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Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as cert...
Let X be an arithmetic hyperbolic surface, {\psi} a Hecke-Maass form, and {\gamma} a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of ...
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in t...
We prove $L^q$ bounds on the restriction of spectral clusters to submanifolds in Riemannian manifolds equipped with metrics of $C^{1,\alpha}$ regularity for $0 \leq \alpha \leq 1$. Our results allow f...
We prove a certain unexpected regularity of geodesic restrictions for the (hyperbolic) Casimir operator. We prove a nontrivial bound on L2-norm of a geodesic restriction for eigenfunctions of the Cas...
In this paper, we present two methods, induction and restriction procedures, to construct new stable equivalences of Morita type.
In [4] Tait identifies a set of reflection principles which he calls 􀀀(2)n -reflection principles which Peter Koellner has shown to be consistent relative to an Eros cardinal (!) in [1].
We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group Diff1(S1) of all smooth and orientation-preservi...
A series of aggressive measures was launched by the Chinese government to reduce pollutant emissions from Beijing and surrounding areas during the Olympic Games. Observations at Miyun, a rural site 10...
To represent an optimization problem as a linear programming (LP), there are several assumptions needed. Among them, there is the ”Deterministic” assumption that requires all the coefficients of the L...
Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For ...

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