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] 22 vwheeler@uow.edu.au • Gabjin Yun [Myingji University] gabjin@mju.ac.kr 23