3,831 reputation
1032
bio website people.virginia.edu/~aa4cr/…
location University of Virginia
age
visits member for 5 years
seen Jul 15 at 17:19

I am a mathematical physicist working on:

• Constructive quantum field theory.

• Rigorous renormalization group methods.

• Mathematical statistical mechanics.

• Combinatorics related to Feynman diagrams and cluster expansions.

• Classical invariant theory, and applications of the classical symbolic method to problems in algebraic geometry and representation theory.


Jul
7
awarded  Yearling
Jun
22
awarded  Necromancer
May
22
comment $\mathcal S'(\mathbb R^d)$ is separable
@Eric: see the reference in my edit, or the book mentioned by Igor.
May
22
reviewed Leave Open $\mathcal S'(\mathbb R^d)$ is separable
May
22
comment $\mathcal S'(\mathbb R^d)$ is separable
@Igor: Reed and Simon is standard among mathematical physicists, but I don't know if it so for the majority of users of the theory of distributions. In any case, Barry Simon did much to emphasize this sequence space connection.
May
22
revised $\mathcal S'(\mathbb R^d)$ is separable
added 525 characters in body
May
22
comment $\mathcal S'(\mathbb R^d)$ is separable
why so many votes to close? One could say this is a "basic question" in the theory of distributions and therefore perhaps more suited for math.stackexchange. But how many textbooks on distributions contain the answers to such basic questions?
May
22
answered $\mathcal S'(\mathbb R^d)$ is separable
May
21
answered Weakly correlated Bernoulli field
May
20
answered What's the relation between spin model for subfactors theory and physics?
May
20
comment cumulant problem
Unfortunately G-C Rota passed taking away with him potential explanations of many mysterious statements like the one in the quote above...Somewhat related is this MO question: mathoverflow.net/questions/107526/…
May
7
comment $S_k(x+y)-S_k(x)-S_k(y)$ where $S_k$ is symmetric polynomial
It's a good start but one has sums $\sum_i x_i^a y_i^b$ say with $a>b$ and one has to peel off the $x_i^{a-b}$ from the $(x_i y_i)^b$ somehow.
May
7
comment $S_k(x+y)-S_k(x)-S_k(y)$ where $S_k$ is symmetric polynomial
$S_k$ for the elementary symmetric functions, what a horrible notation...
May
4
reviewed Leave Open Examples of $C^*$-algebras in Noncommutative Geometry from A. Connes
May
4
reviewed Approve If the quotient of an algebraic space $X$ by a finite group is a scheme, is $X$ a scheme?
Apr
22
comment Squaring random Schwartz distributions
Thanks Martin. I didn't know that your magnum opus contained a generalization of the LV extension theorem...
Apr
21
comment Squaring random Schwartz distributions
@Martin: yes this is also the impression I got. Complete dependence is not preserved under weak convergence of the joint probability distributions. So indeed their paper does not go as far as constructing a map $Sq$. I was wondering if 1) by working harder one could refine their result and construct such a map which would give the same join distribution or 2) there is some no-go theorem which would show that 1) is impossible. A related question is if there is a nonconstructive way of showing some $Sq$ map exists as in the theorem of Lyons and Victoir.
Apr
21
revised Squaring random Schwartz distributions
fixed formula
Apr
15
answered Existence of an invariant measure on an infinite dimensional space via Lyapunov functional
Apr
11
revised Criterion for weak convergence of probability measures on S' or D'
deleted 1 character in body