76,966 reputation
5173381
bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 34
visits member for 5 years, 8 months
seen 1 hour 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
comment What conditions imply that a function over $\mathbb{Z}$ is a polynomial?
A minor extension of Liouville's theorem: If $f: \mathbb{C} \to \mathbb{C}$ is holomorphic, and $|f(z)| = O(|z|^N)$ as $|z|\to \infty$, then $f$ is a polynomial of degree $\leq N$. Is this the sort of thing you are looking for?
1d
comment Is Every Holomorphic Near an Entire?
A natural attempted fix would be to require "for any disc $D$ in $\mathbb{C}$ with $\partial D \subseteq K$ and any holomorphic $g$ on $D$, we have $\int_{\partial D} f(z) g(z) dz=0$." Any idea if the statement is true with that condition?
Jun
28
awarded  Nice Answer
Jun
24
comment A probability distribution in n dimensional space which its projection on any line is a uniform distribution?
See mathoverflow.net/questions/6964 for $n=2$
Jun
20
comment Give an example about flatness.
@NicholasProudfoot Well, there are stupid counter-examples. Set $R = k[t, \epsilon]/(t \epsilon, \epsilon^2)$, with $t$ in degree $0$ and $\epsilon$ in degree $1$. Then $\mathrm{Spec}(R)$ is not flat over $\mathrm{Spec}(R_0)$, but $\mathrm{Proj}(R)$ is empty. There are probably ways to add hypotheses to rule out that sort of silliness, though.
Jun
19
comment Does there exist a nonconstant, periodic, real analytic function with period 1 and rational Maclaurin coefficients?
Can't you inductively construct some sequence $g_k$ such that $\sum g_k (\sin (2 \pi x))^k$ is uniformly convergent on a neighborhood of the real axis and has rational coefficients?
Jun
19
comment Which degree does a motivic Galois representation show up in?
Regarding the question of whether every modular form has an ordinary prime, I asked a related question a long time ago: mathoverflow.net/questions/8003/…
Jun
17
revised Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix?
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Jun
17
revised Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix?
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Jun
17
answered Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix?
Jun
16
comment for which values of $\theta$ does this equation $x_{n+1}=\cos(\theta)x^2_{n}-\sin(\theta)x^2_{n-1}$ have bounded solutions?
Whenever $\cos \theta > \sin \theta$, the point $(x,x)$ is fixed where $x = 1/(\cos \theta - \sin \theta)$. So that gives a bounded solution half of the time.
Jun
15
answered How to realize any non-crossing matching as $\mathrm{Re}[p(z)]=0$
Jun
15
comment Non-algebraic K3 surfaces in characteristic $p$
To add a useful comment for beginners: The big difference between $\mathbb{C}$ and $\mathbb{F}_p$ here is that we can talk about convergence of power series over $\mathbb{C}$. Thus, we can take the formal power series in the $x_i$ and plug in nonzero complex numbers to get non-algebraic $K_3$'s. Over $\mathbb{F}_p$, the power series still exist, but it doesn't make sense to evaluate them anywhere except at $0$.
Jun
11
reviewed Approve Restriction from $GL_n$ to $S_n$
Jun
10
revised Restriction from $GL_n$ to $S_n$
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Jun
10
revised Conditions for the consistency of a system of affine polynomials
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Jun
10
revised Conditions for the consistency of a system of affine polynomials
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Jun
10
answered Conditions for the consistency of a system of affine polynomials
Jun
9
comment Should we post on arXiv only papers in publishable shape (or very close)?
Regarding this, I would say that the presentation should be of publishable quality, even if the importance of the result doesn't seem publishable.
Jun
9
answered Can every genus $2$ curve be written as ramified cover of elliptic curve?