bio | website | math.mit.edu/~bottman |
---|---|---|
location | Cambridge, MA | |
age | 24 | |
visits | member for | 2 years, 9 months |
seen | 1 hour ago | |
stats | profile views | 517 |
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? |