15,628 reputation
23099
bio website front.math.ucdavis.edu/…
location Cornell
age 45
visits member for 5 years, 7 months
seen 4 hours ago
Math professor at Cornell, PhD 1996

May
19
comment What are the most misleading alternate definitions in taught mathematics?
Okay, I'll agree that both IEEE definitions suck, without opining as to which one sucked first.
May
18
comment Nilpotent orbits and subspaces
What does "$X$ is even" mean? It's always even-dimensional, so I presume that's not what you mean.
May
5
comment A geometric construction of the complex projective plane?
Is it perchance computing $Proj\ \mathbb R[x,y,z]$, i.e. $\mathbb{CP}^2$ mod complex conjugation? I hope I'm thinking about this right.
May
5
comment Is there a Lie II theorem for monoids?
In your "standard example", by "all" Lie algebra representations you mean (continuous and) finite-dimensional, apparently?
May
2
comment Is there a Lie II theorem for monoids?
Consider the two embeddings $GL(n) \hookrightarrow M_n$, $GL(n) \stackrel{-1}\to GL(n) \hookrightarrow M_n$. What do you want such a criterion to say, in these examples? Is the Lie algebra side perhaps about pairs $(\mathfrak g,C)$ where $C$ is a subcone of $\mathfrak g$'s positive Weyl chamber?
Apr
27
comment A homomorphism in the long exact sequence of a fibration for a homogeneous space of a Lie group
You're not even using $G$ a group, just the map $\pi_1(X/H) \to H$ from the usual theory of covering spaces (here $X \to X/H$).
Apr
24
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