bio  website  www2.unine.ch/alain.valette 

location  Neuchâtel, Switzerland  
age  56  
visits  member for  4 years, 1 month 
seen  20 hours ago  
stats  profile views  4,903 
1d

comment 
How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?
An easier question, which I think must be answered first, is: what is $\mathbb{Q}\backslash\mathbb{A}$? For answers, see e.g. this paper by A. Robert: retro.seals.ch/… You may also enjoy Weil's Basic number theory. 
May 16 
comment 
Which padic algebraic groups are type I?
Thanks to David for reviving my question of 2 years ago. My reason for asking was a computation (joint with Henrik Petersen) of $L^2$Betti numbers for locally compact groups, valid under a type I assumption; see arxiv.org/pdf/1307.0379.pdf 
May 16 
revised 
Which padic algebraic groups are type I?
corrected spelling 
May 16 
comment 
Which padic algebraic groups are type I?
Thanks David, welcome to MO! 
May 12 
awarded  Nice Answer 
May 3 
comment 
Define “Mathematics Colloquium”?
My advice for colloquium speakers, is to target 1st year graduate students in the audience. 
Apr 27 
comment 
How does one calculate/estimate/guarantee the girth of a nonAbelian Cayley graph?
Probably not, as the word "girth" does not appear in that paper... 
Apr 27 
comment 
How generic are Cayley graphs of nonAbelian groups with logarithmic girth?
@Anirbit: If $G$ is abelian noncyclic, than the girth is at most 4 because $[a,b]=aba^{1}b^{1}=1$ for every $a,b\in G$. If $G$ is metabelian, i.e. solvable of degree 2, then the girth is at most 16 because $[[a,b],[c,d]]=1$ for every $a,b,c,d\in G$. Etc... 
Apr 27 
answered  How does one calculate/estimate/guarantee the girth of a nonAbelian Cayley graph? 
Apr 26 
comment 
How generic are Cayley graphs of nonAbelian groups with logarithmic girth?
@user6818: If $G$ is solvable of solvability degree $n$, then the girth of any Cayley graph is at most $4^n$ (= the length of an $n$iterated commutator in the generators of a free group). So you may forget about solvable groups. 
Apr 26 
comment 
How generic are Cayley graphs of nonAbelian groups with logarithmic girth?
math1.math.huji.ac.il/~alexlub/PAPERS/ramanujan%20graphs/… 
Apr 26 
comment 
How generic are Cayley graphs of nonAbelian groups with logarithmic girth?
@Anirbit: Theorem 3.4 in LPS is exactly the logarithmic girth!!! 
Apr 26 
comment 
How generic are Cayley graphs of nonAbelian groups with logarithmic girth?
@Anirbit: The Ramanujan graphs based on $SL_2(\mathbb{F}_p)$ have logarithmic girth, see the 1988 by A. Lubotzky, R. Phillips and P. Sarnak in Combinatorica. 
Apr 26 
awarded  rt.representationtheory 
Apr 25 
answered  Irreducible representation of $C^*(D_\infty)$, group $C^*$algebra of an infinite dihedral group 
Apr 25 
comment 
Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
The universal representation $(U_t)$ of the real line is not norm continuous (reason: $\U_t1\=2$ for $t\neq 0$). This should discourage you to use the norm topology on $U(\mathcal{H})$ for your problem. 
Apr 21 
comment 
Determining the primitive ideal space of Cstar algebras
The example you consider is very special, as it is the $C^*$algebra of the infinite dihedral group, which is notoriously type I. The spectrum in that case is "an interval with 2+2 endpoints", i.e. the union of two closed intervals identified along their interiors. This wellknown fact can be found e.g. in these notes by I. Putnam: math.uvic.ca/faculty/putnam/t/Math_533_Lecture_Notes.pdf 
Apr 21 
revised 
“Relative cone types” for groups relative to some collection of subgroups
Fixed spelling 
Apr 18 
awarded  Yearling 
Apr 16 
comment 
Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
What are the assumptions on $G$, exactly? And what do you mean by "a/the unitary universe"? Is it the universal representation (so that $G$ is secretly locally compact)? 