3,955 reputation
820
bio website
location Prague, Czech Republic
age 28
visits member for 3 years, 5 months
seen 25 mins 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).


Feb
13
answered Homogenous Polynomial Functions and the Symbol of a Differential Operator
Feb
13
answered How to prove this result about connectedness?
Feb
13
comment On surjectivity of exponential map for Lie groups
Thank you, nice example.
Feb
12
comment On surjectivity of exponential map for Lie groups
@David: correct me if I am wrong, but the sphere is not a local object, is it? I mean, for every point of the sphere, we can find a ball in $\mathfrak g$ around that point it that still maps to an open set.
Feb
12
revised On surjectivity of exponential map for Lie groups
More detailed proof of exp being closed and open
Feb
12
comment On surjectivity of exponential map for Lie groups
@David: thank you for the first example, I'll think about it. As for the second, I don't follow. Where does the set you've given lie and how is it related to the property of local homeomorphism?
Feb
12
asked On surjectivity of exponential map for Lie groups
Feb
12
comment Universal Covering Group of $SO(1,3)^{\uparrow}$
Thanks, that's a nice argument. The adjoint rep. won't work in general, but finding any isomorphism of Lie algebras will, so I guess that's good enough.
Feb
12
comment Universal Covering Group of $SO(1,3)^{\uparrow}$
I'd say it's purely coincidental and follows from identification of vectors and antisymmetric matrices in dimensions $3$. In any case, could you elaborate how does the adjoint rep. of $su(2)$ help us prove that $SU(2)$ is a universal cover of $SO(3)$?
Feb
11
comment Limit of $\epsilon t-f(t)$
Are you sure this a correct statement of the problem? If a function $\epsilon t - f(t)$ is unbounded on $[0, \infty]$ then your limit is infinite by definition of unbounded.
Feb
11
comment Product of polynomials with negative coefficients
Product with what?
Feb
8
comment Formula for evaluation of character on a transposition
@Alexander: ah, right, thanks. I confused this with characters that are homomorphisms (as opposed to just functions, like here).
Feb
8
comment Formula for evaluation of character on a transposition
So, for $\lambda = \lambda^t$ we get zero on the RHS. That seems strange. Also, what is $\chi(1)$ supposed to mean? My characters use to have $\chi(1) = 1$. Unless I am misunderstanding something trivial, this formula is very weird...
Feb
6
revised Question about a functional equation
Added further discussion upon request
Feb
5
comment Quotient map is closed
@goobie: $W$ intersects $X$ in the boundary. The moving of $W$ is supposed to cover all the new pieces of the boundary that $D$ covers (I am not sure this helps, a picture would be worth thousand words here). Anyway, looking forward to your answer. You're welcome.
Feb
5
comment Quotient map is closed
@goobie: Interior. I thought this was standard notation, but now I am not sure.
Feb
5
answered Quotient map is closed
Feb
5
comment Quotient map is closed
@Arthur: That $q$ is closed is what one wants to prove here, so that's not helpful. Also, projections are quotient maps which are not closed (they are open though).
Feb
5
answered Question about a functional equation
Feb
5
comment Question about a functional equation
But regarding your two ODEs for $A$ and $B$, if you plug $B(t,T) = 0$ into them, you obtain contradictory $\partial_t A = 0$ and $\partial_t A = -1$. Aren't you missing a $\partial_t B$ term in the second one?