bio  website  

location  Austin, Texas  
age  28  
visits  member for  5 years, 1 month 
seen  9 hours ago  
stats  profile views  2,087 
I am a postdoc at Indiana University. I got my Ph.D. in May 2014 from UT Austin.
14h

comment 
All nonsplit Cartan subroups of $GL_2(\mathbb{Z}/n\mathbb{Z})$ are conjugate
Dear @grghxy, By unmarried, you mean unramified? :) 
Apr 18 
comment 
What's the difference between Euler systems and Kolyvagin systems?
Dear @user70666, Probably arxiv.org/abs/1312.4052 (at least). 
Mar 24 
comment 
Connected components of algebraic groups
If the base field isn't separably closed, it's possible that a nonidentity 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, $\mu_3=\mathrm{Spec}(\mathbf{Q}[X]/(X^31))$ has two components, both single points, and the nonidentity 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 
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How to generalize balanced and absorbing sets to Rmodules?
Don't you want $R$ to be a topological ring? Then it is canonically a uniform space. 
Mar 18 
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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 
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When does $\overline{U(0,1)}=B(0,1)$ hold?
The open unit ball in a nonArchimedean 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 
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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 
Heckemodule structure implicit in definition of automorphic forms in BorelJacquet's Corvallis article
Yes, you should have just gotten it! I didn't realize I had to click the +50 below the checkmark. Congratulations on your first bounty! 
Jul 29 
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Heckemodule structure implicit in definition of automorphic forms in BorelJacquet'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  Heckemodule structure implicit in definition of automorphic forms in BorelJacquet's Corvallis article 
Jul 24 
awarded  Promoter 
Jul 23 
accepted  $C^\infty$vectors in general representations of Lie groups on locally convex spaces 