Workshop in String Theory, General Relativity and Partial Differential Equations

May/June, 2009, Organizers: Shing-Tung Yau, Lydia Bieri, Li-Sheng Tseng

Harvard University, SC 507

Participants include:

  • Spyros Alexakis (MIT)
  • Michael Anderson (Stony Brook)
  • Melanie Becker (Texas A&M)
  • Michael Eichmair (MIT)
  • Tamar Friedmann (MIT)
  • Sergey Grigorian (AEI Golm)
  • Lan-Hsuan Huang (Stanford)
  • Jeff Jauregui (Duke)
  • Lizhen Ji (Michigan)
  • Conan Leung (CUHK)
  • Bong Lian (Brandeis)
  • Chiu-Chu Melissa Liu (Columbia)
  • Kefeng Liu (UCLA)
  • Maria Psarelli (CUNY)
  • Joel Smoller (Michigan)
  • Xiaofeng Sun (Lehigh)
  • Robert Strain (Princeton/UPenn)
  • Andrey Todorov (UC Santa Cruz)
  • Jens Vogelgesang (Uni Bonn)
  • Mu-Tao Wang (Columbia)
  • Damin Wu (Ohio State)
  • Eric Zaslow (Northwestern)

Week of June 1-5, 2009, SC 507

FrJune5, 2 PMAndrey Todorov (UC Santa Cruz) Maximal unipotent monodromy and topological decomposition of hypersurfaces

Week of May 25-29, 2009, SC 507

MoMay25, 10AMLizhen Ji (Michigan) Coarse Schottky problem and equivariant cell decomposition of Teichmuller spaces
MoMay25, 2PMConan Leung (CUHK) Quantum cohomology for flag varieties
TuMay26, 10AMKefeng Liu (UCLA) Time-periodic solutions of the Einstein field equations
TuMay26, 1:30PMMelanie Becker (Texas A&M) Chiral supergravity and log supergravity
WeMay27, 10AMJoel Smoller (Michigan) A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the Standard Model of Cosmology
WeMay27, 2PMMichael Anderson (Stony Brook) Recent progress on the Bartnik static extension conjecture
ThMay28, 10AMMu-Tao Wang (Columbia) The limit of quasilocal energy-momentum at infinity
ThMay28, 2PMLan-Hsuan Huang (Stanford) Center of mass and constant mean curvature foliations for isolated systems
ThMay28, 4PMMichael Eichmair (MIT) Non-Variational Existence Problems in Geometry and General Relativity
FrMay29, 9:30AMRobert Strain (Princeton/UPenn) Recent global results for the relativistic Boltzmann equation
FrMay29, 11AM Maria Psarelli (CUNY) Decay properties of nonlinear massive Maxwell-Klein-Gordon fields in Minkowski space
FrMay29, 2PM Bong Lian (Brandeis) Maximal unipotent monodromy for complete intersection CY manifolds

Week of May11-15, 2009, SC 507 and 530

MoMay11, 4PMIvan Cheltsov (Edinburgh) Alpha-invariants of Fano orbifolds
TuMay12, 4PMPaolo Aluffi (FSU) Unexpected applications of characteristics classes for singular varieties
ThMay14, 3PMEric Zaslow (Northwestern) Constructible sheaves and the Fukaya category
ThMay14, 9AMS.T. Yau, Spyros Alexakis (MIT), PoNing Chen, Michael Eichmair (MIT), Marc Nardmann, Markus Schmuck (MIT), Lydia Bieri Two-body problem in General Relativity, tracking apparent horizons of black holes


Melanie Becker (Texas A&M) Chiral supergravity and log supergravity.

Abstract: We give an overview of recent developments in the context of 3D gravity and construct the supersymmetric version of chiral gravity and log gravity. More explicitly, we study the linearized approximation of N=1 topologically, massive supergravity around AdS3. Linearized gravitino fields are explicitly constructed. For appropriate boundary conditions, the conserved charges demonstrate chiral behavior, so that "chiral gravity" can be consistently extended to "chiral supergravity." The existence of a logarithmic gravitino mode indicates that a consistent supersymmetric extension of log gravity, alias "log supergravity" might be constructed. We comment on the possible relation between these theories and string theory.

Lan-Hsuan Huang (Stanford) Center of mass and constant mean curvature foliations for isolated systems.

Abstract: I will first introduce the concept of initial data sets in general relativity. An asymptotically flat (AF) initial data set is a model of an isolated system. I will discuss the concept of center of mass of such manifolds from both Hamiltonian and geometric points of view. Then the rest of talk is devoted to the geometric aspect: the existence and uniqueness of the constant mean curvature foliation at infinity. Whether a constant mean curvature foliation uniquely exists in an AF manifold was a question proposed by Yau in the 80's. For manifolds with special asymptotics, some results have been obtained by Huisken-Yau, Ye, and Metzger. We generalize their results to AF manifolds with the parity condition at infinity. It is known that center of mass is defined for those manifolds. Moreover, we show the geometric center of the foliation is indeed center of mass, so the foliation provides a geometric description of center of mass.

Michael Anderson (Stony Brook) Recent progress on the Bartnik static extension conjecture.

Abstract: We will discuss recent work on a conjecture of Bartnik on the existence of AF static vacuum Einstein metrics with prescribed inner boundary data. The conjecture is motivated by Bartnik's definition of quasi-local mass.

Joel Smoller (Michigan) A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the Standard Model of Cosmology.

Abstract: Following up on an idea of Blake Temple that the anomalous acceleration of the universe might be due to a secondary expansion wave reflected back from the shock wave in our shock wave cosmology model (and numerical computations of his student, Zeke Vogler, using a locally inertial numerical method that Temple and Groah derived), Temple invited me to join him on this project when he held the Gehring Chair at the University of Michigan. Together we discovered a surprising new family of expansion waves which perturb the Standard Model of Cosmology, and lead to a mathematically rigorous, non-ad-hoc possible explanation of the accelerating universe based only on Einstein's equations of General Relativity.