bio  website  math.berkeley.edu/~ianagol 

location  Berkeley  
age  44  
visits  member for  4 years, 9 months 
seen  13 hours ago  
stats  profile views  11,064 
I'm a professor at UC Berkeley working predominantly in the field of lowdimensional topology.
2d

comment 
BorelSerre compactification of $\mathbb{H}^3 / SL_2(\mathcal{O}_K)$
There's a minor correction: for $K=\mathbb{Q}[\sqrt{1}], \mathbb{Q}[\sqrt{3}]$, the cusp is actually an orbifold quotient of the elliptic curve by the group of units. 
Jul 22 
comment 
Are there infinitely many commensurable classes of finitecovolume hyperbolic Coxeter groups?
@HaoCHEN: I see, yes, this is similar to the technique of GromovPiatetskiiShapiro I was alluding to. I wasn't aware of these examples (even though I downloaded a copy of Vinberg's paper :). 
Jul 22 
comment 
Fake versus Exotic
The formula near the end of the paper looks reminiscent of a formula for geodesic torsion (but missing a $\cos(\phi_i)$ factor). Since the geodesic torsion of a curve of intersection of surfaces intersecting at constant angle is the same, I think this reproves your formula (maybe with a $\cos(\phi_i)$ factor or using $\sin(2\phi_i)$ instead)? encyclopediaofmath.org/index.php/Geodesic_torsion 
Jul 22 
awarded  Enlightened 
Jul 22 
awarded  Nice Answer 
Jul 20 
comment 
A question on involutions on the Lie algebra of vector fields
On odd dimensional spheres, the antipodal map works. 
Jul 20 
comment 
A question on involutions on the Lie algebra of vector fields
What do you have in mind for the Killing form for the space of vector fields? 
Jul 18 
answered  Orbit spaces of crystallographic groups 
Jul 17 
comment 
Is $\mathbb{H}^n$ quasiisometric to a leaf of a codimension 1 foliation of a compact manifold?
The question of embedding RAAGs in $Diff(\mathbb{R})$ is now resolved: front.math.ucdavis.edu/1404.5559 However, I don't believe that the embedding they obtain admits a free orbit in general, so this leaves the answer to the question in the smooth category still open. 
Jul 16 
comment 
Why do noncocompact arithmetic Kleinian groups have quadratic trace fields?
Incidentally, I think it would be a good topic to study quaternion algebras associated to representations of 3manifolds. In fact, there should be a tautological one defined over the function field of the character variety. 
Jul 15 
answered  Why do noncocompact arithmetic Kleinian groups have quadratic trace fields? 
Jul 15 
answered  Origin of number theoretic invariants associated to hyperbolic 3manifolds 
Jul 15 
comment 
Origin of number theoretic invariants associated to hyperbolic 3manifolds
The original extension of these invariants to 3manifolds was by Neumann and Reid: math.columbia.edu/~neumann/preprints/nrarith.pdf 
Jul 11 
awarded  Enlightened 
Jul 10 
awarded  Nice Answer 
Jul 10 
comment 
Ellipses on spheres (and other surfaces)
Yes, it works on any surface (my original answer was only for the sphere) assuming there are not conjugate points on E. 
Jul 10 
revised 
Ellipses on spheres (and other surfaces)
added 23 characters in body 
Jul 10 
answered  Ellipses on spheres (and other surfaces) 
Jul 5 
answered  Mathematicians who made important contributions outside their own field? 
Jul 2 
awarded  Curious 