Topics: geometry/topology of manifolds, symplectic geometry, complex algebraic geometry
AW=Alan Weinstein MH=Michael Hutchings RK=Rob Kirby RL=Robert Littlejohn
(physics) 

AW: Can you compute morse the Morse homology of some space?  (I did a 
round 2-sphere).  What about one with a nontrivial differential?  How do 
you compute the signs? 
MH: Can I get a (not-necessarily invariant) homology in this manner for 
any generic Morse-Smale vector field?  
RK: What's Gromov's compactness theorem say?
AW: We're not at that section yet.
RK: Ok.
AW: How do you show Morse homology is isomorphic to singular homology?  
How do you show it's invariant without reference to singular homology? 
MH: How do you know the index 1 moduli space is compact?

RK: What's Gromov's compactness theorem say?  
AW: We're not there yet.  Why don't you ask him a topology question?
RK: How do you define the Chern classes of a complex vector bundle?  
What if it's not over a compact manifold?  How do you compute the 2nd
Chern class of the K3 surface?  How do you define the Chern classes
inductively using the Euler class?

RK: What's Gromov's compactness theorem say?  
AW: Do the loops that get pinched have to bound disks?
RL: Do you know what the Hamilton-Jacobi equations are?  
(No; he defines them).  For the phase space R^2, can you always find 
the S that solves them?  What about globally?  Now for R^n.  What 
condition on dS/dx_i are needed so that you can find S?  What kind of 
manifold is the graph of a closed 1-form on R^n?

MH: Do you know Riemann-Roch?  
Me: No.
MH: Say something about divisors and line bundles.
AW: What does it mean that the quotient of local defining functions for an 
irreducible divisor is holomorphic and gives you a line bundle, given that 
you're dividing by a function with zeros?