300 reputation
29
bio website math.mit.edu/~bottman
location Cambridge, MA
age 24
visits member for 2 years, 8 months
seen Sep 7 at 5:00
Grad student at MIT studying symplectic geometry.

Jul
2
awarded  Curious
Nov
27
awarded  Yearling
Nov
27
revised Fourier--Mukai transforms and adjunction
added 85 characters in body
Nov
27
comment Fourier--Mukai transforms and adjunction
@QiaochuYuan thanks! If preservation of limits and colimits is an important consequence, then I will try and think about what that means for the derived category of coherent sheaves. I guess I failed to mention in my question that what I'm really interested in is geometric consequences for $D^b$, not "abstract nonsense consequences" that always happen when both $(F,G)$ and $(G,F)$ are adjoint pairs.
Nov
27
asked Fourier--Mukai transforms and adjunction
Oct
27
awarded  Commentator
Oct
27
comment Can symplectic blow up increase symplectic capacities?
Neat question. Seems plausible for Gromov width. What is your motivation?
Oct
24
comment Why is there a connection between enumerative geometry and nonlinear waves?
@Javier: thanks! That looks like just what I need.
Oct
23
comment Automorphisms of the affine quadric $z_1^2+\dots+z_n^2=1$
I think this is not true. Set $g: V \to V$ to be the identity, and define $g_1, \ldots, g_n$ by setting $g_1(z) := z_1 + \left(z_1^2 + \cdots + z_n^2 - 1\right)$ and $g_i(z) := z_i$ for $i > 1$. Am I missing something?
Oct
22
awarded  Nice Question
Oct
22
asked Why is there a connection between enumerative geometry and nonlinear waves?
Jul
16
accepted What is known about the strong Arnold conjecture?
May
29
revised What is known about the strong Arnold conjecture?
added 845 characters in body
May
29
comment What is known about the strong Arnold conjecture?
Hi Thomas! You are right, I was mixing up the versions with and without the "nondegenerate" hypothesis. I will edit my question.
May
13
comment Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety?
@David I agree you can get all the Betti numbers except in the middle dimension (and that too, if you can get the Euler characteristic). But does this say much about the ring structure?
May
12
accepted How many “elementary” characterizations of twisted SU(2) representation varieties are known?
May
12
comment Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety?
OK, thanks Mariano. I find it really surprising that the ring structure of a projective hypersurface isn't easy to compute!
May
11
revised Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety?
added 10 characters in body; added 81 characters in body
May
11
asked Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety?
May
7
awarded  Teacher