bio  website  front.math.ucdavis.edu/… 

location  Cornell  
age  45  
visits  member for  5 years, 6 months 
seen  45 mins ago  
stats  profile views  10,876 
Math professor at Cornell,
PhD 1996
2d

awarded  Nice Answer 
Apr 21 
comment 
What are the most misleading alternate definitions in taught mathematics?
It's completely maddening that the IEEE standard for the definition of "b mod n" gives a number in $\{0,1,\ldots,n1\}$ only for $b\geq 0$. For $b<0$ it's supposed to take values in $\{1n,\ldots,0\}$! So in order to have invariance under the finite group $\pm$ they give up the infinite group of translation invariance by $n\mathbb Z$. Just horrible. 
Apr 21 
comment 
What are the most misleading alternate definitions in taught mathematics?
I believe this terminology is due to Souriau. 
Apr 21 
comment 
Must an algebraic variety with trivial tangent bundle be an abelian variety?
...since any affine algebraic group gives an example. 
Apr 9 
comment 
Algebraic Ktheory of complex varieties
I'm not sure the question makes sense  if I take an analytic but not algebraic open set, what is its algebraic Ktheory supposed to be? 
Apr 8 
comment 
Families of ideals with a given initial ideal
Sorry, all I mean is that you should put in a coefficient for every possible term, then use the above to constrain the coefficients. This answer makes no assumption of genericity; it really does find every ideal with this initial ideal. 
Apr 8 
answered  Quotient of Flag varieties 
Apr 8 
answered  Families of ideals with a given initial ideal 
Apr 7 
comment 
Unitary representation of finitedimensional unitary group
I did not say it was unitarily equivalent to that tensor product. I said it was the largest component. And en.wikipedia.org/wiki/Exterior_algebra#The_exterior_power 
Apr 6 
comment 
Homotopy type of certain maps on complex grassmanian
abx, he's using * in his formula; this is not an algebraic identification. The map backwards is $A \mapsto image(A)$. 
Apr 5 
comment 
Unitary representation of finitedimensional unitary group
This is absolutely not true already for $n=3$, already for the adjoint representation. The true statement is that the irrep with highest weight ${a,b,c}$ is the largest component of $\Phi_{ab}\otimes \Phi_{bc}^c \otimes (det)^c$. That does generalize, with the general factor being $Sym^N(Alt^k \mathbb C^n)$. For $k=n1$ one has $Alt^k(\mathbb C^n) \cong det \otimes (\mathbb C^n)^*$, which allowed you to use $\Phi^c_N$ instead. 
Apr 5 
answered  Iterated blowups above a point 
Apr 2 
comment 
Connected vs Irreducible Subvarieties
Yes $\ \ \ \ \ \ \ \ $ 
Apr 1 
revised 
Equivalence of Lie subalgebras, within a (irreducible) representation
added 19 characters in body 
Mar 31 
comment 
Flatness and intersection of fibers
Let $X_1 = \{(x,0)\}$, $X_2 = \{(x,x)\}$, $f = $projection to the first factor. Then $X_1,X_2,X_1\cup X_2$ are all flat over $Y$, and their generic fibers do not intersect. But the intersection is supported over $0\in Y$. (Maybe this was Matthieu's example.) 
Mar 31 
comment 
Finiteness of geometric valuations
Since these $E$ aren't in $X$, but in various possibilities for $Y$, I'd say there's a proper class of such $E$. Are you really looking for something like the set of valuations on the structure sheaf of $X$, centered at $Z$? 
Mar 30 
comment 
Singular/Smooth locus of Schubert variety of the affine grassmannian
I'm pretty sure that's true for $\lambda$ dominant, but it's definitely not always true, e.g. if $\dim X_\lambda=1$. 
Mar 29 
comment 
Picard group of Schubert varieties
Indeed; one way to think about it is that we know the map $c_1:Pic\to H^2$ is an isomorphism for $G/B$, and this restriction fact says that the same is true for $X_w$. Since $X_w$ is a union of $G/B$'s cells it's easy to compute the map $H^2(G/B) \to H^2(X_w)$ and it has the kernel you describe. 
Mar 29 
revised 
Root in positive Weyl chamber
added 68 characters in body 
Mar 28 
answered  Root in positive Weyl chamber 