927 reputation
917
bio website cs.toronto.edu/~yuvalf
location Princeton, NJ
age 32
visits member for 5 years, 1 month
seen Aug 31 at 21:15

Postdoc in the IAS.


Apr
5
accepted Orthogonal basis for the multilinear polynomials with zero “trace”
Apr
5
awarded  Revival
Apr
5
comment Orthogonal basis for the multilinear polynomials with zero “trace”
Qing Xiang and Rafael Plaza pointed me to this paper.
Apr
5
answered Orthogonal basis for the multilinear polynomials with zero “trace”
Apr
1
comment About expectation norms on graphs
Cross-posted on cs.se: cs.stackexchange.com/questions/40929/….
Mar
8
comment About the small set expansion conjecture
I think cstheory.se would be a better fit for this question. The OP should also reveal their sources – specifically where the statement "one seems to prove" comes from. Meanwhile, let me just comment that a set of measure $\delta$ is what the OP thinks it is.
Feb
5
awarded  Necromancer
Feb
4
comment Orthogonal basis for the multilinear polynomials with zero “trace”
@VladimirDotsenko It's available here: cs.toronto.edu/~yuvalf/WimmerFriedgut.pdf.
Feb
3
comment Orthogonal basis for the multilinear polynomials with zero “trace”
The conjecture is actually known to be true now.
Feb
3
comment Orthogonal basis for the multilinear polynomials with zero “trace”
@VladimirDotsenko They are multilinear in the sense that the square of a variable never appears. It's a summation $\sum$ rather than a product $\prod$. The first few vectors are $x_1-x_2$, $x_1+x_2-2x_3$, $x_1+x_2+x_3-3x_4$, and so on. Looks pretty multilinear to me. Moreover, for given $d$, the basis function is a homogeneous degree $d$ polynomial, so in this example, everything is a (homogeneous) linear polynomial.
Jul
18
awarded  Yearling
Jul
2
awarded  Curious
May
9
comment Orthogonal basis for the multilinear polynomials with zero “trace”
@darij I obtained the basis by taking the double cosets corresponding to $\binom{[n]}{k}$, computing Young's orthogonal representation, summing all rows (or all columns), and normalizing to remove all the square roots. I'm not sure that's the same as what you'd get from Young's natural representation, but I didn't check.
May
8
asked Orthogonal basis for the multilinear polynomials with zero “trace”
Dec
15
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I would say that most of history's greatest researchers restricted themselves to one "field" such as physics, chemistry or biology. They might have contributed to more than one area, however. The same can be said about many great mathematicians. Mathematics is vast enough.
Dec
14
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I'm not worried about the lack of practical use. Not everything has to be measured against being practical. The practical use of novels and poetry is diminishing (unless you're lucky), though literary skills are invaluable in defending criminals; this is no reason to stop aspiring authors.
Dec
13
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
What the kid needs is an appreciation of abstraction. Computing the Jordan forms of 100 matrices isn't going to help with that. S/he needs to see some real mathematics, do some problem solving, develop some toy theories. Even do some calculations on paper. It helps develop intuition.
Dec
13
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I hope the kid is beyond this level...
Dec
13
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
Strongly disagree. Being a successful mathematician is a fulfilling life, and it doesn't prevent one from living life to its fullest.
Oct
30
awarded  Popular Question