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bio website math.lsa.umich.edu/~speyer
location Ann Arbor
age 34
visits member for 5 years, 5 months
seen 12 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.


2d
awarded  Nice Answer
2d
answered Polyhedra containing hexagones only
2d
comment Computing $\prod_p(\frac{p^2-1}{p^2+1})$ without the zeta function?
@VladimirDotsenko Yes it is. That's why I didn't wind up sending this anywhere. See testcase's answer below.
Mar
27
answered Are there any Algebraic Geometry Theorems that were proved using Combinatorics?
Mar
25
accepted Are there any natural differential operators besides $d$?
Mar
25
comment Are there any natural differential operators besides $d$?
Following links from your paper, the answer to the specific question I asked is Theorem 5.7 in "Natural vector bundles and natural differential operators" by Terng jstor.org/stable/2373910, and appears to have been proved around the same time by several Russian authors whom I haven't read yet. Thanks for the reference! I definitely appreciate your point about how the problem becomes different with only diffeomorphisms in the picture -- and much harder.
Mar
25
comment Are there any natural differential operators besides $d$?
I'm reading the paper you linked now. It seemed to me that any natural linear operator would be the direct sum of its projections onto the Schur factors, so the Schur case does everything. But maybe it will be clear what I am missing after I finish reading the article you linked.
Mar
25
revised Are there any natural differential operators besides $d$?
added 5 characters in body
Mar
25
comment Are there any natural differential operators besides $d$?
A bigger problem for the specific formalism I set up is that vector fields are sections of the dual of $T^{\ast} X$, and dual is not a Schur functor (it is contravariant, not covariant!). This is why you have to restrict to diffeomorphisms when working with vector fields.
Mar
25
comment Are there any natural differential operators besides $d$?
@VladimirDotsenko Couldn't you make them arguments of one argument though, by thinking of them as a map from $(\mbox{vector fields}) \otimes (\mbox{whatever}) \to \mbox{whatever}$? Contractions don't obey Liebnitz in the sense I wrote, but there might be something you could build from Lie derivatives.
Mar
25
awarded  Nice Question
Mar
24
awarded  Good Answer
Mar
22
asked Are there any natural differential operators besides $d$?
Mar
13
comment Is there a method to simultaneously block-diagonalize a set of group matrices?
Wait, is this a group in characteristic zero? Then I would compute the center of this group algebra (linear algebra) and diagonalize the central elements (since they commute).
Mar
13
comment Is there a method to simultaneously block-diagonalize a set of group matrices?
See math.stackexchange.com/a/185001/448 . If someone reading this knows a better place to point people than my answers, please do so!
Mar
13
comment Estimate self crossings of a curve parameterized by a trigonometric polynomial
Related (but also unanswered) mathoverflow.net/questions/90856
Mar
12
comment Examples of eventual counterexamples
Sorry, comment two earlier should read $\sqrt{(10^n+1) m}$, not $\sqrt{10^n+1}$.
Mar
12
comment Examples of eventual counterexamples
For example,$13^2|10^{39}+1$ and $384615384615384615384615384615384615385^2 = (147928994082840236686390532544378698225)*(10^{39}+1)$, reflecting that $5/13 = 0.384615\cdots$.
Mar
12
comment Examples of eventual counterexamples
@DavidMandellFreeman If $(10^n+1) m$ is square for $m<10^n$, then $10^n+1$ must have a square divisor, say $10^n+1 = s^2 t$ and $m = r^2 t$. Then $\sqrt{10^n+1} = rst \approx 10^n (r/s)$. So the RHS will look very close to a decimal expansion of $r/s$. The first non-squarefree numbers of the form $10^n+1$ are $11^2 | 10^{11}+1$ and $7^2 | 10^{21}+1$. If you search further, I'm sure other denominators occur.
Mar
12
comment Two questions about discriminants of polynomials in Q[x]
@wishcow Oops! Fixed, thanks.