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bio website math.lsa.umich.edu/~speyer
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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  Nice Answer
2d
awarded  Enlightened
2d
awarded  Nice Answer
Jul
22
revised Constructing quintic number fields with certain splitting behaviour
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Jul
22
comment Computing the Chern class of $S^6$
Does the following count: "$c_{top}(E)$ is the number of zeroes of a section of the vector bundle $E$ (counted with appropriate multiplicity). When $E$ is the tangent bundle, and your base space is a smooth compact manifold $X$, then the number of zeroes is the Euler characteristic $\chi(X)$. This is the Poincare-Hopf theorem and is deducible from the Lefschetz fixed point theorem mathoverflow.net/questions/153289 or Morse theory." To me, this is just describing some ways to think about Euler class without using that word, but maybe you disagree.
Jul
22
comment Constructing quintic number fields with certain splitting behaviour
I have now edited in Don's point.
Jul
22
revised Constructing quintic number fields with certain splitting behaviour
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Jul
22
comment Constructing quintic number fields with certain splitting behaviour
@so-calledfriendDon Excellent point! You are right! Strange that Bhargava doesn't point that out; this argument shows that Bhargava's formula is always an upper bound.
Jul
22
answered Constructing quintic number fields with certain splitting behaviour
Jul
22
awarded  Good Question
Jul
22
answered Constructing quintic number fields with certain splitting behaviour
Jul
21
comment Constructing quintic number fields with certain splitting behaviour
Agreed. I was confused by Bhargava talking about $K$ etale over $\mathbb{Q}_p$. I thought he was abusing language and meant $\mathcal{O}_K$ etale over $\mathbb{Z}_p$ (at which point, other things didn't make sense) but the statement is perfectly sensible taken literally, and then Jeremy Rouse is right that this isn't enough.
Jul
21
revised Non-vanishing of elements in cohomology of full Flag varieties
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Jul
21
answered Non-vanishing of elements in cohomology of full Flag varieties
Jul
21
comment Constructing quintic number fields with certain splitting behaviour
I haven't digested Bhargava's terminology well enough to tell, but does Theorem 1.3 in arxiv.org/abs/1402.0031 do the job?
Jul
21
answered Isomorphism of matrix ring over ore domain
Jul
21
comment Constructing quintic number fields with certain splitting behaviour
I don't follow why square free implies (3). If $p$ factors as $\mathfrak{p}^2 \mathfrak{q}$, where $\mathcal{O}_K/\mathfrak{q} \cong \mathbb{F}_{p^3}$, I think the discriminant is squarefree. That said, you might want to look at Kedlaya arxiv.org/abs/1103.5728 for some statements about sieving for square free discriminant.
Jul
18
revised Second betti number of compact analytic spaces
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Jul
18
comment Second betti number of compact analytic spaces
Many thanks to Tara Holm for asking me a number of years ago how to get at the actual cohomology of a toric variety, and how it related to the Fulton-Sturmfels computation. Of course, any errors introduced are mine.
Jul
18
answered Second betti number of compact analytic spaces