# All Questions

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### How to compute modular forms of weight one on Shimura curves?

Classical modular forms of weight $k\geq 1$ can be computed explicitly by exhibiting their $q$-expansion. When the weight is at least two, the most standard method uses modular symbols. When the ...
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### How do sutured TQFT fit into the larger TQFT picture?

In https://arxiv.org/abs/0807.2431, Honda--Kazez--Matic introduce a definition of (1+1 dimensional) sutured TQFT; see also e.g. Mathews http://arxiv.org/abs/1006.5433 and Fink https://arxiv.org/abs/...
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### Why is $R_{\Omega}R_{\Omega}^{*}=R_{\Omega}$ in matrix completion?

In the matrix completion literature, a restriction or sampling operator is defined as follows. Let $X$ be the unknown matrix to be recovered and $\{w_{\alpha}\}_{\alpha=1}^{n^2}$ be some orthonormal ...
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### A (second-order) axiomatic characterization of the integers which rules out surreal/hyperreal versions

I've seen it stated, for example here, that the integers are the unique commutative ordered ring with identity whose positive elements are well-ordered. I understand why the integers are the ...
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### Importance of $E_n$-algebras over ring structures on $\pi_*(E)$

Hopefully this question is not too vague to be closed. I am looking for examples of when a construction/theorem that involves $E$-(co)homology or even simply the ring $E_*$ requires an understanding ...
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### An asymptotic formula involving the $2$-torsion subgroup of the class group of real quadratic fields

Let $R$ be an order in some number field $K$ (not necessarily maximal). Then the class number $\text{Cl}(R)$ is equal to the cardinality of the Picard group of $R$, which is the group of equivalence ...
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### An Example to Marsden-Weinstein Theorem [on hold]

Suppose that the action of a compact Lie group $G$ on the closed symplectic manifold $(M,\omega)$ is Hamiltonian, with moment map $\mu : M\to \mathfrak{g}^*$. From the Hamiltonian condition it ...
Consider univariate polynomials $f(x)=\sum_{i=0}^{r_f}f_ix^i$ and $g(x)=\sum_{i=0}^{r_g}g_ix^i$ in $\Bbb Z[x]$ with only distinct real roots $\alpha_1,\dots,\alpha_{r_f}\in\Bbb R$ and \$\beta_1,\dots,\...