71,530 reputation
5155355
bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 34
visits member for 5 years, 1 month
seen 3 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.


1h
awarded  Nice Question
6h
asked A funny factorization of the Jacobian coming from the lines on the Fermat cubic
7h
comment Powers of traces, integrals over spheres and class functions
Its probably worth explicitly pointing out that, if the eigenvalues of $A$ are $\lambda_1$, $\lambda_2$, ..., $\lambda_n$, then $\mathrm{Tr}((A \otimes A \otimes \cdots \otimes A) P_{sym})$ is $\sum_{k_1+\cdots+k_n=k,\ k_i \geq 0} \lambda_1^{k_1} \lambda_2^{k_2} \cdots \lambda_n^{k_n}$.
7h
answered Decidable theorem or result that is not weaker than Tarski's theorem
1d
comment Powers of traces, integrals over spheres and class functions
I think your denominator on the $k=3$ expression should be $n^3+3n^2+2n=n(n+1)(n+2)$, not $3n(n+1)$. Up to the question of scaling, it looks like $\alpha_k(A)$ is the trace of $A$ acting on $\mathrm{Sym^k}(V)$.
1d
comment Hirzebruch's motivation of the Todd class
@GHfromMO Thanks for the sign correction. Changed "inverse function theorem" to "holomorphic inverse function theorem". Rouche or the argument principle shows that $h$ exists, but how do you know it is differentiable, let alone holomorphic, if you cite those theorems?
1d
revised Hirzebruch's motivation of the Todd class
deleted 27 characters in body
1d
answered Hirzebruch's motivation of the Todd class
Nov
21
answered Can all $L^2$ holomorphic functions on a domain vanish at a particular point?
Nov
21
awarded  Nice Answer
Nov
18
awarded  Revival
Nov
18
revised What makes the Cartier operator “tick”?
added 2 characters in body
Nov
18
answered What makes the Cartier operator “tick”?
Nov
18
awarded  Nice Answer
Nov
17
comment How many Pythagorean triples are there in which every member is triangular?
@JeremyRouse I don't want a tag as much as I want someone to ask the question: What is known about algorithms for finding/bounding integral points on K3 surfaces?
Nov
15
comment Trace map for sepeared morphism of non-singular varieties
Do I understand correctly that the proof in Zannier would be correct if Zannier imposed that $X$ was non-singular, not just normal? (And, therefore, Zannier's paper is a correct answer to the stated question.)
Nov
15
comment Trace map for sepeared morphism of non-singular varieties
To spell out the counterexample in the paper a bit better, let $\mathrm{char(k)} \neq 0$, let $X' = \mathrm{Spec} k[u,v]$ and let $X = \mathrm{Spec} k[u^2, uv, v^2]$, with the obvious map. Then $Tr(u dv)$ should be $2 u dv$. We have $2 u dv = (u/v) d(v^2) = 2 d(uv) - (v/u) d(u^2)$, so $2 u dv$ is regular on the smooth part of $X$, but it isn't regular at the singular point.
Nov
15
awarded  Enlightened
Nov
15
awarded  Nice Answer
Nov
13
revised Two (other) rings…are they isomorphic?
added 627 characters in body