28,790 reputation
153133
bio website math.berkeley.edu/~ianagol
location Berkeley
age 44
visits member for 4 years, 9 months
seen 13 hours ago

I'm a professor at UC Berkeley working predominantly in the field of low-dimensional topology.


2d
comment Borel-Serre 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 finite-covolume hyperbolic Coxeter groups?
@HaoCHEN: I see, yes, this is similar to the technique of Gromov-Piatetskii-Shapiro 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 $\mathbb{H}^n$ quasi-isometric 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 3-manifolds. 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 3-manifolds
Jul
15
comment Origin of number theoretic invariants associated to hyperbolic 3-manifolds
The original extension of these invariants to 3-manifolds 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