69,307 reputation
5145334
bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 34
visits member for 4 years, 10 months
seen 21 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.


18h
comment Without Skolem–Mahler–Lech Theorem?
Duplicate of math.stackexchange.com/questions/705877 , with a nice elementary proof by Noam Elkies.
1d
revised Roots of truncations of e^x - 1
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2d
comment Arbitrarily large $n$ divides $F_n$
To respond to the original version which didn't ask for infinitely many prime factors, $F_{5(2n+1)} = 5 (5 F_{2n+1}^5 - 5 F_{2n+1}^3 + F_{2n+1})$ so we can show inductively that $5^k | F_{5^k}$.
Aug
19
comment Maximal score for the 2048 game
math.stackexchange.com/a/902535/448
Aug
19
comment Maximal score for the 2048 game
I put up a quick proof that $2^{16}$ is an upper bound on the math.SE with only $2$'s on the math.SE thread. Similarly, $2^{17}$ is an upper bound with $2$'s and $4$'s. I agree that the state of that thread is a little embarrassing; I'm not sure that anyone has given a proof that $2^{17}$ is achievable.
Aug
19
comment An infinite set of identities using Stirling numbers 1st kind - are they all zero?
I see. Okay, that makes sense (and the sign turned out to be a global sign anyway, so it doesn't matter). Neat!
Aug
19
comment An infinite set of identities using Stirling numbers 1st kind - are they all zero?
Very slick. I think you mean $k s_1(k,k-R) = s_1(k+1, k-R) - s_1(k, k-R-1)$ (you have the opposite sign).
Aug
18
comment Cohomology of the toric variety $X_\Sigma=\mathbb C^2\sqcup \mathbb C^2\big/\left((x,y)_1\sim(x^{-1},y^{-1})_2\right)_{x,y\neq 0}$
Your gluing description and your fan description are isomorphic to each other, but they are not compatible with your blow up description. They are both $\mathbb{P}^1 \times \mathbb{P}^1 \setminus \{ \mbox{two points} \}$. As @MatthiasWendt says, you should be able to compute this via Meyer-Vietores. I get that there is a nontrivial class in $H^3$, so cohomology is not the same as Chow.
Aug
16
revised Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
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Aug
16
revised Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
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Aug
16
answered Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
Aug
15
comment Embed one Coxeter System into another
Duplicate of mathoverflow.net/questions/138083 ? Whether or not it is a duplicate, Stembridge's manuscript math.lsa.umich.edu/~jrs/papers/folding.ps.gz seems like a good answer to both questions.
Aug
15
comment algebraic de Rham cohomology of singular varieties
One might as well fill in the details. Take $A = k[x,y]/(y^2-x^3)$, $\mathrm{char}(k) \neq 2$, $3$. Make this a graded ring where $\deg x = 2$, $\deg y=3$ and grade $\Omega^1$ so that $d$ preserves grade. The degree $5$ part of $\Omega^1_A$ is two dimensional, spanned by $y dx$ and $x dy$. (One might naively think that $3 y dx = 2 x dy$, as this equality holds away from the cusp, but the derivation $A \to A/\langle x,y \rangle$ sending $x \to 1$ and $y \to 0$ shows otherwise.) The degree $5$ part of $A$ is only one dimensional, so $\Omega^1_A/d A$ is nontrivial in degree $5$.
Aug
15
comment How many turns will it take to draw all cards from a deck with shuffling and replacement?
Indeed it is, and the Wikipedia article on the coupon collector problem is quite thorough.
Aug
15
comment Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
By the way, Kemper has a result which lets us mostly ignore finite generation issues: There is a finitely generated subring $R$ of $\mathcal{O}(X)^G$ so that anything which is collapsed by the map $X \to \mathrm{Spec}(R)$ is also collapsed by $X \to \mathrm{Spec}(S)$ for any subring $S$ of $\mathcal{O}(X)^G$. So, although $\mathcal{O}(X)^G$ is not necessarily finitely generated, there are finitely generated subrings of it which are "good enough". See ams.org/mathscinet-getitem?mr=2532166 and the references therein, which will probably give a more accurate history than I have.
Aug
15
comment Stein Manifolds and Affine Varieties
Goodman and Hartshorne must have an implicit assumption that $X$ is separated, the result as stated is false for the line with doubled origin. (Of course, Stein implies separated, so your main answer is fine.)
Aug
15
comment Canonical Metric on Grassmann Manifold
If you want an explicit formula, see mathoverflow.net/questions/141483/…
Aug
14
comment Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
One strategy to prove that $Y$ is quasi-affine would be to show that $Y \to \mathrm{Spec}(A_0)$ is etale and of generic degree $1$, where $A_0$ is the ring of invariant functions. I think that should force an open immersion when $Y$ is separated, while having a good chance of being true even when $Y$ isn't.
Aug
14
revised Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
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Aug
14
answered Quasi-affineness of the base of a $\mathbb{G}_a$-torsor