2,272 reputation
730
bio website mysbfiles.stonybrook.edu/…
location Simons Center
age 31
visits member for 5 years
seen 2 days ago

Research Asst Professor

Interested in Symplectic geometry, complex Algebraic geometry, Gromov-Witten theory, Mirror symmetry, Calabi-Yau threefolds, Enumerative geometry, Abelian surfaces, Moduli space of objects with real structure, ...


Apr
10
awarded  Yearling
Apr
6
awarded  Popular Question
Mar
30
comment Symplectic form/Kahler metric on a toric manifold
Even for m=2 case of example above, it seems to me that the equality you want does not hold. The coefficient of $dz\wedge d\bar{z}$ in $f^*w_{FS}$ is equal to $[a(4|z|^4+|w|^2)-4|z|^4|w|^2]/a^2$, with $a=(1+|z|^4+|z|^2|w|^2+|w|^4)$, which is different from the corresponding coefficient of $dz\wedge d\bar{z}$ in $w_{FS}$ of $\mathbb{P}^1$.
Mar
30
comment Symplectic form/Kahler metric on a toric manifold
Have you checked this for $f:\mathbb{P}^1\to \mathbb{P}^{m}$, $[z,w]\to[z^m,z^{m-1}w,\ldots, w^m]$? here, everything is explicitly checkable.
Mar
28
comment Symplectic form/Kahler metric on a toric manifold
are not they equal? up to scaling?
Feb
18
revised Triviality of holomorphic vector bundles over contractible Stein manifolds
deleted 2 characters in body
Jan
31
accepted A question on compact sets
Jan
31
comment A question on compact sets
This proof readily extends to compact sets inside any metrizable topological space, instead of $\mathbb{R}^n$. Do you see a way of changing the proof that does not involve the use of metric.
Jan
28
comment A question on compact sets
N is just a number.
Jan
28
reviewed Approve A question on compact sets
Jan
28
comment A question on compact sets
:) YES (I knew someone would say that ;))
Jan
28
asked A question on compact sets
Dec
23
accepted Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
Dec
1
comment Question about the h-principle
You question is not readable!
Nov
27
awarded  Popular Question
Nov
27
comment Moment map coordinates in tours action
originally, a metric $g$ is a pairing between vectors, but it also induces a metric on convectors or any other tensor field; this is the first one. For the second one, you can apply the one form $dz_i$ to the vector field valued 1-form $\nabla \tau_k$ and the result is a 1-form which you want to be zero.
Nov
25
comment Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s
I have no answer for your question, but, is there any related argument for Enrique surfaces?
Nov
21
comment Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
Sure, but this is as abstract as the original definition.
Nov
17
accepted Reference request for cohomology of coverings
Nov
17
comment Reference request for cohomology of coverings
cool example, thanks.