The 11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI)
The Role of Metrics in the Theory of Partial Differential Equations

Contents

Program

Schedule

* The lectures in the morning will be delivered at Conference Hall during July 2 - July 6,
            and at Akira Suzuki Hall during July 9 - July 13, respectively.

July 2 (Mon.)
10:30 - 10:40Opening Remarks
10:40 - 11:30 Sergiu Klainerman
On the mathematical theory of black holes, I
Slides
13:30 - 14:50 Poster Session (Venue: Conference Room 1)
Session A (Venue: Conference Hall)
15:00 - 15:50Gerhard Huisken
Mean curvature flow with surgery of embedded mean-convex surfaces in 3-manifolds
16:00 - 16:50Mu-Tao Wang
Quasilocal mass and isometric embedding
Slides
Session B (Venue: Conference Room 1)
15:00 - 15:50 Yi Zhou
Global instability of the multi-dimensional plane shocks for the isothermal Euler equations
Slides
16:00 - 16:50Piero D'Ancona
On the defocusing supercritical wave equation outside a ball
Slides

July 3 (Tue.)
09:30 - 10:20 Mihalis Dafermos
Black hole interiors and the strong cosmic censorship conjecture in general relativity, I
10:40 - 11:30 Sergiu Klainerman
On the mathematical theory of black holes, II
Slides
Session A (Venue: Conference Hall)
13:30 - 14:00Toru Kajigaya
Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow
14:10 - 14:40Norihiro Tanahashi
Separability of Maxwell equation in rotating black hole spacetime and its geometric aspects
Slides
15:00 - 15:50Gilbert Weinstein
Harmonic maps with prescribed singularities and applications in general relativity
Slides
16:00 - 16:50Sumio Yamada
Harmonic maps in general relativity
Session B (Venue: Conference Room 1)
13:30 - 14:00Mamoru Okamoto
Random data Cauchy problem for the energy-critical nonlinear Schrodinger equations
14:10 - 14:40Takahisa Inui
Global behavior of solutions to the energy critical nonlinear damped wave equation
15:00 - 15:50Kenichi Ito
Asymptotics of generalized eigenfunctions on manifold with Euclidean and/or hyperbolic ends
Slides
16:00 - 16:50Wei-Min Wang
Time quasi-periodic solutions to the nonlinear Klein-Gordon equations
Slides

July 4 (Wed.)
09:30 - 10:20 Jean-Marc Delort
Long time existence results for Hamiltonian non-linear Klein-Gordon equations on some compact manifolds, I
Slides
10:40 - 11:30 Mihalis Dafermos
Black hole interiors and the strong cosmic censorship conjecture in general relativity, II
12:00 -   Excursion

July 5 (Thu.)
09:30 - 10:20 Sergiu Klainerman
On the mathematical theory of black holes, III
Slides
10:40 - 11:30 Jean-Marc Delort
Long time existence results for Hamiltonian non-linear Klein-Gordon equations on some compact manifolds, II
13:30 - 14:50 Poster Session (Venue: Hall)
Session A (Venue: Conference Hall)
15:00 - 15:50Vanessa Styles
Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
16:00 - 16:50Richard Tsai
Volumetric extensions of variational problems defined on surfaces
Session B (Venue: Conference Room 1)
15:00 - 15:50Joachim Krieger
On stability of blow up solutions for the critical co-rotational wave maps problem
16:00 - 16:50Soichiro Katayama
Global existence and the asymptotic behavior for systems of nonlinear wave equations violating the null condition

July 6 (Fri.)
09:30 - 10:20 Mihalis Dafermos
Black hole interiors and the strong cosmic censorship conjecture in general relativity, III
10:40 - 11:30 Jean-Marc Delort
Long time existence results for Hamiltonian non-linear Klein-Gordon equations on some compact manifolds, III
Session A (Venue: Conference Hall)
13:30 - 14:00 Koya Sakakibara
Numerical analysis of one-harmonic equation with values in matrix Lie group
14:10 - 14:40 Tatsu-Hiko Miura
Singular limit problem for the Navier-Stokes equations in a curved thin domain
15:00 - 15:50Seiro Omata
Free boundary problems of hyperbolic type with a focus on the free boundary conditions
16:00 - 16:50 Selim Esedoglu
Algorithms for motion of networks by weighted mean curvature
Session B (Venue: Conference Room 1)
13:30 - 14:00 Masahiro Ikeda
Blow-up of solutions to semilinear wave equation with a scaling invariant critical damping
Slides
14:10 - 14:40 Hayato Miyazaki
The initial value problem for the generalized KdV equation with low degree of non-linearity
Slides
15:00 - 15:50Jacob Sterbenz
Local energy decay and the vector field method
16:00 - 16:50 Ning-An Lai
Weighted L2 - L2 estimate for wave equation and its application
Slides

July 9 (Mon.)
10:40 - 11:30 Felix Otto
Nonlinear partial differential equations and interfacial motions as gradient flow, I
13:30 - 14:50 Poster Session (Venue: Foyer)
Session A (Venue: Akira Suzuki Hall)
15:00 - 15:50 Akito Futaki
Geometric nonlinear problems and GIT stability through moment maps
16:00 - 16:50 Yoshihiro Tonegawa
Existence theorem for Brakke flow
Session B (Venue: Seminar Room 2)
15:00 - 15:50 Hiroyuki Takamura
Multipliers on the wave-like blow-up for nonlinear damped wave equations
Slides
16:00 - 16:50 Yuichiro Sekiguchi
Numerical relativity: generating space-time on computers
Slides

July 10 (Tue.)
09:30 - 10:20 Antonin Chambolle
Anisotropic and crystalline mean curvature flows, I
Slides
10:40 - 11:30 Felix Otto
Nonlinear partial differential equations and interfacial motions as gradient flow, II
Session A (Venue: Akira Suzuki Hall)
13:30 - 14:00 Shouhei Honda
Recent developments on metric measure spaces with Ricci bounds from below
14:10 - 14:40 Kelei Wang
Simons cone and saddle solutions of the Allen-Cahn equation
Slides
15:00 - 15:50Kazuo Akutagawa
Edge-cone Einstein metrics and Yamabe metrics
Slides
16:00 - 16:50 Matteo Novaga
Evolution by curvature of planar networks
Slides
Session B (Venue: Seminar Room 2)
13:30 - 14:00 Yusuke Sugiyama
Global existence and degeneracy in finite time for 1D quasilinear wave equations
Slides
14:10 - 14:40 Takiko Sasaki
The blow-up curve of solutions for semilinear wave equations with Dirichlet boundary conditions in one space dimension
Slides
15:00 - 15:50Karen Yagdjian
A novel integral transform approach to solving hyperbolic equations in the curved spacetimes
Slides
16:00 - 16:50 Makoto Nakamura
On some effects of background metrics for several partial differential equations

July 11 (Wed.)
09:30 - 10:20 Charles M. Elliott
Variational, geometric and surface PDEs in cell biology, I
10:40 - 11:30 Antonin Chambolle
Anisotropic and crystalline mean curvature flows, II
12:00 -   Excursion

July 12 (Thu.)
09:30 - 10:20 Felix Otto
Nonlinear partial differential equations and interfacial motions as gradient flow, III
10:40 - 11:30 Charles M. Elliott
Variational, geometric and surface PDEs in cell biology, II
13:30 - 14:50 Poster Session (Venue: Foyer)
Session A (Venue: Akira Suzuki Hall)
15:00 - 15:50 Miyuki Koiso
Uniqueness problem for closed non-smooth hypersurfaces with constant anisotropic mean curvature
16:00 - 16:50 Neshan Wickramasekera
Regularity of minimal and CMC stable hypersurfaces
Session B (Venue: Seminar Room 2)
15:00 - 15:50 Masaharu Taniguchi
Multidimensional traveling fronts in reaction-diffusion equations
16:00 - 16:50 Elliott Ginder
Approximation methods for oscillatory and constrained interfacial dynamics

July 13 (Fri.)
09:30 - 10:20 Antonin Chambolle
Anisotropic and crystalline mean curvature flows, III
10:40 - 11:30 Charles M. Elliott
Variational, geometric and surface PDEs in cell biology, III
Session A (Venue: Akira Suzuki Hall)
13:30 - 14:00 Qing Liu
Large exponent behavior of power curvature flow and applications
Slides
14:10 - 15:00 Yoshihito Kohsaka
On the dynamics for the volume-preserving geometric flows
15:10 - 16:00 Katsuyuki Ishii
Convergence of a threshold-type algorithm for mean curvature flow
Session B (Venue: Seminar Room 2)
13:30 - 14:00 Bronwyn Hajek
Analytical solutions of nonlinear reaction-diffusion equations in various coordinate systems
Slides
14:10 - 15:00 Petrus van Heijster
Pinned localised solutions in a heterogeneous three-component FitzHugh-Nagumo model
15:10 - 16:00 Sanjeeva Balasuriya
Stochastic sensitivity of finite-time Lagrangian motion
16:00 - 16:10Closing

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