todd.oliynyk@monash.edu
• Pierre Portal [Australian National University]
pierre.portal@gmail.com
• Sasmita Kumari Pradhan [Sambalpur University]
sasmita.gita91@gmail.com
• Alan Pryde [Monash University]
alan.pryde@monash.edu
• Juncheol Pyo [Pusan National University]
jcpyo@pusan.ac.kr
• Tristan Rivière [ETH]
tristan.riviere@math.ethz.ch
• Calum Robertson [Monash University]
calum.robertson@monash.edu
• Richard Schoen [University of California, Irvine]
rschoen@math.uci.edu
• Jason Sharples [University of New South Wales]
j.sharples@adfa.edu.au
• Abhishek Singh [Birla Institute of Technology and Science]f2014752@hyderabad.bits-pilani.ac.in
• Arthur Suvorov [University of Melbourne]
suvorova@student.unimelb.edu.au
• Samhita Vadrevu [Birla Institute of Technology and Science]
• Paritosh Verma [Scuola Normale Superiore di Pisa]
• Gilbert Weinstein [Ariel University]
vadrevu.samhita@gmail.com
paritosh.dwarf05@gmail.com
gilbert.weinstein@gmail.com
• Valentina Wheeler [University of Wollongong]
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vwheeler@uow.edu.au
• Gabjin Yun [Myingji University]
gabjin@mju.ac.kr
23