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Professor, Chiba University
Room 309, Science Building 1
Department of Mathematics and Informatics, Faculty of Science, Chiba University
1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
ohara (at) math.s.chiba-u.ac.jp
Energy of knots.
To produce ''canonical knots'' for each knot type as energy minimizers.
Where is the ``best place'' to locate a street light?
The Riesz energy function (Brylinski beta function) and the residues of manifolds.
Identify finite metric spaces by their magnitude, related quantities, or polynomials.
The configuration space of polygons.
(Nov 2018)
Notice:
I will retire in March 2028.
Research Interests: (see Research)
Geometric knot theory, in particular, Knot energies (Wiki) including Möbius energy (Wiki). Movies of knots evolving themselves to decrease the energy are available on web. Youtube by Rob Scharein (the creator of KnotPlot), by Kazushi Ahara, a site by John Sullivan. One hour presentation file
Möbius Geometry of curves and surfaces (with Remi Langevin), one hour presentation file
Regularization of Riesz potential and energy of submanifolds (with Gil Solanes), residues of manifolds, generalized centers, and application to integral geometry, one hour presentation file
Topology of the spaces of knots (Configuration space of equilateral and equiangular hexagons) and linkages
Magnitude of metric spaces
Papers:
Magnitude function identifies generic finite metric space, to appear in Discrete Analysis, arXiv:2401.00786
Residues of manifolds, J. Geom. Anal. 33, 357 (2023), 1-68, DOI:10.1007/s12220-023-01393-9, arXiv:2012.01713
(with Gil Solanes) Regularized Riesz energies of submanifolds, Math. Nachr. 291 (2018), 1356-1373.
Renormalization of potentials and generalized centers, Adv. Appl. Math. 48 (2012), 365-392, arXiv
(with Remi Langevin) Conformal arc-length as 1/2-dimensional length of the set of osculating circles, Comm. Math. Helv. 85 (2010) 273-312, arXiv
(with R. Langevin) Conformally invariant energies of knots, J. Institut Math. Jussieu 4 (2005), 219-280, arXiv
Family of energy functionals of knots, Topology Appl. 48 (1992), 147-161
Energy of a knot, Topology 30 (1991), 241-247
Preprints:
Book:
Energy of knots and conformal geometry. Series on Knots and Everything Vol. 33, World Scientific, Singapore, 304 pages. ISBN 981-238-316-6, 2003, Errata updated Sept. 2018
Mini-Course:
17-28 Jun 2019, Summer Conference on Topology and its Applications, Biology, Analysis, Geometry, Energies, Links [bagel19] ~ videos:
1 Energies and residues of manifolds and configuration spaces of polygons,
2 Energy of knots and regularization of divergent integrals,
3 Hadamard regularization and regularization via analytic continuation,
4 How to define energies and residues of manifolds (From analysis to geometry)
Talks:
Current projects:
Regularization of Riesz energies (Brylinski's beta functions) of submanifolds, residues, and application to (integral) geometry
Magnitude of finite metric subspace of Euclidean spaces
``Extrinsic Conformal Geometry'' (with Remi Langevin) and 2nd edition of ``Energy of knots and conformal geometry''
Mathematical Reviews Author ID 632389
Scopus id 24318067100
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