14,661 reputation
13978
bio website zakuski.math.utsa.edu/~jagy
location Berkeley, California
age 58
visits member for 4 years, 9 months
seen 22 mins ago
My main activity is in number theory of integral positive ternary quadratic forms. This began through years of working with Irving Kaplansky. Much of his unpublished writing on quadratic forms can be found as pdfs at http://zakuski.math.utsa.edu/~kap/forms.html and about Lie and Jordan superalgebras at http://zakuski.math.utsa.edu/~kap/superalgebra.html One of my own email addresses can be found easily using the search feature at http://www.ams.org/cml and just putting in my last name

Oct
16
awarded  Good Answer
Oct
16
comment Isotropy of Apollonian disk-packing
@JosephO'Rourke, surprised that changing a single multiplier to $$ w^2 + x^2 + y^2 + z^2 = wx+wy+wz+xy+xz+yz $$ gives non-negative solution entries, a single root $(0,1,1,1),$ and a loss of the tree property, although still a partially ordered set... math.stackexchange.com/questions/966156/…
Oct
16
comment Isotropy of Apollonian disk-packing
@JosephO'Rourke, twwo articles last year in the Bulletin, ams.org/journals/bull/2013-50-02/home.html one by Kontorovich, one by Fuchs.
Oct
6
awarded  Nice Answer
Oct
6
comment Longest sequence of sum of distinct squares
@RichardStanley, probably because the wording closely resembles the homework questions on MSE; something assigned rather than happened upon.
Oct
5
revised Why do roots of polynomials tend to have absolute value close to 1?
added 43 characters in body
Oct
5
comment Why do roots of polynomials tend to have absolute value close to 1?
@Lucia, thanks, i will edit that in.
Oct
5
comment Why do roots of polynomials tend to have absolute value close to 1?
@AndrejBauer, glad you saw this.
Oct
5
revised Why do roots of polynomials tend to have absolute value close to 1?
added 111 characters in body
Oct
5
answered Why do roots of polynomials tend to have absolute value close to 1?
Oct
4
comment Why do roots of polynomials tend to have absolute value close to 1?
Igor, Eric Kostlan said the late post by Phantom Hoover is what he would have said, later added "Its even easier, if you are willing to be non-rigorous. If you generate random polynomials in any of a number of "natural ways", the middle coefficients tend to grow fast. For example, one model which gives roots equi-distributed on the Riemann sphere gives the i-th coefficient a variance of (n choose i). So forcing all the coefficients to have the same variance is sort of like forcing the middle coefficients to be zero. So roughly speaking, this starts to look like x^n +- 1."
Oct
2
comment Why do roots of polynomials tend to have absolute value close to 1?
Igor, glad you think so. If he does not put anything on MO within a few days, I will forward your opinion.
Oct
2
comment Why do roots of polynomials tend to have absolute value close to 1?
I see Eric's paper with Edelman is a reference for the Transactions article. I wrote to Eric, maybe he will have something to add.
Oct
2
comment Why do roots of polynomials tend to have absolute value close to 1?
Just a name, my classmate Eric Kostlan worked on roots of random polynomials. See if I can find anything specific..
Sep
30
awarded  Explainer
Sep
23
comment Bounds re Asymptotic Formula for the Sum of Largest Prime Factors
I don't see effective estimates; those are rare. The first edition of Handbook of Number Theory by Mitrinovich, Sandor, and Crstici point to a 1993 paper by J. Lin with a more precise estimate than yours, but still has an error term with unspecified constant. You might check the second edition.
Sep
22
revised Constructing sums of squares identities
added 185 characters in body
Sep
22
answered Constructing sums of squares identities
Sep
22
comment What do you call a fixed point theorem for a mapping from a subset of a space to the whole space?
@WłodzimierzHolsztyński, I do not actually know what theorems he has in mind; I am just picturing an open disc in $\mathbb R^2,$ continuous mapping, if you can just translate the thing you do not get any fixpoint; surjectivity would rule that out. Meanwhile, surjectivity is not a feature of Brouwer, Lefschetz theorems, where a space is mapped to itself. Oh, I think it disables @ signs when a notification will be automatic.
Sep
22
comment What do you call a fixed point theorem for a mapping from a subset of a space to the whole space?
@WłodzimierzHolsztyński, alright. That strikes me as a possible name or part of a phrase, a likely feature of many such things, either as a hypothesis or early conclusion on the way to proof.