21,156 reputation
13061
bio website facebook.com/paterz1
location Montreal, Canada
age 23
visits member for 3 years, 5 months
seen 6 hours ago

I finished my undergraduate studies in mathematics at University of Montreal. I am doing my Ph.D at the Berlin Mathematical School in algebraic geometry. My current interests, besides algebraic geometry, are number theory, analysis, topology, measure theory, representation theory and commutative algebra.


5h
answered Inductive proof of the degree of a polynomial
6h
comment Isotrivial, elliptic and semistable fibrations over $\mathbb P^1(\mathbb C)$
What do you have against the moduli space of curves? :(
1d
comment Compute a multiple integral$\iint_{[0,1]^2} (xy)^{xy} dxdy$
This explains why you need to take a limit : wolframalpha.com/input/?i=Plot[t^t%281%2BLog[t]%29%2C+{t%2C0%2C1}] (okay for some reason the link is not entirely "put in blue"... copy paste it in your URL bar.)
1d
comment Compute a multiple integral$\iint_{[0,1]^2} (xy)^{xy} dxdy$
@GEE20151011 : Next time ask the answerer of the question for that haha :) $e^u = e^{t \ln t} = (e^{\ln t})^t = t^t$ and $du = (\ln t + 1) dt$. So you get the integral $\int_{u(0)}^{u(1)} e^u du = 0$ (because $u(0) = \lim_{t \to 0^+} t \ln t = 0$ and $u(1) = 1 \ln 1 = 0$).
1d
comment Compute a multiple integral$\iint_{[0,1]^2} (xy)^{xy} dxdy$
It is interesting to note that in this case you can switch the order of integration because $t^t 1/s$ is non-negative ; this is Fubini's theorem. +1
2d
answered How to prove this equality about e
2d
revised How to prove this equality about e
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2d
revised Why is the topology of compactly supported smooth function in $\mathbb R^d$ not first countable?
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Oct
19
comment Terminology of “G over H”
Do you know anything about quotient groups? This is what you're looking for.
Oct
19
comment Intuitive Understanding of the First Isomorphism Theorem
You should learn LaTeX, it's very useful in mathematics! For the question, see my answer. Feel free to discuss.
Oct
19
answered Intuitive Understanding of the First Isomorphism Theorem
Oct
19
revised Intuitive Understanding of the First Isomorphism Theorem
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Oct
19
comment Big list of books on counterexamples and other clever observations in different topics
@learning maths : You should avoid using english chat shortcuts such as "u can try" on this website.
Oct
19
answered Find the limit of a sequence $(\frac{z^n}{n!})_{n=1}^{\infty}$
Oct
19
comment Find the limit of a sequence $(\frac{z^n}{n!})_{n=1}^{\infty}$
If you know that the series converges, you have shown that its terms tend to zero, but these statements are not equivalent. So proving that the series converges does imply that the terms tend to zero and is not a wrong way of proceeding.
Oct
19
comment Show that a complex polynomial of degree $n$ doesn't have zeros in a unit ball
If it's of any help, you can suppose without loss of generality that $c_0 = 1$. I realized this by considering the limit case $c_0 = \cdots = c_n = 1$, in which case the roots are $n+1^{\text{th}}$ roots of unity. I am still thinking about the problem though.
Oct
17
comment Spotting mistake: unnecessary given condition
@ChrisJanjigian : Note that I'm not --supposed-- to assume this has anything to do with economics... there is nowhere mentioned "economics" in the question (except in the tag), so I just assume this is a question on partial orders... from my point of view it was super confusing to see this. Anyway, it's okay, I'm cool with it!
Oct
17
comment Spotting mistake: unnecessary given condition
It's okay, if you see a point, keep it there, but my question was legitimate. Anyway. I think if you take a trivial partial order $(X,\le)$ (i.e. the only $y$ related to $x$ is $x$ itself), then you have an example of a non-complete partial order with $D(A) = A \neq \varnothing$ for all $A$, so the statement is definitely wrong.
Oct
17
comment Spotting mistake: unnecessary given condition
I think the correct statement would be : prove that $\le$ is complete if and only if $D(A) \subsetneq A$.
Oct
17
comment Spotting mistake: unnecessary given condition
Yes, but the question itself has nothing to do with it. It's like putting a physics tag on an elliptic curve question, yes there are applications of elliptic curves in physics, but the question is about elliptic curves.