bio  website  math.lsa.umich.edu/~speyer 

location  Ann Arbor  
age  34  
visits  member for  5 years, 6 months 
seen  12 hours ago  
stats  profile views  33,160 
Associate Professor of Mathematics at the University of Michigan. My research interests are in combinatorial algebraic geometry, particularly Schubert calculus, matroids and cluster algebras. I also enjoy thinking about number theory and computational mathematics.
2d

awarded  Nice Answer 
Apr 22 
comment 
“Diagonalizing” an associative algebra
Regarding the infinite dimensional case: $k[x]$ does not have a basis of orthogonal idempotents: The only idempotent elements are $0$ and $1$. 
Apr 22 
revised 
A Polynomial With Positive Prime Density
added 18 characters in body 
Apr 22 
awarded  Nice Answer 
Apr 21 
revised 
A Polynomial With Positive Prime Density
added 4 characters in body 
Apr 21 
comment 
A Polynomial With Positive Prime Density
Oh! I didn't realize that the square brackets mean round down! 
Apr 21 
answered  A Polynomial With Positive Prime Density 
Apr 20 
answered  Factoring constant rank maps into a submersion and an immersion 
Apr 18 
awarded  Altruist 
Apr 18 
awarded  Nice Question 
Apr 18 
awarded  Nice Answer 
Apr 17 
comment 
Factoring constant rank maps into a submersion and an immersion
Thanks! That does it, then. My only thought for a hypothesis to add that might save the day is to ask that $\phi: X \to Z$ be proper. 
Apr 17 
accepted  Factoring constant rank maps into a submersion and an immersion 
Apr 17 
comment 
Factoring constant rank maps into a submersion and an immersion
So Exercise 513 is true, but the map $X \to Y$ may not be continuous with respect to the topology for $Y \to Z$ is an immersion. (Again, think about the line mapping to a nodal cubic.) 
Apr 17 
comment 
Factoring constant rank maps into a submersion and an immersion
@IgorRivin I'm looking though Lee's book at webmath2.unito.it/paginepersonali/sergio.console/lee.pdf . I didn't find the Theorem you reference, but I did find Exercise 513, which makes this claim. At first I thought this had to be wrong, (think about the line mapping to a nodal cubic) but then I checked his definition of immersed submanifold (p. 119). His definition is very generous: It just says that $\phi(X)$ can be given some topology such that $\phi(X) \to Z$ is an injective immersion. (continued) 
Apr 17 
comment 
Ordering subsets of the cyclic group to give distinct partial sums
I'm only saying that the low degree terms are $0 \bmod 2$. So $P \equiv 0 \bmod \langle 2, x_1^6, x_2^6,\ \ldots,\ x_6^6 \rangle$. Doesn't seem obviously wrong to me. 
Apr 16 
comment 
Factoring constant rank maps into a submersion and an immersion
Presumably, the way you'd want to do this is to define an equivalence relation $\sim$ on $X$ by $x_1 \sim x_2$ if $\phi(x_1) = \phi(x_2)$ and $x_1$ and $x_2$ are in the same connected component of $\phi^{1}(\phi(x_1))$. Then show that $X/\sim$ is a smooth manifold. But this seemed hard to me, which was when I decided to ask. 
Apr 16 
comment 
Factoring constant rank maps into a submersion and an immersion
There is something called the global constant rank theorem, but it only says that, for each $z \in Z$, the fiber $\pi^{1}(z)$ is a submanifold of $X$. It doesn't say that the connected components of the $\phi^{1}(z)$'s can be organized into a manifold. 
Apr 16 
comment 
Factoring constant rank maps into a submersion and an immersion
@IgorRivin All the sources I found only said that this is locally true: I.e., for any $x \in X$, there is an open $U \ni x$ where I can make such a factorization. It doesn't seem obvious to me how to glue all of these into a global $Y$. 
Apr 16 
comment 
Ordering subsets of the cyclic group to give distinct partial sums
math.lsa.umich.edu/~speyer/foo6.txt Interestingly, all the coefficients are even. 