bio  website  

location  Austin, TX  
age  28  
visits  member for  4 years, 8 months 
seen  8 hours ago  
stats  profile views  1,103 
I recently finished my PhD at UPenn under the supervision of Jonathan Block. I will be starting a postdoc 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 $i$. 