Graduate student seminar on pseudoholomorphic curves
Tuesdays and Thursdays, 4:00-5:30, MIT, room 2-146
This seminar is aimed at graduate students interested in symplectic geometry
and related areas, and will try to give a comprehensive introduction to
pseudoholomorphic curves. Most of the talks will be given by students.
(For a more advanced seminar on a similar subject, try the
symplectic dinner seminar
organized by Chris Wendl).
The main reference for the first part of the seminar is: D. McDuff,
D. Salamon, J-holomorphic curves and symplectic topology,
American Math. Society, 2004.
One of the two weekly meetings (Tuesday) will be
more structured, with postdocs and faculty welcome to attend,
while the other weekly meeting (Thursday) will be completely informal.
Contacts: Y. Lekili, D. Auroux, K. Wehrheim
Program of the seminar
(Tuesday meetings only)
Tuesday September 12: Denis Auroux, Katrin Wehrheim:
Introductory talk; organization of the seminar.
Tuesday September 19: Ana Rita Pires:
symplectic manifolds (Darboux theorem, ...), symplectomorphisms and
Hamiltonian vector fields, Lagrangian submanifolds, almost complex
structures (tame/compatible, contractible spaces), first Chern class.
[Cannas da Silva]
Tuesday September 26: Yanki Lekili:
J-holomorphic maps (global and in local coordinates), energy and
energy identity, comparison with holomorphic functions: unique
continuation, isolated critical points, somewhere
injective/simple/multiply covered, positivity of intersections
[McDuff-Salamon, ch. 2]
Tuesday October 3: Maksim Maydanskiy:
moduli spaces (with marked points, modulo reparametrization, as zero
set of a section),
implicit function theorem for Fredholm section of Banach bundle,
linearized Cauchy-Riemann operator, statement of Fredholm and
[McDuff-Salamon, 3.1 and Thm.A.3.3.]
Tuesday October 17: Fangyun Yang:
real Cauchy-Riemann operators (elliptic estimates, Fredholm property,
Riemann-Roch); including with boundary conditions.
Thursday October 26: Maksim Lipyanskiy:
nonlinear elliptic regularity and compactness (for bounded gradient),
Tuesday October 31: Maksim Lipyanskiy:
bubbling effect (rescaling), removable singularity (sketch of
proof?), compactness modulo bubbling.
Tuesday November 7: Maksim Maydanskiy: compactified moduli space,
evaluation maps, Gromov-Witten invariants, stable curves.
Tuesday November 14: Yanki Lekili: non-squeezing theorem.
Tuesday November 21: Ronen Mukamel: Morse homology.
Tuesday November 28: Matt Hedden: Lagrangian Floer homology -
action functional and holomorphic strips.
Tuesday December 5: Aleksandar Subotic: Lagrangian Floer homology -
bubbling and compactness.
Tuesday December 12: Katrin Wehrheim: Lagrangian Floer homology -