5,349 reputation
1941
bio website math.stanford.edu/~church
location Stanford
age
visits member for 5 years, 2 months
seen yesterday

Dec
11
reviewed Reject $E_n$ structures on Symmetric Monoidal Stable infinity-categories
Nov
19
answered Breaking up the free Lie algebra into Gl irreps
Nov
14
comment Questions about the “universal elliptic curve” over the affine $j$-line punctured at 0 and 1728
What you had was right (if $\text{SL}_2(\mathbb{Z})$ acts only on $\mathcal{H}^\circ$, it won't descend). The problem is there's no ("fine") universal elliptic curve: Let $T$ be the randomly-chosen $T=\mathbb{C}/\langle m+n(1+i)\rangle$. Let $\mathbb{Z}$ act on $T\times \mathbb{R}$ by $(t,x)\mapsto (-t,x+1)$, and set $X=(T\times\mathbb{R})/\mathbb{Z}$. This is an elliptic curve bundle over $S^1$ with every fiber $\simeq T$, but it cannot be pulled back from your $E_2$ (or any family over the $j$-line). [$X$ is nontrivial because e.g. $H_1(X)=\mathbb{Z}\neq \mathbb{Z}^3=H_1(T\times S^1)$.]
Nov
14
comment Questions about the “universal elliptic curve” over the affine $j$-line punctured at 0 and 1728
It looks to me like $E_2$ is a $\mathbb{P}^1$-bundle over $\text{SL}_2(\mathbb{Z})\backslash \mathcal{H}^\circ$; for $\gamma=-\text{Id}$ you have $\gamma\cdot(z,\tau)=(-z,\tau)$, so the fiber over $\tau\in \text{SL}_2(\mathbb{Z})\backslash \mathcal{H}^\circ$ is $E_\tau/\langle\pm 1\rangle\simeq \mathbb{P}^1$. (This commment may not make sense in the future if the question is revised.)
Nov
9
awarded  Custodian
Nov
9
reviewed Reviewed CD - continuous development
Nov
9
awarded  Custodian
Nov
9
reviewed Approve Questions related to a previous question about interpolation based on non-decreasing polynomials
Oct
12
awarded  Yearling
Aug
30
comment Corvallis 1979 proceedings
The AMS pages for these books are now ams.org/books/pspum/033.1 and ams.org/books/pspum/033.2; however they no longer seem to be freely available.
Jun
26
reviewed Reject nontrivial theorems with trivial proofs
Jun
17
reviewed Reject nontrivial theorems with trivial proofs
Jun
15
revised $G_\mathbb{Z}$-homotopy type of rational Tits building $\Delta_{G, \mathbb{Q}}$
clarify result for orbits of chains, add remark on PID
Jun
15
revised $G_\mathbb{Z}$-homotopy type of rational Tits building $\Delta_{G, \mathbb{Q}}$
correct ell = |K_0| to ell = |K_0| - 1
Jun
15
answered $G_\mathbb{Z}$-homotopy type of rational Tits building $\Delta_{G, \mathbb{Q}}$
Jun
8
comment Integral of sin(x)/sqrt(x) from 0 to \pi
@NoamD.Elkies I agree that the downvotes may have been hasty; I didn't downvote, but I easily could have. However questions like this about evaluating definite integrals seem to be more at home at math.SE (even quite difficult integrals, which often receive extremely impressive answers there!). So the best outcome may be for this question to be moved to math.SE.
Jun
4
awarded  Custodian
Jun
4
reviewed Reject nontrivial theorems with trivial proofs
Jun
4
reviewed Reject nontrivial theorems with trivial proofs
May
14
comment Some question about polynomial representations of $GL(V)$
This is just about the difference between "rational" and "polynomial". Let's consider $\text{GL}(1)$. The irreducible rational representations of $\text{GL}(1)=\mathbb{C}^\times$ (or $\mathbb{G}_m$) are indexed by integers $k\in \mathbb{Z}$, with $k\in \mathbb{Z}$ corresponding to the 1-dimensional representation on which $z\in \mathbb{C}^\times$ acts by $z^k$. This is a rational function of $z$, matching the terminology. But $z^k$ is only a polynomial when $k\geq 0$, so the irreducible polynomial representations are indexed by $k\geq 0\in \mathbb{Z}$.