76,208 reputation
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bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 34
visits member for 5 years, 7 months
seen 11 mins ago

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 genus-0 surface?
Also, nice answer!
May
23
comment Is every closed curve in 3D a geodesic on a genus-0 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 $GCD(2-1, N)=1$, 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
comment 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 Lucas-Lehmer 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
comment How did Cole factor $2^{67}-1$ in 1903
Although the issue about the prime tables not existing still bothers me...
May
22
comment 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
comment 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
comment Permutations with all cycles odd length and permutations with all cycles even length
@MartinRubey Yes, this works to biject pairs of fixed-point-free-involutions with all-even-permutations. More precisely, you need a rule for how to turn a red-blue 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 all-odd case this way seems harder, though.
May
19
comment Permutations with all cycles odd length and permutations with all cycles even length
Yes, I mean bijective.