2,037 reputation
1824
bio website
location Austin, Texas
age 28
visits member for 5 years
seen 9 mins ago

I am a postdoc at Indiana University. I got my Ph.D. in May 2014 from UT Austin.


Mar
24
comment Connected components of algebraic groups
If the base field isn't separably closed, it's possible that a non-identity connected component might not have a rational point, in which case it can't possibly be given the structure of a group scheme over the base field. For example, $\mu_3=\mathrm{Spec}(\mathbf{Q}[X]/(X^3-1))$ has two components, both single points, and the non-identity one is not a $\mathbf{Q}$-rational point (and incidentally splits into two components over $\mathbf{Q}(\zeta_3)$). But maybe you want your base field to be algebraically closed?
Mar
20
comment How to generalize balanced and absorbing sets to R-modules?
Don't you want $R$ to be a topological ring? Then it is canonically a uniform space.
Mar
18
comment When does $\overline{U(0,1)}=B(0,1)$ hold?
In any metric space whose metric satisfies the strong triangle inequality, open and closed balls are clopen sets.
Mar
17
comment When does $\overline{U(0,1)}=B(0,1)$ hold?
The open unit ball in a non-Archimedean field (such as $\mathbf{C}_p$ or $\mathbf{Q}_p$) is closed in the metric topology. So to say that the closure of the open unit ball equals the closed unit ball (which is the ring of integers $\mathscr{O}_{\mathbf{C}_p}$) is to say that the open ball coincides with the closed ball. But the open ball is the unique maximal ideal of the closed unit ball, so in particular, a proper ideal, and the two can never coincide.
Mar
2
awarded  Yearling
Feb
8
revised $C^\infty$-vectors in general representations of Lie groups on locally convex spaces
added 10 characters in body
Jan
21
comment Abelian varieties as analytic manifolds
The topology on $X(k)$ when regarding it as a locally $k$-analytic manifold is not the Zariski topology induced from $X$. I should have added "separated" to ensure that the topology on the $k$-points $X(k)$ (which is described in great detail in a paper of Brian Conrad which you can find on his website) is Hausdorff. And yes, I'm talking about Serre's book on Lie algebras and Lie groups.
Jan
21
answered Abelian varieties as analytic manifolds
Dec
7
comment What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$-adic field?
Dear @David, Thank you for this answer! It's especially nice for those of us who aren't at MSRI this semester to see all of this fantastic stuff in person.
Sep
24
awarded  Autobiographer
Jul
30
comment Whittaker models for $GL_n$ and Fourier coefficients
Dear @Rex, The first occurrence of $G$ seems inconsistent with the later occurrences of it (where it seems like it is the reductive group $\mathrm{GL}_2$).
Jul
29
awarded  Nice Question
Jul
29
awarded  Benefactor
Jul
29
comment Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article
Yes, you should have just gotten it! I didn't realize I had to click the +50 below the check-mark. Congratulations on your first bounty!
Jul
29
comment Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article
Dear @GH from MO, Thank you so much for working through this with me. It's something that has confused me for a long time, but this is a simple, clear answer. I appreciate it!
Jul
29
accepted Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article
Jul
24
awarded  Promoter
Jul
23
accepted $C^\infty$-vectors in general representations of Lie groups on locally convex spaces
Jul
23
comment $C^\infty$-vectors in general representations of Lie groups on locally convex spaces
Dear @user56365, Thank you very much! This is great!
Jul
23
comment $C^\infty$-vectors in general representations of Lie groups on locally convex spaces
Dear @Qiaochu, Yes, Hahn-Banach holds for locally convex spaces. That's a nice idea for a candidate akin to how one defines vector-valued integrals in some cases. Is it clear that one recovers the usual notion when $V$ is a Banach space? One (possible) defect is that it doesn't (to me anyway) suggest a natural definition of a tangent map at a point.