bio  website  math.northwestern.edu/… 

location  Chicago  
age  30  
visits  member for  5 years 
seen  Oct 6 at 0:04  
stats  profile views  1,084 
I am a Ph.D student at Northwestern University interested in algebraic geometry and representation theory, working under the supervision of David Nadler. I will be graduating this June.
12h

awarded  Yearling 
Oct 21 
awarded  Yearling 
Aug 17 
awarded  Nice Answer 
Oct 21 
awarded  Yearling 
Jul 12 
comment 
Is the Springer resolution a blowup?
In the simplest case of $\mathfrak{sl}_2$, the Springer resolution is easily seen to be the blowup at the origin. In general, however, the Springer resolution is not a blowup. 
Mar 6 
comment 
The `set' of all principal G bundles over `all' spaces
Within the context of stacks in algebraic geometry, $BG$ (or $pt/G$) is absolutely the notation that would be used. I suppose you don't like this because it is also the notation for the classifying space of $G$? From my perspective, I don't particularly like the notation $Bun(G)$, only because $Bun_G(X)$ is typically used to denote the moduli of $G$bundles on the space $X$. But maybe others disagree. I'm struggling to think of a good alternative though. 
Feb 12 
answered  A^1invariant for Vector Bundles? 
Feb 11 
comment 
What is the dimension of a sheaf?
The sheaf in question is a sheaf over the residue field, which means that it can be viewed as vector space over the residue field. 
Jan 23 
answered  Simple question in the representation of SL(2,C) 
Jan 5 
comment 
$(\mathfrak{g},K)$modules and parabolic category $\mathcal{O}$
A general reference for category $\mathcal{O}$ that I really like: Humphreys' "Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$" 
Nov 19 
comment 
Classification of certain algebraic curves
One more comment: If you are simply looking for curves which possess a line bundle satisfying the equality, then any curve possessing a $g^1_4$ obviously works. This includes all hyperelliptic curves, but also all curves of genus at most $6$. More generally, you might try checking when the BrillNoether number associated to $d=deg(L)$ and $r=\frac{1}{2}deg(L)1$ is nonnegative. I haven't done the calculation, but it seems that using this strategy you might find that every curve possesses a line bundle satisfying your equality? 
Nov 19 
comment 
Classification of certain algebraic curves
This questions seems unclear at the moment. First of all, every curve has a special line bundle satisfying the equality $h^0(L) = \frac{1}{2}deg(L)+1$; namely the canonical bundle. Hyperelliptic curves are unique because they also possess a line bundle which satisfies the equality which is neither the trivial bundle nor the canonical bundle. So, is your question asking which curves possess some special line bundle satisfying $h^0(L) = \frac{1}{2}deg(L)$? Or, are you asking for a list of all line bundles on all curves which satisfy the equality, akin to Clifford's theorem? 
Nov 9 
comment 
real orbits of highest weight vectors
Regarding question 1: Fix a Borel subgroup $B$ and corresponding highest weight vector $v_{\lambda}$. Then for any other Borel subgroup $B'$, there exists $g \in G$ such that $gBg^{1} = B'$. In this case, the highest weight vector $v_{\lambda}'$ associated to $B'$ is simply $gv_{\lambda}$. Therefore $G$ does act transitively on highest weight vectors. It seems to me that the stabilizer would then be the unipotent radical of $B$. 
Nov 9 
awarded  Good Answer 
Nov 8 
comment 
Is base affine space a trivial fibration?
Presumably the base affine space is $G/U$ (I haven't heard the terminology 'base affine space' before)? I think it's helpful to consider the case where $G=SL_2$, so that the flag variety is $\mathbb{P}^1$ and $G/U$ is the complement of the origin in $\mathbb{A}^2$, which isn't a trivial $\mathbb{G}_m$bundle over $\mathbb{P}^1$. 
Nov 8 
comment 
Deformation of Line bundles over dual numbers
A short exact sequence $0 \to L \to M \to L \to 0$ enables you to give $M$ the structure of a module over $X'$. You just need to be able to say how $\epsilon$ acts on $M$. Composing the projection $M \to L$ with the inclusion $L \to M$ tells you how $\epsilon$ acts. 
Oct 22 
awarded  Yearling 
Oct 19 
awarded  Autobiographer 
Sep 27 
comment 
Which bundles does the character vareity parameterize?
When $G = U(n)$, the character variety parameterizes vector bundles over $C$. This is the NarasimhanSeshadri Theorem. When $G = GL_n$, the character variety parameterizes Higgs bundles. This is part of what's known as nonAbelian Hodge theory. 
Sep 27 
comment 
What is a coalgebra intuitively?
I think the Davids would approve of this answer. 