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Summer Graduate School

H-Principle (INdAM) July 29, 2019 - August 09, 2019
Parent Program: --
Location: Cortona, Italy
Organizers LEAD Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)
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The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

Local Organizing Committee:
Giorgio Patrizio (Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM))
Adriano Tomassini  (Università di Parma and Scuola Matematica Interuniversitaria (SMI))

This two week summer school, jointly organized by MSRI with INdAM (Istituto Nazionale di Alta Matematica) and  SMI (Scuola Matematica Interuniversitaria), will introduce graduate students to the theory of h-principles.  After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.

h-principles in smooth topology (Emmy Murphy)
Euler equations and fluid dynamics (Phil Isett)
Contact and symplectic flexibility (Emmy Murphy)
Foliation theory and diffeomorphism groups (Takashi Tsuboi)

Suggested Prerequisites:

  • Basic Analysis and PDE;
  • elementary algebraic topology (homotopy and homology groups).
  • elementary differential topology (manifolds, vector fields and differential form calculus, basic Morse theory, vector bundles and characteristic classes). 

For eligibility and how to apply, see the Summer Graduate Schools homepage

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.

Keywords and Mathematics Subject Classification (MSC)