# Mathematical Sciences Research Institute

Home » Videos » Semester(08-01-2005 - 12-31-2005)

1. # WorkshopRecent Results in Nonlinear Elliptic Equations and their Interactions with Geometry

Frank Pacard, Neil Trudinger and Paul Yang

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. # WorkshopAnalytical and Stochastic Fluid Dynamics

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

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. # WorkshopIntroductory Workshop in Nonlinear Dispersive Equations

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

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. # WorkshopIntroductory 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.

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. # WorkshopMSRI 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.

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 SchoolCR Geometry: Complex Analysis Meets Real Geometry and Number Theory

John D’Angelo

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)