1,510 reputation
11025
bio website
location Austin, TX
age 28
visits member for 4 years, 8 months
seen 8 hours ago

I recently finished my PhD at UPenn under the supervision of Jonathan Block. I will be starting a post-doc at UT Austin in the Fall.


13h
answered Moment map coordinates in tours action
Nov
17
awarded  Citizen Patrol
Nov
7
comment When are the Dolbeault and de Rham dgas homotopy equivalent?
Thanks, Matthias!
Nov
7
accepted When are the Dolbeault and de Rham dgas homotopy equivalent?
Nov
5
asked When are the Dolbeault and de Rham dgas homotopy equivalent?
Sep
24
awarded  Autobiographer
Jul
26
revised Complex structures on Riemann surfaces
added 169 characters in body
Jul
25
comment Complex structures on Riemann surfaces
Thanks @JasonStarr, I've fixed it.
Jul
25
revised Complex structures on Riemann surfaces
added 4 characters in body
Jul
25
asked Complex structures on Riemann surfaces
Jul
24
answered A Lie algebra identity
Jul
2
awarded  Curious
Jun
27
comment Integrating representations of Lie algebroids
Thanks for the nice answer!
Jun
27
accepted Integrating representations of Lie algebroids
Jun
26
asked Integrating representations of Lie algebroids
May
12
awarded  Favorite Question
Apr
21
awarded  Enlightened
Apr
21
awarded  Nice Answer
Apr
20
comment If there exists a nontrivial vector field $V$ such that $\nabla_{X}V=0$ for any vector field $X$, the manifold must be flat?
I should say that above $n = \dim M$.
Apr
20
comment If there exists a nontrivial vector field $V$ such that $\nabla_{X}V=0$ for any vector field $X$, the manifold must be flat?
Say $V_1,\ldots,V_n$ is a collection of linearly independent (everywhere on $U$) vector fields that are parallel, i.e. $\nabla_X V_j = 0$ for all vector fields $X$. For any vector fields $X,Y$, $R(X,Y)$ is an endomorphism of the tangent bundle, where $R$ is the Riemann curvature tensor. Since it is an endomorphism (as opposed to a differential operator), to show it is zero it suffices to show it vanishes on a frame of the tangent bundle. But $R(X,Y) V_i = \nabla_X \nabla_Y V_i -\nabla_Y\nabla_X V_i - \nabla_{[X,Y]} V_i = 0$ for all $i$.