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

location  Ann Arbor  
age  34  
visits  member for  5 years, 7 months 
seen  11 mins ago  
stats  profile views  33,518 
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.
1d

awarded  Popular Question 
1d

comment 
Existence of a ring with specified residue fields
Nice reference, but your summary of Heitmann's paper is wrong. Hietmann's Theorem A requires the fields to be countable, so it will not "always hold if your collection of residue fields is finite". 
May 24 
awarded  Nice Answer 
May 23 
comment 
Is every closed curve in 3D a geodesic on a genus0 surface?
Also, nice answer! 
May 23 
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Is every closed curve in 3D a geodesic on a genus0 surface?
It seems to me that, even if the surface exists locally, it might be a Mobius strip rather than an annulus. Of course, in this case, $\gamma''$ must still vanish somewhere, as otherwise it would provide a choice of normal direction. For example, take a Mobius strip in $\mathbb{R}^3$ and take a geodesic on it realizing a generator of $\pi_1$. 
May 23 
awarded  Good Question 
May 22 
answered  How did Cole factor $2^{67}1$ in 1903 
May 22 
awarded  Nice Question 
May 22 
accepted  How did Cole factor $2^{67}1$ in 1903 
May 22 
comment 
How did Cole factor $2^{67}1$ in 1903
Nope, issue with the factor tables sill exists in $1903$. @AnthonyQuas Since $2^{67} \equiv 1 \bmod N$, and $GCD(21, N)=1$, for any prime $p$ dividing $N$, there is a nontrivial $67$th root of unity modulo $p$, and that forces $p \equiv 1 \bmod 67$. 
May 22 
revised 
How did Cole factor $2^{67}1$ in 1903
added 43 characters in body 
May 22 
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How did Cole factor $2^{67}1$ in 1903
@SamHopkins Whoa, how did I get that wrong? 1876 is the date that Lucas invents the LucasLehmer test to show that $N$ is composite. Fixing the title, thanks. And now back to Dickson to see which prime tables existed... 
May 22 
revised 
How did Cole factor $2^{67}1$ in 1903
edited title 
May 22 
comment 
How did Cole factor $2^{67}1$ in 1903
Actually, it takes us down to $2$ a minute, since the odd numbers are already not in our table of primes. 
May 22 
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How did Cole factor $2^{67}1$ in 1903
Although the issue about the prime tables not existing still bothers me... 
May 22 
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How did Cole factor $2^{67}1$ in 1903
Ah, thank you. And that takes us down to a little under $1$ a minute, which isn't crazy, though still hard. 
May 22 
asked  How did Cole factor $2^{67}1$ in 1903 
May 21 
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How long can a cycle of antichains in a finite partial order be?
A quick note: If we take $n_1+1$, $n_2+1$, ... to be the first block of primes $2$, $3$, $5$, ..., $p$, chosen to have sum as close as possible to $n$, then $p \approx \sqrt{n \log n}$ and $LCM(2,3,\ldots, p) \approx e^p \approx \exp(\sqrt{n \log n})$. So we are trying to separate an $\exp(cn)$ upper bound and an $\exp(n^{1/2+\epsilon})$ lower bound. 
May 19 
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Permutations with all cycles odd length and permutations with all cycles even length
@MartinRubey Yes, this works to biject pairs of fixedpointfreeinvolutions with allevenpermutations. More precisely, you need a rule for how to turn a redblue coloring of an unoriented $2k$ cycle into an orientation of that $2k$ cycle. There is no particularly natural choice but, for example, you could choose to oriented such that the red edge incident to the largest entry in the cycle is oriented away from that entry. Dealing with the allodd case this way seems harder, though. 
May 19 
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Permutations with all cycles odd length and permutations with all cycles even length
Yes, I mean bijective. 