64,054 reputation
5129311
bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 33
visits member for 4 years, 6 months
seen 2 hours 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
revised Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2 - x^3 + x)$
added 42 characters in body
1d
revised Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2 - x^3 + x)$
added 317 characters in body
1d
revised Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2 - x^3 + x)$
edited body
1d
answered Holomorphic trivialization of $(x,y) \subset \mathbb{C}[x,y]/(y^2 - x^3 + x)$
2d
awarded  Nice Answer
Apr
13
comment Geometric explanation of Hutton's formula?
You're welcome! Sorry for the missing scalar factors in the first version; added now.
Apr
13
revised Geometric explanation of Hutton's formula?
added 143 characters in body
Apr
13
answered Geometric explanation of Hutton's formula?
Apr
12
awarded  Enlightened
Apr
12
awarded  Nice Answer
Apr
9
comment Cyclic extensions
You may be looking for Kummer's theorem: If $n$ is relatively prime to the characteristic of $K$, and $x^n-1$ splits in $K$, THEN every degree $n$ cyclic extension of $K$ is of the form $L=K(a)$ with $a^n \in K$. The answers below indicate why each hypothesis is needed.
Apr
9
comment How to check whether a matrix is completely positive or not?
I suspect the closers misread this question as the far easier one abx understood; I'm voting to reopen.
Apr
9
comment How to check whether a matrix is completely positive or not?
@abx The $x_i$ are required to be $\geq 0$; this is more restrictive than being positive definite. (I was confused by this for quite a while as well.)
Apr
8
revised How to flow submanifolds?
deleted 54 characters in body
Apr
8
revised How to flow submanifolds?
deleted 83 characters in body
Apr
8
answered How to flow submanifolds?
Apr
8
comment What is the Tutte polynomial encoding?
We don't know the dimension of the vector space in $K_0$ spanned by all matroids, although we do know from Derksen-Fink that it is spanned by Schubert matroids. Alex and I did some preliminary work investigating positivity properties of this $K$-class, but nothing we are willing to state publicly yet.
Apr
8
comment What is the Tutte polynomial encoding?
@მამუკაჯიბლაძე Thanks! Not much more progress beyond what's in our paper, no. (There are results in the paper which are not in this answer.) For the study of the invariant in $K_0(G(d,n))$, the starting point is Derksen-Fink arxiv.org/abs/0908.2988 , which works out the vector space of matroids modulo "obvious $K$-theory relations". This has dimension $\binom{n}{d}$ and has basis the Schubert matroids. Since $\binom{n}{d} = \dim K_0(G(d,n))$, I had hoped the obvious relations were all of them, but they are not, because the fact that $\dim Z \leq n-1$ also gives relations. (continued)
Apr
6
answered Convergence of the Double Integral of a Polynomial Reciprocal
Apr
6
answered How to recognize a Hopf algebra?