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Schedule, Notes/Handouts & Videos

Geometric Flows (Crete, Greece) June 19, 2022 - July 01, 2022

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Jun 19, 2022
Sunday
11:45 PM - 12:15 AM
  Registration
Jun 20, 2022
Monday
12:15 AM - 12:30 AM
  Welcome
Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Charalambos Makridakis (Institute of Applied & Computational Mathematics)
12:30 AM - 01:30 AM
  Pre-Lecture: Review of Curvature, Commutator Identities for Covariant Derivatives
01:30 AM - 02:00 AM
  Coffee Break
02:00 AM - 03:15 AM
  Ricci Flow: Definition of Ricci Flow, Some Basic Examples, Self-Similar Solutions, Evolution of Curvature, Curvature Algebra in Three Dimensions
Simon Brendle (Columbia University)
03:15 AM - 03:45 AM
  Informal Questions
03:45 AM - 05:30 AM
  Lunch
05:30 AM - 06:30 AM
  Post-Lecture & Problem Session
11:45 PM - 12:45 AM
  Pre-Lecture: Heat Equation on R^n and on Manifolds
Jun 21, 2022
Tuesday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Ancient Solutions to Parabolic Equations: Ancient Solutions to the Heat Equation and to the Semi-Linear Heat Equation
Panagiota Daskalopoulos (Columbia University)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
11:45 PM - 12:45 AM
  Pre-Lecture: Maximum Principle for Scalar Heat Equations, Interior Estimates
Jun 22, 2022
Wednesday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Ricci Flow: Hamilton’s Maximum Principle for Systems, Preservation of Nonnegative Ricci in Three Dimensions, Pinching and Convergence in Three Dimensions, Curvature Conditions in Higher Dimensions
Simon Brendle (Columbia University)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussion between Students
11:45 PM - 12:45 AM
  Pre-Lecture: Log-Sobolev Entropy and Nash Entropy
Jun 23, 2022
Thursday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Ricci Flow: Perelman’s Entropy, and Noncollapsing
Simon Brendle (Columbia University)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
11:45 PM - 12:45 AM
  Pre-Lecture: Extrinsic Curvature of Hypersurfaces, and Evolution Equations for Extrinsic Geometric Flows
Jun 24, 2022
Friday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Inverse Mean Curvature Flow: Properties of Smooth Solutions to IMCF
Gerhard Huisken (Math. Forschungsinstitut Oberwolfach; Eberhard-Karls-Universität Tübingen)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
Jun 26, 2022
Sunday
11:45 PM - 12:45 AM
  Pre-Lecture: Level Set Approach to Extrinsic Geometric Flows (and the Relation to the Parametrized Version of the Flow); Weak Mean Curvature
Jun 27, 2022
Monday
01:00 AM - 02:15 AM
  Inverse Mean Curvature Flow: Weak Solutions for Inverse Mean Curvature Flow
Gerhard Huisken (Math. Forschungsinstitut Oberwolfach; Eberhard-Karls-Universität Tübingen)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
11:45 PM - 12:45 AM
  The 2-Dimensional Ricci Flow
Jun 28, 2022
Tuesday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Ancient Solutions to Geometric Flows: Ancient Solutions to the 2-Dim Ricci Flow
Panagiota Daskalopoulos (Columbia University)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
11:45 PM - 12:45 AM
  Pre-Lecture: Asymptotically Flat 3-Manifolds, their Role in General Relativity, the ADM-Mass and the Dominant Energy Condition
Jun 29, 2022
Wednesday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Inverse Mean Curvature Flow: Applications to General Relativity
Gerhard Huisken (Math. Forschungsinstitut Oberwolfach; Eberhard-Karls-Universität Tübingen)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
05:00 AM - 06:00 AM
  Post-Lecture & Problem Session
06:00 AM - 07:00 AM
  Informal Discussions between Students
11:45 PM - 12:45 AM
  Pre-Lecture: Curve Shortening Flow on the Plane
Jun 30, 2022
Thursday
12:45 AM - 01:15 AM
  Coffee Break
01:15 AM - 02:30 AM
  Ancient Solutions to Geometric Flows: Ancient Solutions to the Curve Shortening Flow
Theodora Bourni (University of Tennessee)
02:30 AM - 03:00 AM
  Informal Questions
03:00 AM - 05:00 AM
  Lunch
06:00 AM - 07:00 AM
  Informal Discussions between Students
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