13,670 reputation
12047
bio website warwick.ac.uk/alexbartel
location University of Warwick, UK
age 31
visits member for 3 years, 10 months
seen Sep 12 at 19:08

I am currently a Zeeman Lecturer at Warwick University. My research interests lie in algebraic number theory and representation theory, more specifically integral Galois module structures, the arithmetic of elliptic curves, and (integral and rational) representation theory of finite groups.


Sep
2
answered Sum of degrees of irreducible complex characters for certain groups
Sep
2
comment What are major algebraic number theory attempts, results and progressions toward Goldbach's Conjecture?
See this MO question: mathoverflow.net/questions/43434/…
Jul
25
awarded  Enlightened
Jul
25
awarded  Nice Answer
Jul
4
comment Cosets/ Cyclic group
Can you name any coset at all? Can you then find an element of $G$ not in that coset?
Jul
3
comment What kind of algebraic structure is this
Consider the orbit of the unit element under scalar multiplication. That will give you a copy of the scalar field inside the field (use the fact that a field has no non-zero proper ideals). In your example, the subfield consists of scalar matrices. Conversely, whenever you have a field with a subfield, the big field is clearly an algebra under the subfield, just using multiplication in the big field.
Jul
3
comment What kind of algebraic structure is this
It's just a field with a subfield.
May
15
comment Is Writing a Semi Group?
From Wikipedia: "Monoids are studied in semigroup theory as they are semigroups with identity".
May
15
revised Prove this simple arithmetic relation
Fixed tagging
May
12
comment Showing $U$ open in topological group $G$ $\implies$ $gU$ is open
All you need to do is unwrap the definitions. What does "continuous" mean? What is the topology on $G^2$? If you cannot do this, you had better ask more elementary questions about the concepts that you are having difficulty with.
May
12
answered Nilpotent groups are monomial
Apr
30
comment nonsemisimple $k$-algebra
@QiaochuYuan: Nice!
Apr
30
answered nonsemisimple $k$-algebra
Apr
22
revised Dihedralize Twice - dihedralize a dihedral group $D_n$
retagged
Apr
22
comment Dihedralize Twice - dihedralize a dihedral group $D_n$
As the link already says, $g\mapsto g^{-1}$ is only an automorphism if $G$ is abelian. So you have not defined "dihedralise" in the context in which you are using it. And I agree with Derek that the question has got nothing to do with representation theory, so I retagged it.
Apr
17
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
@Alyosha You need to be fairly comfortable with $p$-adic numbers, and to know some basic measure theory. That would be enough to give it a go, and fill in the gaps as you progress. It doesn't require that much high-flying theory, the main difficulty for novices is that it takes a completely new point of view, compared to the classical one. Note that Tate also proves the analytic class number formula in the same big sweep, so it would help if you knew the statement of that.
Apr
4
revised The way conjugation acts on embeddings
added 40 characters in body
Apr
4
comment Integer solutions of $x^4 + 16x^2y^2 + y^4 = z^2$
So do I!$ $ $ $
Apr
4
answered The way conjugation acts on embeddings
Apr
2
comment Class number of $\Bbb Q(a)$ with $a^3-a+1 = 0$ is $1$
Clearly, an integer polynomial $f(x)$ in one variable cannot be irreducible modulo all primes: plug in any $\alpha$ for which $f(\alpha)\neq \pm 1$ and take any prime divisor $p$ of $f(\alpha)$. Then $f(\alpha)\equiv 0\pmod{p}$, so $(x-\alpha)$ is a factor of $\bar{f}$ modulo $p$.