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bio website front.math.ucdavis.edu/…
location Cornell
age 45
visits member for 5 years, 6 months
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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 $\{0,1,\ldots,n-1\}$ only for $b\geq 0$. For $b<0$ it's supposed to take values in $\{1-n,\ldots,0\}$! 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 K-theory 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 K-theory 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 finite-dimensional 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 finite-dimensional 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 $\Phi_{a-b}\otimes \Phi_{b-c}^c \otimes (det)^c$. That does generalize, with the general factor being $Sym^N(Alt^k \mathbb C^n)$. For $k=n-1$ 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 blow-ups 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