41 citations · 73 across the 16 of their papers we have counts for
17 papers
Coarse geometry of metric measure spaces
Takayuki Okuda, Takashi Shioya
Using ideas from optimal transport theory, we introduce a notion of measured coarse equivalence for metric measure spaces and define a corresponding variant of the uniformly finite…
A proof of Kobayashi's properness criterion from a viewpoint of metric geometry
Kento Ogawa, Takayuki Okuda
Let be a locally-compact group and a pair of closed subgroups of . For the cases where is a real linear reductive Lie group, T. Kobayashi [Math. Ann. '89, J. Lie…
Functoriality of Bose-Mesner algebras and profinite association schemes
Makoto Matsumoto, Kento Ogawa, Takayuki Okuda
We show that taking the set of primitive idempotents of commutative association schemes is a functor from the category of commutative association schemes with surjective morphisms…
Quantum circuits for exact unitary -designs and applications to higher-order randomized benchmarking
Yoshifumi Nakata, Da Zhao, Takayuki Okuda +9
A unitary -design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general .…
Explicit construction of exact unitary designs
Eiichi Bannai, Yoshifumi Nakata, Takayuki Okuda +1
The purpose of this paper is to give explicit constructions of unitary -designs in the unitary group for all and . It seems that the explicit constructions were so…
On the spectrum and linear programming bound for hypergraphs
Sebastian M. Cioabă, Jack H. Koolen, Masato Mimura +2
The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigen…
Approximation of integration over finite groups, difference sets and association schemes
Hiroki Kajiura, Makoto Matsumoto, Takayuki Okuda
Let be a finite group and be a function. For a non-empty finite subset , let denote the average of over . Then, is th…
Abundance of nilpotent orbits in real semisimple Lie algebras
Takayuki Okuda
We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements cor…
Relation between spherical designs through a Hopf map
Takayuki Okuda
Cohn--Conway--Elkies--Kumar [Experiment. Math. (2007)] described that one can construct a family of designs on from a design on . In this paper, we pr…
Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action
Takayuki Okuda
In the study of discontinuous groups for non-Riemannian homogeneous spaces, the idea of "continuous analogue" gives a powerful method (T. Kobayashi [Math. Ann. 1989]). For example,…
Tight maps and holomorphicity, exceptional spaces
Oskar Hamlet, Takayuki Okuda
We show that there are no tight nonholomorphic maps from irreducible domains into exceptional codomains, the only exception being the already known tight nonholomorphic maps from t…
Nonexistence of tight spherical design of harmonic index 4
Takayuki Okuda, Wei-Hsuan Yu
We give a new upper bound of the cardinality of a set of equiangular lines in with a fixed angle for each satisfying certain conditions. Our techniques are based…
Smallest complex nilpotent orbits with real points
Takayuki Okuda
Let us fix a complex simple Lie algebra and its non-compact real form. This paper focuses on non-zero adjoint nilpotent orbits in the complex simple Lie algebra meeting the real fo…
Spherical designs of harmonic index t
Eiichi Bannai, Takayuki Okuda, Makoto Tagami
Spherical -design is a finite subset on sphere such that, for any polynomial of degree at most , the average value of the integral on sphere can be replaced by the average va…
Great antipodal sets of complex Grassmannian manifolds as designs with the smallest cardinalities
Hirotake Kurihara, Takayuki Okuda
The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.
Singular fibers in barking families of degenerations of elliptic curves
Takayuki Okuda
Takamura established a theory on splitting families of degenerations of complex curves. He introduced a powerful method for constructing a splitting family, called a barking family…
Classification of semisimple symmetric spaces with proper SL(2,R)-actions
Takayuki Okuda
We give a complete classification of irreducible symmetric spaces for which there exist proper SL(2,R)-actions as isometries, using the criterion for proper actions by T. Kobayashi…