bio  website  front.math.ucdavis.edu/… 

location  Cornell  
age  44  
visits  member for  4 years, 9 months 
seen  4 hours ago  
stats  profile views  9,489 
Math professor at Cornell,
PhD 1996
18h

comment 
Theorems for nothing (and the proofs for free)
Finite division rings commute. 
Jul 17 
comment 
GIT over integers
For the first one, I definitely get confused in the situation that $G$ doesn't have enough $\mathbb Z$points. Say $\mathbb G_m$ acts on $Spec\ \mathbb Z[x,y]$ with weights $+1,1$ on the coordinates. What does $A^G$ mean here, where the $\mathbb Z$points of $\mathbb G_m$ are just $\pm 1$? Do we first think of the ring $A$ as an algebraic variety of infinite type, on which $G$ is acting algebraically? 
Jul 16 
comment 
Is every Noetherian *connected* ring a quotient of a Noetherian domain?
Could you embed the primary components disjointly in a common space, then start gluing that space to itself? 
Jul 16 
comment 
Rational normal curves on Grassmanians
I'm confused: I would have thought that [BKT] would give a birational isomorphism of this space with $G(2k,n)$, which obviously isn't happening here. 
Jul 15 
comment 
Sum over growing Young tableaux
If I understand right, for every infinite sequence $\lambda$, you have an associated $f$? Anyway all that occurs to me is the hooklength formula, which says that $f_{\lambda_i}/f_{\lambda_{i1}}$ is a reasonably simple fraction. 
Jul 14 
comment 
Vector bundles, Higgs bundles and the Langlands program
Tiny thing: in general, a $\mathcal D$module on $M$ has a characteristic cycle on $T^* M$. 
Jul 14 
answered  Semicontinuity of degree of fibers for a proper map 
Jul 14 
comment 
counting the number of ordered pairs in a permutohedron
I don't know that this question has a particularly satisfying answer, but I do know that the order you're using is opposite "weak Bruhat order", and recommend you reverse it before confusing people. Have you computed the first few numbers and checked the OEIS? 
Jul 13 
comment 
Blowup and tangent cone
I agree with Jason. I would first look at $N_{E/X} \to N_{p/Y} \hookrightarrow T_p Y$, and observe that this is dilationequivariant. I guess your question is whether this can actually be projectivized? How about the map $\mathbb A^1 \to \mathbb A^1$, $z\mapsto z^3$, $p = 0$? 
Jul 9 
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Surprising connection between linear algebra and graph theory
Linear algebra is so powerful that we use it to study all other mathematical objects (de Rham cohomology comes to mind), graphs just being one example. 
Jul 8 
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Cohomology of BottSamelson varieties?
This is exactly what the original Bott and Samelson paper is about, and you should look at it. (Only later did people even realize that these manifolds are algebraic varieties, much less that they provide resolutions of singularities.) 
Jul 2 
awarded  Inquisitive 
Jul 2 
awarded  Curious 
Jun 22 
comment 
maximal chain in (strong) Bruhat order satisfying constraint
People talk about "left weak order" and "right weak order". Strong order is symmetric under taking inverses, but the weak orders aren't. 
Jun 19 
revised 
Positroids and Totally Nonnegative Complex Grassmanian
disambiguated last sentence 
Jun 17 
answered  Which linear combinations of simple roots are roots 
Jun 14 
comment 
A property of compact involutions of semisimple Lie algebras?
It seems like everything you're asking transforms nicely under the Weyl group, so one could replace "highest root" by "any long root", even a simple one. 
Jun 10 
revised 
Euler characteristics with and without compact support of algebraic varieties
stratUM 
Jun 8 
comment 
Rlinear representations of sl(2,C)
Oops: my question was essentially the answer for $\mathfrak{sl}_2(\mathbb R)$, not its square $\mathfrak{sl}_2(\mathbb C)$. I should have been tipped off by your mention of Lorentz. 
Jun 8 
comment 
Rlinear representations of sl(2,C)
I don't know about a reference, but here goes. A complex irrep is the complexification of a real irrep iff it's selfdual, and then, if the unique invariant bilinear form is symmetric. (The others are quaternionic, and in particular evendimensional.) On dominant weights, duality is given by $w_0$, so for $sl_2$ they're all selfdual. The odddimensional ones $V_{2n}$ are obviously real. The 2d one $V_1$ is obviously quaternionic. So each $V_{2n+1} \leq V_{2n} \otimes V_1$ is quaternionic. Summary: each odddimensional irrep is the complexification of a real irrep, and that's all of them. 