References of "Mathematische Annalen"
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See detailInterrogating surface length spectra and quantifying isospectrality
Parlier, Hugo UL

in MATHEMATISCHE ANNALEN (2018), 370(3-4), 1759-1787

This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to the ... [more ▼]

This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to the following: how many questions do you need to ask a length spectrum to determine it completely? In answering this, a quantitative upper bound is given on the number of isospectral but non-isometric surfaces of a given genus. [less ▲]

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See detailTrace decategorification of categorified quantum sl2
Beliakova, Anna; Habiro, Kazuo; Lauda, Aaron D. et al

in Mathematische Annalen (2017), 367(1), 397440

The trace or the 0th Hochschild–Mitchell homology of a linear category C may be regarded as a kind of decategorification of C. We compute the traces of the two versions U˙ and U∗ of categorified quantum ... [more ▼]

The trace or the 0th Hochschild–Mitchell homology of a linear category C may be regarded as a kind of decategorification of C. We compute the traces of the two versions U˙ and U∗ of categorified quantum sl2 introduced by the third author. The trace of U is isomorphic to the split Grothendieck group K_0(U˙), and the higher Hochschild–Mitchell homology of U˙ is zero. The trace of U∗ is isomorphic to the idempotented integral form of the current algebra U(sl2[t]). [less ▲]

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See detailIsometries of Lorentz surfaces and convergence groups
Monclair, Daniel UL

in Mathematische Annalen (2015), 363(1), 101-141

We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of Diff(S ... [more ▼]

We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of Diff(S^1) obtained are semi conjugate to subgroups of finite covers of PSL(2,R) by using convergence groups. Under an assumption on the conformal boundary, we show that we have a conjugacy in Homeo(S^1 ) [less ▲]

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See detailCompatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
Arias De Reyna Dominguez, Sara UL; Dieulefait, L.; Shin, S. W. et al

in Mathematische Annalen (2015), 361(3), 909-925

This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the ... [more ▼]

This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer n and any positive integer d, PSp_n(F_{l^d}) or PGSp_n(F_{l^d}) occurs as a Galois group over the rational numbers for a positive density set of primes l. The result is obtained by showing the existence of a regular, algebraic, self-dual, cuspidal automorphic representation of GL_n(A_Q) with local types chosen so as to obtain a compatible system of Galois representations to which the results from Part II of this series apply. [less ▲]

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See detailRank n swapping algebra for PGLn Fock--Goncharov X moduli space
Sun, Zhe UL

in Mathematische Annalen (2000)

The rank $n$ swapping multifraction algebra is a field of cross ratios up to $(n+1)\times (n+1)$-determinant relations equipped with a Poisson bracket, called the {\em swapping bracket}, defined on the ... [more ▼]

The rank $n$ swapping multifraction algebra is a field of cross ratios up to $(n+1)\times (n+1)$-determinant relations equipped with a Poisson bracket, called the {\em swapping bracket}, defined on the set of ordered pairs of points of a circle using linking numbers. Let $D_k$ be a disk with $k$ points on its boundary. The moduli space $\mathcal{X}_{\operatorname{PGL}_n,D_k}$ is the building block of the Fock--Goncharov $\mathcal{X}$ moduli space for any general surface. Given any ideal triangulation of $D_k$, we find an injective Poisson algebra homomorphism from the rank $n$ Fock--Goncharov algebra for $\mathcal{X}_{\operatorname{PGL}_n,D_k}$ to the rank $n$ swapping multifraction algebra with respect to the Atiyah--Bott--Goldman Poisson bracket and the swapping bracket. Two such injective Poisson algebra homomorphisms related to two ideal triangulations $\mathcal{T}$ and $\mathcal{T}'$ are compatible with each other under the flips. [less ▲]

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