33,036 reputation
252120
bio website math.princeton.edu/~wsawin
location Princeton, NJ
age 21
visits member for 3 years, 7 months
seen 3 hours ago

I am a graduate student at Princeton studying arithmetic algebraic geometry.


5h
comment When do boring objects exist?
What about the polynomial $x-y$?
6h
comment For what real $t$ is $\{n^t : n \geq 1\}$ linearly independent over $\mathbb{Q}$?
@DouglasZare In fact each relation rules out a countable set, because any linear combinations of $n^t$ is a nonconstant analytic function, so has finitely many zeros in an interval.
8h
awarded  Nice Answer
11h
answered For what real $t$ is $\{n^t : n \geq 1\}$ linearly independent over $\mathbb{Q}$?
12h
comment Is the set $ AA+A $ always at least as large as $ A+A $?
It seems plausible that estimates giving a lower bound for $|A+ \lambda A|$ or $|A+B|$ in terms of $|A+A|$ would be helpful here, but the best one I've found is by Ruzsa calculus, which gives $|AA||A+A| \leq |A+AA|^2$, which is not helpful at all because it is only useful when $|AA| \geq |A+A|$, and then the identity $|AA+A| \geq |AA|$ already solves the problem. Are there better estimates of this type?
12h
comment Will (general points + small number of arbitrary points) impose independent condtions on plane curves?
@Drew I added more details, and I've been thinking about this same question. I think you want to take $m= \chi(O(d))-3n$ so that the $m$ points define a rank $3n$ linear system. I think for a generic rank $3n$ linear system, every $n$ distinct points impose independent conditions, but I don't know how to prove the linear system is generic. Perhaps somehow trying a similar argument on $(\mathbb P^2)^n$ would work, but I don't see how.
12h
revised Will (general points + small number of arbitrary points) impose independent condtions on plane curves?
added 1580 characters in body
16h
answered Will (general points + small number of arbitrary points) impose independent condtions on plane curves?
1d
awarded  Revival
1d
answered Counterexamples to Elkik's theorem in the non-Noetherian case
1d
comment A combinatorial question about orthonormal bases
@DouglasZare For any such function, pullback by $O(n)$ gives another such function. So the space of such functions is a representation of $O(n)$, and because continuous functions decompose into spherical harmonics, this will decompose into different irreducible representations of $O(n)$. So you just have to test the different spherical harmonics.
1d
comment Do those manifolds atrached to L-functions give rise naturally to motives?
Maybe. If you want to define something significant in this field, you should almost certainly try to construct it rather than characterize it. It is very hard to find good constructions of things related to automorphic forms/Galois representations, so characterizations are not so useful unless you know how to construct something satisfying them. It would also clarify what you mean, which is not very clear right now. Note that there is also no tensor product of abstract topological spaces.
1d
comment Do those manifolds atrached to L-functions give rise naturally to motives?
There's no such thing as the tensor product of abstract varieties, which you use in the definition of $X_F$. Your second question doesn't really make sense - each variety has a motive attached to it, but you can't interpret a variety as a motive - and your third question seems like a restatement of one of the Langlands conjectures.
1d
comment Can Shor's Algorithm be modified to run efficiently on a classical computer?
@CraigFeinstein Yes, the classical steps of the computation are permutation matrices, which are not problematic. What I mean by "just the Fourier transform" is that the only thing we do to the sequence $x^a$ mod $n$ is compute it and then apply the Fourier transform. We don't investigate its properties using deep number theory technology.
1d
answered Can Shor's Algorithm be modified to run efficiently on a classical computer?
2d
awarded  Enlightened
2d
awarded  Nice Answer
2d
comment Are curves over imperfect fields defined over a smaller field?
@grghxy Good point! If the function field of $C$ is not $K$-separable, I guess the answer is no. Take $L$ to be the field of $p$th powers of $K$. Then if the function field of $C'$ is spearable, the function field of $C'_K$ will also be separable, and if the function field of $C'$ is not separable, then $C'_K$ will not be reduced.
2d
revised Are curves over imperfect fields defined over a smaller field?
added 86 characters in body
2d
comment Are curves over imperfect fields defined over a smaller field?
@grghxy Maybe the way I wrote my question was a little bit misleading.