14,318 reputation
23092
bio website front.math.ucdavis.edu/…
location Cornell
age 45
visits member for 5 years, 2 months
seen 1 hour ago
Math professor at Cornell, PhD 1996

1h
answered Unifying Geometry for Characteristic Classes
19h
comment Companion to theoretical physics for working mathematicians
And yet there exists a Princeton Companion to Mathematics.
Dec
22
revised Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
added 175 characters in body
Dec
22
asked Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
Dec
20
comment Does an arbitrary product of $f$ and $f^\dagger$ belong to a universal enveloping algebra of the Heisenberg algebra?
For somebody learning the subject, I think saying there's "no essential difference" between, e.g., a finite-dimensional and infinite-dimensional vector space is very confusing. "The representation theory is the same" is good and one should leave it at that.
Dec
13
comment Codimension in zero and positive characteristic
Is this a properness over $Spec\ \mathbb Z$ issue?
Dec
13
comment kostant partition function vs Haar measure
I would say "the Kostant partition function is the Fourier transform of the reciprocal of the Weyl denominator", in that the first is a function on the weight lattice of a torus and the second is a function on the torus itself.
Dec
10
revised Can a subset of the plane have nontrivial $H_2$ or $\pi_2$?
edited body
Nov
26
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
If your matrix is special then it's unlikely that Schur-Horn gives the best possible results.
Nov
26
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
Consider the case $A$ real diagonal, and realize, "No."
Nov
25
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
Let $\vec v = \sum_j c_j \vec e_j$, where $\vec v$ is the $i$th vector in your orthonormal basis, and the $(e_j)$ are an orthonormal eigenbasis (with eigenvalues $(\lambda_i))$, and $\sum_i |c_i|^2=1$. Then $A_{ii} = \langle \vec v,A \vec v\rangle = \sum_i |c_i|^2 \lambda_i \in [\lambda_{min},\lambda_{max}]$. It's a little weird to credit Schur and Horn with this.
Nov
25
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
If you're asking what I think you're asking, the answer is "Very obviously yes," enough so that I wonder if I'm misunderstanding the question.
Nov
25
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
By "improvement", I assumed that the question was "if we impose more conditions, do we get a better result?" i.e. that the matrices were still Hermitian. Then my dumb trick says "no, we don't". As to the second comment: any orthonormal basis will work, giving you the same permutahedron.
Nov
25
comment Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?
For the first one, can't you just add a multiple of the identity to embed the usual problem into the semidefinite one, i.e. they're the same level of difficulty?
Nov
24
awarded  Nice Question
Nov
23
comment Determinant of the oriented adjacency matrix of a tree
I added an example to show a cut vertex in action; darij is right.
Nov
23
revised Determinant of the oriented adjacency matrix of a tree
added 209 characters in body
Nov
23
comment Determinant of the oriented adjacency matrix of a tree
I want to know whether it's $1$ or $-1$.
Nov
23
asked Determinant of the oriented adjacency matrix of a tree
Nov
23
comment Is there an “adjacency matrix” for weighted directed graphs that captures the weights?
It is unfortunate that the "low-temperature" limit, which is very reasonable terminology, is also called the "tropical" limit (outside Japan, where the convention is reversed).