423 reputation
27
bio website chalmers.se/math/SV/kontakt/…
location Göteborg, Sweden
age
visits member for 1 year, 8 months
seen 2 days ago
I'm a PhD student at Chalmers University of Technology. I'm interested in combinatorics and discrete probability.

Apr
9
comment Find minimal set of progressions which intersections, unions or negations covers given set
What if you take a set with no 3-term APs? There are known examples when such a set is fairly big.
Apr
9
comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Thanks a lot. So I accept your answer as now I can safely say that without GRH the problem is hard and wide open.
Apr
9
accepted Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Apr
9
comment Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Correct me if I am wrong but it seems that the unconditional version of the Chebotaryov density is just not strong enough to provide the desired bound (and the conditional version does give it), since the power beta goes to 1 as N is large.
Apr
9
asked Uniform bound for the number primes $p$ s.t. a polynomial has a root modulo $p$
Feb
10
comment Number of solutions of linear homogenous Diophantine equation inside a box
Thanks for the nice answer. In fact, it works for all boxes larger than some constant which depend only on $d$ and $c$, which is important since in my case $a_i$ may depend on $N$ but not on the dimension and $c$.
Feb
10
accepted Number of solutions of linear homogenous Diophantine equation inside a box
Feb
10
comment Number of solutions of linear homogenous Diophantine equation inside a box
What do you mean by averaging? since the equation is homogeneous one can of course assume that $a_i$ sum up to $1$.
Feb
8
comment Number of solutions of linear homogenous Diophantine equation inside a box
Thanks, but after a quick look it seems that they always assume the coefficients are at least rational, don't they?
Feb
7
asked Number of solutions of linear homogenous Diophantine equation inside a box
Oct
3
comment Separating pairs of points in R^n
And I suppose $n$ in $\mathbb{R}^n$ is not the same $n$ which is the maximal number of points in an open set of diameter 2?
Sep
12
comment How to efficiently sample uniformly from the set of p-partitions of an n-set?
I would imagine that a Markov chain with rapid mixing might be useful here, though it would give only approximately uniform distribution.
Sep
7
awarded  Enlightened
Sep
7
awarded  Nice Answer
Aug
27
comment A Balog-Szemeredi-Gowers-type question
It indeed looks promising, but all my previous attempts failed at the point where we need to find to subsets $U$ and $W$ of moderate size, such that $U-U/U-U$ and $W-W/W-W$ are disjoint. The regularity lemma says that if only these sets are $\ll B$ then we can find sufficiently many pairs with large intersection of neigborhoods and we are done, but I didn't find a trick how to guarantee disjointness of the quotient sets (or at least that their intersection is small).
Aug
27
comment A Balog-Szemeredi-Gowers-type question
It's a nice adaptation! Unfortunately, in the application I have in mind exactly the opposite case is crucial, i.e. when $|B|$ is small, and so is $B-B/B-B$.
Aug
27
comment A Balog-Szemeredi-Gowers-type question
Brendan, unfortunately one cannot hope for a strict inclusion. Indeed, suppose in the additive case, that $B$ is an AP and $G$ is such that $B._GB$ contains only odd numbers. Then we cannot find $B'$ such that $B'+B' \subset B+_GB$ (it must contain even numbers), but of course BSG gives us $B'$ with comparable sumset size. However, I don't see how to control $|3B'B'-3B'B'|$ in terms of $|B'B'|$ only, since we inevitably have additional elements not in $B._GB$.
Aug
26
awarded  Yearling
Aug
26
comment A Balog-Szemeredi-Gowers-type question
@BrendanMurphy Thanks for suggestions. I tried to approach the problem this way, like TGF Jones does in his thesis arxiv.org/abs/1301.4853v1 (he uses the Bourgain version of BSG), but I don't see how to handle such complex combination of multiplication and addition.
Aug
23
revised A Balog-Szemeredi-Gowers-type question
Better notation used