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Schedule, Notes/Handouts & Videos

H-principle (Sendai, Japan) July 01, 2024 - July 12, 2024

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Jul 01, 2024
Monday
07:00 AM - 08:30 AM
  Breakfast
08:50 AM - 09:00 AM
  Opening Remarks
09:00 AM - 10:30 AM
  H-principles in smooth topology: 1) h-principle philosophy, examples, and holonomic approximation statement
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Riemannian geometry and applications to fluid dynamics: The Nash-Kuiper theorem 1: historical background, proof idea and "stage" proposition
Dominik Inauen (Universität Leipzig)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Welcome dinner with G-RIPS Sendai
08:00 PM - 10:00 PM
  Free Discussions
Jul 02, 2024
Tuesday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  H-principles in smooth topology: 2) Proof of holonomic approximation, and applications
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Riemannian geometry and applications to fluid dynamics: The Nash-Kuiper theorem 2: decomposition into primitive metrics, normal vector fields and proof of the stage proposition
Dominik Inauen (Universität Leipzig)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 03, 2024
Wednesday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  H-principles in smooth topology 3): Convex integration, directed immersions
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Riemannian geometry and applications to fluid dynamics: The Nash-Kuiper theorem 3: "quantitative" version of stage proposition and C^{1,\alpha} isometries
Dominik Inauen (Universität Leipzig)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 04, 2024
Thursday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  H-principles in smooth topology: 4) Wrinkled maps
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Riemannian geometry and applications to fluid dynamics: 4) Euler equations: weak solutions, energy conservation and the Euler-Reynolds system
Dominik Inauen (Universität Leipzig)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 05, 2024
Friday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  H-principles in smooth topology: 5) Convex integration and wrinkling for embeddings
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Riemannian geometry and applications to fluid dynamics: 5) Euler equations: convex integration scheme for continuous dissipative Euler flows
Dominik Inauen (Universität Leipzig)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 08, 2024
Monday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  Contact and symplectic flexibility: 1) Intro to contact and symplectic geometry
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Foliation theory and diffeomorphism groups: 1) Definitions of foliations and examples. Foliations of the 2-dimensional torus
Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 09, 2024
Tuesday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  Contact and symplectic flexibility: 2) h-principles for isotropic immersions/embeddings, isosymplectic/isocontac
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Foliation theory and diffeomorphism groups: 2) Invariants of plane fields. Holonomy of foliations. The Bott vanishing theorem. The Godbillon-Vey invariant
Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 10, 2024
Wednesday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  Contact and symplectic flexibility: 3) Overtwisted 3-manifolds
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Foliation theory and diffeomorphism groups: 3) The h-principle for Diff V invariant differential relations and the h-principle for submersions and the theorem of Phillips
Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 11, 2024
Thursday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  Contact and symplectic flexibility: 4) Loose Legendrians and flexible Weinstein manifolds
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
01:30 PM - 03:00 PM
  Foliation theory and diffeomorphism groups: 4) Definition of Haefliger's Gamma structures and Haefliger's theorem on foliations of open manifolds
Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
03:00 PM - 04:00 PM
  Afternoon Tea
04:00 PM - 05:00 PM
  Working in Small Groups
06:00 PM - 08:00 PM
  Dinner
08:00 PM - 10:00 PM
  Free Discussions
Jul 12, 2024
Friday
07:00 AM - 08:30 AM
  Breakfast
09:00 AM - 10:30 AM
  Contact and symplectic flexibility: 5) Recent results: overtwistedness and convex surface theory in high dimensions
Emmy Murphy (Princeton University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Teaching Assistant Session
12:00 PM - 01:00 PM
  Lunch
01:00 PM - 02:30 PM
  Foliation theory and diffeomorphism groups: 5) Thurston's theorem on the classification of foliations. The Mather-Thurston theory
Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
02:30 PM - 03:00 PM
  Afternoon Tea
03:00 PM - 05:00 PM
  G-RIPs Sendai midterm presentation
06:00 PM - 08:00 PM
  Farewell Party
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