bio | website | front.math.ucdavis.edu/… |
---|---|---|
location | Cornell | |
age | 45 | |
visits | member for | 5 years, 7 months |
seen | 4 hours ago | |
stats | profile views | 10,959 |
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 |
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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 |
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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 |
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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 |
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What are the most misleading alternate definitions in taught mathematics?
I believe this terminology is due to Souriau. |
Apr 21 |
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Must an algebraic variety with trivial tangent bundle be an abelian variety?
...since any affine algebraic group gives an example. |
Apr 9 |
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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 |
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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 |
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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 |
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Connected vs Irreducible Subvarieties
Yes $\ \ \ \ \ \ \ \ $ |
Apr 1 |
revised |
Equivalence of Lie subalgebras, within a (irreducible) representation
added 19 characters in body |