Summer Graduate School

A Holomorphic Curve

Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and four-dimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject. 

Lecturers (minicourses of 2-3 hours each).
Mohammed Abouzaid (Columbia University),  Tobias Ekholm (University of Uppsala), Yakov Eliashberg (Stanford University),Viktor Ginzburg (University of California Santa Cruz), Nancy Hingston (College of New Jersey), Michael Hutchings (University of California, Berkeley), François Lalonde (Université de Montréal), Dusa McDuff (Barnard College, Columbia University), Emmy Murphy (Northwestern University),  Yaron Ostrover (Tel Aviv University), John Pardon (Princeton University),  Paul Seidel (MIT), Michael Usher (University of Georgia, Athens).

Open problems panel (two one hour sessions).
Paul Biran (ETH), Helmut Hofer (Permanent faculty member IAS, Princeton), Leonid Polterovich (Tel Aviv).

The school will also feature exercise sessions and selected talks by young researchers.

Prerequisites:

While a precise list of prerequisites is listed below, some familiarity with the following more specialized, but still accessible, references is a plus:

• D. McDuff, D. Salamon - Introduction to Symplectic Topology, Clarendon Press 1998
• Second half of M.Audin, M.Damian - Morse theory and Floer homology, Springer 2013.

Finally, the technical crux of modern symplectic topology consists in the analysis of moduli spaces of J-holomorphic curves. While this is not a prerequisite to attend this school it is useful to mention here that the basic J-holomorphic machinery is contained in the monograph: 6 D.McDuff, D. Salamon - J-Holomorphic Curves and Symplectic Topology, AMS Monographs, 2004.

Symplectic topology makes use of a variety of techniques from different fields of mathematics and a degree of familiarity with the following is required:

• Basics of manifolds and algebraic topology (such as covered in the book of G. Bredon - Geometry and Topology, Springer 1993);
• Elements of Riemannian geometry (such as the first three chapters of S. Gallot, D. Hulin, J. Lafontaine - Riemannian Geometry, Springer 1987);
• Complex analysis (such as the book of L. Ahlfors - Complex Analysis, McGraw-Hill, 1966);
• The basics of modern Morse theory as covered in the first half of M.Audin, M.Damian - Morse theory and Floer homology, Springer 2013;
• Some elements of Riemann surfaces (such as the first two chapters of H.M.Farkas, I.Kra - Riemann Surfaces, Springer 1980).

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

Special restrictions (for MSRI Support):

1. In addition to the nomination at MSRI, a separate application via the SMS Homepage is required to participate in this summer school.
2. Participation is subject to selection by the organizers
3. Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI. Additional students are highly encouraged to apply directly via the SMS Homepage