514 reputation
310
bio website math.mit.edu/~bottman
location Cambridge, MA
age 24
visits member for 3 years
seen 1 hour ago
Grad student at MIT studying symplectic geometry.

Jan
25
comment Can a symplectic manifold be recovered from its Lagrangians?
@Sasha That's true, though if you add the assumption that $X$ has ample canonical or anticanonical bundle and assume that the equivalence of derived categories is exact, then it's still true.
Jan
25
comment Can a symplectic manifold be recovered from its Lagrangians?
@MichaelBächtold Oh geez, thanks.
Jan
25
asked Can a symplectic manifold be recovered from its Lagrangians?
Jan
14
comment If a (linear) relation maps Lagrangian subspaces to Lagrangian subspaces, is it a Lagrangian relation?
Good point, Max.
Dec
12
awarded  Critic
Dec
11
answered floer homology and viterbo's theorem
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.