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Quantum groups, quantum tori, and the Grothendieck-Springer resolution
We construct an algebra embedding of the quantum group $U_q(\mathfrak{g})$ into the quantum coordinate ring $\mathcal{O}_q[G^{w_0,w_0}/H]$ of the reduced big double Bruhat cell in $G$. This embedding factors through the Heisenbe ... Read More >
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Hyperbolic 3-manifolds admitting no fillable contact structures
In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact str ... Read More >
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A dynamical decomposition of the torus into pseudo-circles
We build an irrational pseudo-rotation of the 2-torus which is semiconjugate to an irrational rotation of the circle in such a way that all the fibres of the semi-conjugacy are pseudo-circles. The proof uses the well-known `fast ... Read More >
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Nearly radial Neumann eigenfunctions on symmetric domains
We study the existence of Neumann eigenfunctions which do not change sign on the boundary of some special domains. We show that eigenfunctions which are strictly positive on the boundary exist on regular polygons with at least 5 ... Read More >
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Affine pavings and the enhanced nilpotent cone
We construct affine pavings of Springer-type fibers over the enhanced nilpotent cone. This resolves a question of Achar-Henderson and implies the existence of perverse parity sheaves on the enhanced nilpotent cone. Read More >
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An Eigenvalue Pinching Theorem for Compact Hypersurfaces in A Sphere
In this article, we prove an eigenvalue pinching theorem for the first eigenvalue of the Laplacian on compact hypersurfaces in a sphere. Let $(M^n,g)$ be a closed, connected and oriented Riemannian manifold isometrically immerse ... Read More >
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Tukia's isomorphism theorem in CAT(-1) spaces
We prove a generalization of Tukia's ('85) isomorphism theorem which states that isomorphisms between geometrically finite groups extend equivariantly to the boundary. Tukia worked in the setting of real hyperbolic spaces of fin ... Read More >
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Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental
Gaussian mixture models are central to classical statistics, widely used in the information sciences, and have a rich mathematical structure. We examine their maximum likelihood estimates through the lens of algebraic statistics ... Read More >
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Steady Prandtl Boundary Layer Expansion of Navier-Stokes Flows over a Rotating D ...
This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier Stokes flows can be decomposed into Euler and Prandtl flows in t ... Read More >
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Complex geodesics, their boundary regularity, and a Hardy--Littlewood-type lemma
We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to $\partial\mathbb{D}$. This example suggests that continuity at the boundary of the complex geodes ... Read More >