449 reputation
39
bio website math.mit.edu/~bottman
location Cambridge, MA
age 24
visits member for 2 years, 9 months
seen 1 hour ago
Grad student at MIT studying symplectic geometry.

Oct
1
comment When do you go hunting for Lagrangian submanifolds?
Interesting that you say twisted Fourier--Mukai --- do you have in mind the family Floer functor of Abouzaid (slash Fukaya?), which lands in twisted coherent sheaves?
Sep
29
revised When do you go hunting for Lagrangian submanifolds?
added 2726 characters in body
Sep
29
awarded  Yearling
Sep
27
answered When do you go hunting for Lagrangian submanifolds?
Sep
23
accepted Is there an $(\infty,2)$-category with morphisms given by $D^b\text{Coh}$?
Sep
23
accepted Fourier--Mukai transforms and adjunction
Sep
23
comment Is there an $(\infty,2)$-category with morphisms given by $D^b\text{Coh}$?
Thanks! Do you know anything about what happens when the "smoothness" hypothesis is dropped?
Sep
23
asked Is there an $(\infty,2)$-category with morphisms given by $D^b\text{Coh}$?
Sep
19
comment If a (linear) relation maps Lagrangian subspaces to Lagrangian subspaces, is it a Lagrangian relation?
I bet it's true under those hypotheses. Decompose $\Lambda$ as the direct sum of $A \oplus \{0\}$, $\text{graph}(\varphi)$, $\{0\} \oplus B$ for subspaces $A,B$ and $\varphi$ an isomorphism from a complement of $A$ to a complement of $B$. Then $A$ and $B$ must be isotropic. But I'm not sure how to show that $\text{graph}(\varphi)$ is isotropic.
Sep
18
revised If a (linear) relation maps Lagrangian subspaces to Lagrangian subspaces, is it a Lagrangian relation?
added 160 characters in body
Sep
18
answered If a (linear) relation maps Lagrangian subspaces to Lagrangian subspaces, is it a Lagrangian relation?
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?