bio | website | math.mit.edu/~bottman |
---|---|---|
location | Cambridge, MA | |
age | 24 | |
visits | member for | 3 years |
seen | 1 hour ago | |
stats | profile views | 581 |
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. |