Summer Graduate School

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)

This two week summer school, jointly organized by SLMath with RIKEN, 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)
Riemannian geometry and applications to fluid dynamics (Dominik Inauen)
Contact and symplectic flexibility (Emmy Murphy)
Foliation theory and diffeomorphism groups (Takashi Tsuboi)

School Structure

The daily schedule consists centrally of two lectures a day. Each of the four courses above will consist of five 90 minute lectures, with the first two being in the first week, and the latter two during the second. The lecturers will prepare a list of problems to be discussed in TA sessions (along with answering students’ questions. The TA and lecturers will also guide the work in small groups in the afternoon sessions. It is possible that the working and discussion groups will continue informally after the dinner.

Reading List

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).

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

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

Venue

The summer school will be held at TOKYO ELECTRON House of Creativity, Katahira Campus, Tohoku University. The participants will lodge together at Hotel Pearl City Sendai, which is five minutes from the venue.  Sendai is located north of Tokyo and can be reached in 90 minutes by Shinkansen (train).