Graduate student seminar on pseudoholomorphic curves
Tuesdays and Thursdays, 4:005:30, MIT, room 2146
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, Jholomorphic 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:
Jholomorphic 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
(statements only).
[McDuffSalamon, 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 CauchyRiemann operator, statement of Fredholm and
transversality properties.
[McDuffSalamon, 3.1 and Thm.A.3.3.]

Tuesday October 17: Fangyun Yang:
real CauchyRiemann operators (elliptic estimates, Fredholm property,
RiemannRoch); including with boundary conditions.
[McDuffSalamon, C.13]

Thursday October 26: Maksim Lipyanskiy:
nonlinear elliptic regularity and compactness (for bounded gradient),
energy.
[IvashkovichShevchishin]

Tuesday October 31: Maksim Lipyanskiy:
bubbling effect (rescaling), removable singularity (sketch of
proof?), compactness modulo bubbling.
[IvashkovichShevchishin]

Tuesday November 7: Maksim Maydanskiy: compactified moduli space,
evaluation maps, GromovWitten invariants, stable curves.

Tuesday November 14: Yanki Lekili: nonsqueezing 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 
gluing.