bio | website | |
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location | Austin, Texas | |
age | 28 | |
visits | member for | 5 years |
seen | 9 mins ago | |
stats | profile views | 2,073 |
I am a postdoc at Indiana University. I got my Ph.D. in May 2014 from UT Austin.
Mar 24 |
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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 |
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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 |
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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 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 |
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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 |
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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 |
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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 |
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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 |
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$C^\infty$-vectors in general representations of Lie groups on locally convex spaces
Dear @user56365, Thank you very much! This is great! |
Jul 23 |
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$C^\infty$-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. |