3,955 reputation
820
bio website
location Prague, Czech Republic
age 28
visits member for 3 years, 5 months
seen 9 hours ago

I study Mathematics at the Charles University in Prague and have a degree in Theoretical Physics from the same school. I am quite fluent in Computer Science and several programming languages as well.

I work on topological aspects of analysis (or perhaps analytical aspects of topology?) such as K-theory, index theory and whatnot. But I also enjoy studying differential topology, groups, number theory and basically anything else I come across. And the more I learn the more I believe in the old cliche that "There is only one mathematics".

People I enjoy reading/watching the most: Serre, Atiyah, Milnor, Bott, A[a-z] (still looking for this guy).


Mar
13
revised intersection form of $CP^2$
Added a concrete explanation
Mar
13
answered intersection form of $CP^2$
Mar
13
answered Summation using residues
Mar
12
comment Summation using residues
@joriki: if I understand the situation correctly, the standard residue method doesn't help with this problem. Is that a satisfactory answer? I was hoping someone would come up with a method that actually works and solve the problem.
Mar
8
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
@Dylan: many arguments involving $\pi$ are circular :) [couldn't resist bad pun, sorry..]
Feb
27
comment staircase functions with compact support are dense in $L^1(\mathbb{R}^n)$
You can use essentially the same argument, just cover the support by small hypercubes.
Feb
27
comment condition for roots of quartic equation to be purely imaginary
When the roots are purely imaginary then $a_1$ is also purely imaginary and so cannot be "real constant different from zero". Something's wrong here...
Feb
27
comment staircase functions with compact support are dense in $L^1(\mathbb{R}^n)$
I just realized that your question perhaps isn't about $L^1(\mathbb R)$ but general $L^1$ spaces. Nevertheless, one can use the compactness in much the same way to cover the support with finite number of sets on which $f$ is nearly constant.
Feb
27
answered staircase functions with compact support are dense in $L^1(\mathbb{R}^n)$
Feb
18
comment Continuous surjective functions from the unit disk to itself that agree nowhere
Please be more specific. Beyond superficial connection with isomorphisms of the unit disk I don't see any relevance of your answer to the OP.
Feb
15
comment Summation using residues
$\sinh(z)$ has zeros on the imaginary axis. I don't see how you account for them.
Feb
13
answered Limit sequence sets
Feb
13
comment $\sum a_n$ converges $\iff \sum (\sqrt{1+a_n}-1)$ converges
When $a_n$ is small (a necessary condition for the convergence of the sum), $\sqrt{1 + a_n} = 1 + a_n / 2 + O(a_n^2)$. So, up to a sum over $a_n^2$ (which converges), these sums are similar. Your job is to find precise estimates.
Feb
13
answered Issue while applying Master Theorem
Feb
13
comment Issue while applying Master Theorem
@chersanya: again, true. But for the function you've written, you can bound $f(n)$ between $n^2 \log n$ and $3 n^2 \log n$. Both of them are regular, and so you can apply the master theorem. Then you get the master theorem for $f(n)$ by sandwiching between these two results (which are equal).
Feb
13
comment Issue while applying Master Theorem
@chersanya: that's true of course, but the additional terms can't spoil the asymptotic behavior (the regularity only needs to hold for $n$ big enough, not for all $n$). So when $n$ is big enough, it's okay (and this can be made rigorous) to assume that $f(n)$ actually is $C n^2 \log(n)$.
Feb
13
revised How to prove this result about connectedness?
Fixed a letter switch
Feb
13
comment How to prove this result about connectedness?
@Stefan: indeed I switched the letters. Thank you :)
Feb
13
answered Uniform and point wise convergence
Feb
13
comment Issue while applying Master Theorem
Why do you think $f$ is not regular? We have $af(n/b) \leq (5/9) f(n)$.