bio  website  front.math.ucdavis.edu/… 

location  Cornell  
age  45  
visits  member for  5 years, 8 months 
seen  17 hours ago  
stats  profile views  11,196 
Math professor at Cornell,
PhD 1996
1d

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Smooth morphism to homogeneous spaces and fibers
I usually use "$f$ is equivariant". 
1d

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Picard group of a quotient of a group by its maximal parabolic subgroup
You can't say "the" maximal parabolic; there's usually more than one, even up to conjugacy. But for every such $P$ this is true. 
1d

answered  Shared maximum eigenvector 
Jun 28 
revised 
What is deforming this noncomplete intersection like?
made title more specific to the question 
Jun 28 
reviewed  Approve What is deforming this noncomplete intersection like? 
Jun 26 
awarded  Nice Question 
Jun 26 
comment 
Number of $\mathbb F_p$ points constant mod $p$?
Your #4 sounds like "what does it imply?" rather than "what does it suggest?" (what would imply it, that one should be on the lookout for?). I have a certain class of varieties; I don't know what properties they have, but now I'm going to try to prove rational connectivity directly for them (not actually imply it from the pointcounting fact). 
Jun 26 
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Number of $\mathbb F_p$ points constant mod $p$?
I'd certainly like to compute $\#X(\bf F_p)$ but don't expect to have much luck. 
Jun 25 
asked  Number of $\mathbb F_p$ points constant mod $p$? 
Jun 21 
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A homeomorphism between total spaces with same fiber and base spaces not homotopic
Or more generally, if $F\to E\to B$ is a bundle with $E$ not a product, then $F\times E \to E$, $F\times E \to F\times B$ works. 
Jun 18 
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Combinatorial results by Poincaré duality
If you're willing to extend this from "Poincar\'e duality" to "properties of Betti numbers", then you could include Hard Lefschetz in your toolset, and get Stanley's proof of the Upper Bound Theorem for the number of faces of a simplicial polytope. 
Jun 17 
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How to embed $U(1)$ into a bigger group, using Dynkin diagrams
The "remove the top root" step amounts to "take the centralizer in $E_7$ of a certain element of adjoint order $2$". Look around MO for Borelde Siebenthal theory, which is about subgroups of the same rank as the big group. 
Jun 16 
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qCatalan numbers from Grassmannians
Hard Lefschetz tells you that the even Betti numbers have to increase to the middle, then decrease (they're "unimodal"). 
Jun 13 
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How to prove this polynomial always has integer values at all integers?
I really don't know how to connect $\mathbb Z$valuedness and evenness. If $x^2=y$ so we can rewrite $P(x)$ as $P(y)$, then $P$ being $\mathbb Z$valued at all $y\in\mathbb Z$ is (much?) stronger than its being $\mathbb Z$valued at all $x\in\mathbb Z$. Do your computed polynomials have $\mathbb Z$coefficients expanded in $\{ {y \choose k} \}$? 
Jun 13 
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How to prove this polynomial always has integer values at all integers?
@DavidLoeffler : yes it has that effect, which means we've lost control of $a_0$ and $a_1$. I wrote "(assuming $Q(0)\in\mathbb Z$)" but meant $P(0)\in\mathbb Z$. How are you using evenness to control $a_1$, to establish this converse? 
Jun 13 
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How to prove this polynomial always has integer values at all integers?
(1) The proper basis for the space of integervalued polynomials is not monomials $\{x^k\}$ but binomial coefficients $\{ {x\choose k} \}$ (a polynomial is $\mathbb Z$valued iff its unique expansion in this basis has $\mathbb Z$coefficients). You should probably look into those expansions. (2) Let $Q(x) = P(x+1)+P(x1)2P(x)$, again even. If $P$ is $\mathbb Z$valued, so is $Q$, and I suspect the converse is true for even functions (assuming $Q(0) \in \mathbb Z$). Perhaps you can use this for an inductive argument. 
Jun 13 
answered  Why there is a relation among the secondorder minors of a symmetric $4\times 4$ matrix? 
Jun 12 
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subvariety of (P^1)^4
It's the closure of a generic $T^4$orbit on the Grassmannian $Gr(2,4)$, so there's something it lies inside. 
Jun 8 
revised 
Real and Quaternionic Representations according to Weights
added 23 characters in body 
Jun 8 
answered  Real and Quaternionic Representations according to Weights 