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Semester Workshops

08-01-2005 - 12-31-2005

  1. Workshop Recent Results in Nonlinear Elliptic Equations and their Interactions with Geometry

    Frank Pacard, Neil Trudinger and Paul Yang

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    Oct 31, 2004
    Sunday
    09:30 AM - 10:30 AM
      Curvature Estimate for 4-dimensional Einstein Equation.
    Gang Tian (Princeton University)
    Oct 31, 2005
    Monday
    11:00 AM - 12:00 PM
      On the Calabi Functional in Kahler Manifold
    Xiu-Xiong Chen
    12:00 PM - 01:00 PM
      Volume Growth, Curvature Decay, and Critical Metrics
    Jeff Viaclovsky (University of Wisconsin)
    02:30 PM - 03:30 PM
      Regularity of Radial Minimizers and Extremal Radial Solutions of Semilinear Elliptic Equations.
    Xavier Cabré (Polytechnical University of Cataluña (Barcelona))
    Nov 01, 2005
    Tuesday
    09:30 AM - 10:30 AM
      Blowup Issues for the Yamabe Equation on High Dimensional Manifolds.
    Richard Schoen (Stanford University)
    11:00 AM - 12:00 PM
      Global Convergence of the Yamabe Flow in Dimension 6 and Higher.
    Simon Brendle (Stanford University)
    12:00 PM - 01:00 PM
      The Prescribed Scalar Curvature Problem.
    Olivier Druet
    02:30 PM - 03:30 PM
      The First Dirac Eigenvalue in a Conformal Class.
    Bernd Ammann
    04:00 PM - 05:00 PM
      Kahler-Ricci Flow and Certain Complex Monge-Ampere Equation.
    Xiaohua Zhu (Peking Univiversity)
    Nov 02, 2005
    Wednesday
    09:30 AM - 10:30 AM
      Rigidity Inequalities Via Inverse Mean Curvature Flow.
    Gerhard Huisken (Math. Forschungsinstitut Oberwolfach)
    11:00 AM - 12:00 PM
      The Mean Curvature Equation in Pseudohermitian Geometry.
    Jih-Hsin Cheng
    12:00 PM - 01:00 PM
      Boundary Estimates for Some Fully Nonlinear PDEs and Applications to Conformal Geometry.
    Szu-yu Sophie Chen
    02:30 PM - 03:30 PM
      Smooth Local Isometric Embedding of Surfaces with Gauss Curvature Changing Sign Monotonically Across a Curve.
    Qing Han
    04:00 PM - 05:00 PM
      Selfdual Variational Principles for PDEs and Evolution Equations.
    Nassif Ghoussoub (University of British Columbia)
    Nov 03, 2005
    Thursday
    09:30 AM - 10:30 AM
      On Semi-linear Conformally Invariant PDE.
    Jie Qing (University of California, Santa Cruz)
    11:00 AM - 12:00 PM
      Complete Hypersurfaces of Constant Curvature in Hyperbolic Space with Prescribed Asymptotic Boundary.
    Joel Spruck (Johns Hopkins University)
    12:00 PM - 01:00 PM
      Einstein Metrics and Higher Rank Geometry.
    Rafe Mazzeo (Stanford University)
    02:30 PM - 03:30 PM
      Getting a Handle on the Helicord.
    Brian White
    04:00 PM - 05:00 PM
      Fully Nonlinear Partial Differential Equations and Applications in Geometry.
    Xu-Jia Wang (Australian National University)
    Nov 04, 2005
    Friday
    11:00 AM - 12:00 PM
      Conformal Invariants Associated with a Smooth Measure.
    Sun-Yung Alice Chang (Princeton University)
    12:00 PM - 01:00 PM
      Conformal Laplacian Operators and Q-curvature on Einstein Manifolds.
    Ashwin Gover
    02:30 PM - 03:30 PM
      Intrinsic Submanifolds of Heisenberg Group.
    Bruno Franchi
    04:00 PM - 05:00 PM
      On the Higher Order Q Curvature on the Sphere.
    Fengbo Hang
  2. Workshop Analytical and Stochastic Fluid Dynamics

    Craig Evans, Susan Friedlander, Boris Rozovsky, Daniel Tataru and David A. Ellwood

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    Oct 10, 2005
    Monday
    09:30 AM - 10:00 AM
      Remarks on the Normal Form of the Navier-Stokes Equations
    Mohammed Ziane
    10:00 AM - 10:45 AM
      Nonlinear Fokker-Planck Navier-Stokes Systems
    Peter Constantin
    11:15 AM - 12:00 PM
      Global Regularity for the Three-dimensional Primitive Equations of Ocean and Atmosphere Dynamics
    Edriss Titi
    02:45 PM - 03:30 PM
      Asymptotic Properties of Some SPDE with Small Dissipation
    Sergej Kuksin
    04:00 PM - 04:45 PM
      Markov Selections and Their Regularity for 3D Stochastic Navier-Stokes Equations.
    Franco Flandoli
    04:45 PM - 05:15 PM
      Spectral Problem for the Euler and Navier-Stokes Equations
    Roman Shvydkoy
    Oct 11, 2005
    Tuesday
    09:30 AM - 10:00 AM
      Simple Solvable Models with Cascade of Energy and Anomalous Dissipation
    Eric Vanden-Eijnden (New York University, Courant Institute)
    10:00 AM - 10:45 AM
      Exponential Mixing for the Degenerately Forced Navier Stokes Equations
    Jonathan Mattingly (Duke University)
    11:15 AM - 12:00 PM
      Regularity of L^{3,\infty} Solutions of the Navier-Stokes Equations
    Vladimir Sverak (University of Minnesota Twin Cities)
    02:45 PM - 03:30 PM
      The Surface QG-alpha Equation
    Charles Fefferman (Princeton University)
    04:00 PM - 04:45 PM
      The Interplay between Local Geometric Properties and the Global Regularity for 3D Inocompressible Flows.
    Thomas Hou
    04:45 PM - 05:15 PM
      Bounded Domain Limit for Navier-Stokes and Euler Equations
    Jim Kelliher
    Oct 12, 2005
    Wednesday
    09:30 AM - 10:00 AM
      One Direction and One Component Regularity for the Navier-Stokes Equations
    Igor Kukavica
    10:00 AM - 10:45 AM
      Electrowetting in a Hele-Shaw Geometry
    Andrea Bertozzi (University of California, Los Angeles)
    11:15 AM - 12:00 PM
      Chaotic Motions and Developed Turbulence: Heuristic Ideas
    Giovanni Gallavotti
    02:45 PM - 03:30 PM
      Analytic Stability and Singularities for Kelvin Helmholtz, Rayleigh Taylor, Problems Comparison with the Stability of Water Waves Problems
    Claude Bardos
    04:00 PM - 04:45 PM
      Regularity for a Free Boundary Problem and a Conjecture of De Giorgi
    Herbert Koch (Rheinische Friedrich-Wilhelms-Universität Bonn)
    04:45 PM - 05:15 PM
      Long time Behavior of Solutions to the 3D Navier-Stokes
    Natasa Pavlovic (University of Texas)
    Oct 13, 2005
    Thursday
    09:30 AM - 10:00 AM
      On the Decay of the Energy Spectrum for Weak Solutions to the Navier-Stokes Equations
    Anna Mazzucato
    10:00 AM - 10:45 AM
      Linear Superposition of Nonlinear Waves
    Anatoli Babine
    Oct 14, 2005
    Friday
    09:30 AM - 10:00 AM
      Passive Scalar Equation in a Turbulent Gaussian Velocity Field
    Boris Rozovsky (Brown University)
    10:00 AM - 10:45 AM
      Scaling Laws in Turbulence
    Alexandre Chorin (University of California, Berkeley)
    11:15 AM - 12:00 PM
      On Stochastic Euler equation
    Remigijus Mikulevicius
    02:45 PM - 03:30 PM
      The Emergence of Large Scale Coherent Structure under Small Scale Random Bombardments
    Xiaoming Wang
  3. Workshop Introductory Workshop in Nonlinear Dispersive Equations

    James Colliander (Toronto), Patrick Gerard (Orsay), Herbert Koch (Dortmund), Natasha Pavlovic (Princeton), Daniel Tataru (Berkeley)

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    Aug 22, 2005
    Monday
    09:15 AM - 10:15 AM
      Nonlinear Dispersive Equations-Lecture I
    Wilhelm Schlag
    10:45 AM - 11:45 AM
      Wave Packet Methods for Hyperbolic Equations I
    Hart Smith (University of Washington)
    02:00 PM - 03:00 PM
      Normal Forms in NLS
    Jean Bourgain (Institute for Advanced Study)
    03:30 PM - 04:30 PM
      Nonlinear Dispersive Equations-Talk
    Gustavo Ponce (University of California, Santa Barbara)
    Aug 23, 2005
    Tuesday
    09:15 AM - 10:15 AM
      Nonlinear Dispersive Equations-Lecture II
    Wilhelm Schlag
    10:45 AM - 11:45 AM
      Wave Packet Methods for Hyperbolic Equations II
    Hart Smith (University of Washington)
    02:00 PM - 03:00 PM
      Nonlinear Dispersive Equations-Talk
    Kenji Nakanishi
    03:30 PM - 04:30 PM
      Non-Generic Blow Up Solutions for the Critical Focusing NLS in1-d
    Joachim Krieger
    Aug 24, 2005
    Wednesday
    09:15 AM - 10:15 AM
      Strichartz Estimates for the Schrodinger Equation with Variable Coefficients
    Claude Zuily
    10:45 AM - 11:45 AM
      Wave Packet Methods for Hyperbolic Equations III
    Hart Smith (University of Washington)
    02:00 PM - 03:00 PM
      Nonlinear Dispersive Equations-Talk
    Ioan Bejenaru
    03:30 PM - 04:30 PM
      Existence and Nonuniqueness for the Nonlinear Schrodinger Equation
    Michael Christ (University of California, Berkeley)
    Aug 25, 2005
    Thursday
    09:15 AM - 10:15 AM
      Dispersive Effects in High Rotating Fluids
    Jean-Yves Chemin
    10:45 AM - 11:45 AM
      Nonlinear Dispersive Equations-Lecture III
    Wilhelm Schlag
    02:00 PM - 03:00 PM
      Nonlinear Dispersive Equations-Talk
    Justin Holmer
    Aug 26, 2005
    Friday
    09:15 AM - 10:15 AM
      Well-Posedness of the Cauchy Problem for the mKdv Equation
    Yoshio Tsutsumi
    10:45 AM - 11:45 AM
      Long-Time Existence for Semilinear Klein-Gordon Equations on Compact Manifolds
    Jeremie Szeftel (Université de Paris VI (Pierre et Marie Curie))
  4. Workshop Introductory Workshop in Nonlinear Elliptic Equations and Its Applications

    Luis Caffarelli, L. Craig Evans, Matt Gursky, Cristian Gutierrez, Paul Yang

    There will be two series of five lectures each by L. Caffarelli and M. Gursky. In addition, each day there will be two more lectures by other speakers.

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    Aug 15, 2005
    Monday
    09:30 AM - 10:30 AM
      Basic Tools for the Regularity Theory of Nonlinear Elliptic Equations, I
    Luis Caffarelli (University of Texas)
    11:00 AM - 12:00 PM
      Some Fully Nonlinear Equations in Geometry, I
    Matthew Gursky (University of Notre Dame)
    01:30 PM - 02:30 PM
      Nonlinear PDE Methods for Analysis of Phase Transitions in Superconducting and Liquid Crystals
    Patricia Bauman
    02:30 PM - 03:30 PM
      Regularity of Quasilinear Subelliptic Equations
    Andras Domokos
    04:00 PM - 05:00 PM
      Resolving the Singularities of Minimal Hopf Cones
    Yu Yuan
    Aug 16, 2005
    Tuesday
    09:30 AM - 10:30 AM
      Basic Tools for the Regularity Theory of Nonlinear Elliptic Equations, II
    Luis Caffarelli (University of Texas)
    11:00 AM - 12:00 PM
      Some Fully Nonlinear Equations in Geometry, II
    Matthew Gursky (University of Notre Dame)
    01:30 PM - 02:30 PM
      Boundary Behavior of Solutions to Second Order Elliptic and Parabolic Equations in Non-smooth Domains
    Mikhail Safonov
    02:30 PM - 03:30 PM
      On the Regularity of Solutions to the Monge-Ampere Equation and its Linearization
    Diego Maldonado
    04:00 PM - 05:00 PM
      Numerical Approximation for Fully Nonlinear Degenerate Equations
    Nikolai Krylov
    Aug 17, 2005
    Wednesday
    09:30 AM - 10:30 AM
      Basic Tools for the Regularity Theory of Nonlinear Elliptic Equations, III
    Luis Caffarelli (University of Texas)
    11:00 AM - 12:00 PM
      Some Fully Nonlinear Equations in Geometry, III
    Matthew Gursky (University of Notre Dame)
    01:30 PM - 02:30 PM
      Nonliner Elliptical Equation and Its Application Lecture
    Fang-Hua Lin
    02:30 PM - 03:30 PM
      A General Perron Method and Application
    David Hartenstine
    04:00 PM - 05:00 PM
      Numerical Approximation for Fully Nonlinear Degenerate Equations-II
    Nikolai Krylov
    Aug 18, 2005
    Thursday
    09:30 AM - 10:30 AM
      Basic Tools for the Regularity Theory of Nonlinear Elliptic Equations, IV
    Luis Caffarelli (University of Texas)
    11:00 AM - 12:00 PM
      Some Fully Nonlinear Equations in Geometry, IV
    Matthew Gursky (University of Notre Dame)
    01:30 PM - 02:30 PM
      Construction of Singular Solutions for a Fully Non-linear Equation in Conformal Geometry
    Maria Gonzalez
    02:30 PM - 03:30 PM
      Fourth Order PDEs of Critical Growth
    Emmanuel Hebey
    04:00 PM - 05:00 PM
      Numerical Approximation for Fully Nonlinear Degenerate Equations, III
    Nikolai Krylov
    Aug 19, 2005
    Friday
    09:30 AM - 10:30 AM
      Basic Tools for the Regularity Theory of Nonlinear Elliptic Equations, V
    Luis Caffarelli (University of Texas)
    11:00 AM - 12:00 PM
      Some Fully Nonlinear Equations in Geometry, V
    Matthew Gursky (University of Notre Dame)
    01:30 PM - 02:30 PM
      Some Liouville Type Theorems
    Yanyan Li
    02:30 PM - 03:30 PM
      A Constant Rank Theorem of Convex Solutions of Fully Nonlinear Equations
    Peng-Fei Guan
    04:00 PM - 05:00 PM
      Second-order Asymptotics for Fast Nonlinear Diffusions
    Robert McCann (University of Toronto)
  5. Workshop MSRI Workshop for Women in Mathematics: An Introduction to Elliptic Partial Differential Equations

    Alice Chang (Princeton) and Lawrence C Evans (UC Berkeley)

    This workshop will be an intensive two-day introductory minicourse on elliptic PDE. L C Evans will present a series of lectures on the basic theory and estimates for linear and nonlinear elliptic equations, with applications to variational problems and to nonlinear systems. A Chang will lecture on applications of elliptic PDE to conformal geometry and other geometric problems.

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    Aug 11, 2005
    Thursday
    09:15 AM - 10:30 AM
      Women in Mathematics: An Introduction to the Elliptic Partial Differential Equations-I
    Lawrence Evans (University of California, Berkeley)
    10:45 AM - 12:00 PM
      Women in Mathematics: Elliptic PDE Problems in Geometry-I
    Sun-Yung Alice Chang (Princeton University)
    01:15 PM - 02:30 PM
      Women in Mathematics: An Introduction to the Elliptic Partial Differential Equations-II
    02:30 PM - 03:45 PM
      Women in Mathematics: Elliptic PDE Problems in Geometry-II
    Sun-Yung Alice Chang (Princeton University)
    Aug 12, 2005
    Friday
    09:00 AM - 10:00 AM
      On Geometric Spectral Invariant: The "Trace" of Laplace Inverse.
    Jean Steiner
    10:15 AM - 10:50 AM
      Prescribing Curvature Forms
    Shirley Yap
    11:00 AM - 11:35 AM
      On the Beltrami Equation and $$\mu$$-Homeomorphisms
    Melkana Brakalova
    01:15 PM - 02:30 PM
      Partial Regulation For Elliptic Systems.
    02:30 PM - 03:05 PM
      The Shapiro-Lopatinskij Condition for Elliptic Boundary Value Problems.
    Katya Krupchyk (University of Helsinki)
    03:10 PM - 03:45 PM
      Coupled Singular Perturbations for Phase Transitions
    Cristina Popovici
    04:15 PM - 05:30 PM
      Women in Mathematics: Elliptic PDE Problems in Geometry-III
    Sun-Yung Alice Chang (Princeton University)
  6. Summer Graduate School CR Geometry: Complex Analysis Meets Real Geometry and Number Theory

    John D’Angelo

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    Jul 25, 2005
    Monday
    09:00 AM - 10:00 AM
      Proper Holomorphic Mappings and CR Geometry.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    10:30 AM - 11:30 AM
      Some Open Problems Concerning Proper Holomorphic Mappings.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    Jul 26, 2005
    Tuesday
    09:00 AM - 10:00 AM
      Group Invariant Proper Maps.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    10:30 AM - 11:30 AM
      Local CR Embeddings Into Spheres.
    Peter Ebenfelt
    Jul 27, 2005
    Wednesday
    09:00 AM - 10:00 AM
      Levi Non-degenerate Hypersurfaces.
    Peter Ebenfelt
    10:30 AM - 11:30 AM
      Proper Maps When the Image Dimension is Large. (A.K.A.: Directions to Alice's Restaurant)
    Dror Varolin
    Jul 28, 2005
    Thursday
    09:00 AM - 10:00 AM
      Hermitian Algebraic Functions and Catlin-D'Angelo Theorem.
    Dror Varolin
    10:30 AM - 11:30 AM
      The Bergman Kernal and Scaling Methods in n -Dimensional Complex Space.
    Jeff McNeal (Ohio State University)
    Jul 29, 2005
    Friday
    09:00 AM - 10:00 AM
      Discussion
    John D'Angelo (University of Illinois at Urbana-Champaign)
    10:30 AM - 11:30 AM
      Discussion on Primality Properties of Group Invariant Maps.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    Aug 01, 2005
    Monday
    09:00 AM - 10:00 AM
      Rigidity Problems in CR Analysis: Survey.
    Xiaojun Huang
    10:30 AM - 11:30 AM
      Rigidity Problems in CR Analysis: Survey II.
    Xiaojun Huang
    Aug 02, 2005
    Tuesday
    09:00 AM - 10:00 AM
      Complexification, Segrevarieties, and the X-Variety.
    Bernhard Lamel
    10:30 AM - 11:30 AM
      Volumes of Holomorphic Images of Balls.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    Aug 05, 2005
    Friday
    09:00 AM - 10:00 AM
      CR Geometry -1st Lecture.
    John D'Angelo (University of Illinois at Urbana-Champaign)
    10:30 AM - 11:30 AM
      CR Geometry -2nd Lecture.
    John D'Angelo (University of Illinois at Urbana-Champaign)