This research results report meeting is held to exchange research results
of this year and confirm (and propose) the future research plan of Division
of Joint Research of Geometry and Narural Science.
2025
Research Results Report Meeting 2025
Date： December 20, 2025
Place：Tokyo University of Science, Kagurazaka Campus, 242 room, 4-th floor,
Building No.2
Speaker:
・Katsuhiko Suzuki
(Department of Physics, Faculty of Science Division I, Tokyo University
of Science)
・Masayuki Sakurai
(Research Institute for Biomedical Sciences, Tokyo University of Science)
・Kazutoshi Inoue
(Advanced Institute for Materials Research, Tohoku University)
・Toru Kajigaya
(Department of Mathematics, Faculty of Science Division I, Tokyo University
of
Science)
・Naoyuki Koike
(Department of Mathematics, Faculty of Science Division I, Tokyo University
of
Science)
Title and Abstract:
・Katsuhiko Suzuki
Title: Quantum-Walk description of quantum eff ects on the classical
motion
of Dirac particles
Abstract:
It is known that the Dirac equation for the relativistic quantum mechanics,
can be described by aquantum walk on a discretized spacetime lattice.
In this study, we reproduce the Dirac equationsvia quantum walks by
incorporating
the effects of a U(1) gauge field and curved spacetime into thecoin
operator on
a discretized 1+1-dimensional spacetime. Using these formulations,
we evaluated
quantum effects on classical motion in the curved spacetime.
・Masayuki Sakurai
Title: Geometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing
Enzymes
Abstract:
RNA molecules that function in the intermediate steps of the central dogma
adopt diverse secondary structures, and their modes of folding and twisting
modulate how genetic information is interpreted. Among various RNA
modifications, A-to-I RNA editing is a reaction in which the enzyme ADAR
binds
double-stranded RNA (dsRNA) and deaminates adenosine (A) to inosine (I),
thereby influencing codon readout, splicing regulation, and self-RNA
discrimination. However, numerous sites exhibit context-dependent editing,
even
when the underlying sequence is identical, suggesting intrinsic limitations in
sequence-based descriptions alone.
The aim of this study is to reinterpret A-to-I editing not only through sequence
features but also through the shape of local RNA structures, captured
in
geometric and topological terms. Specifically, dsRNA structures in the
vicinity of
experimentally edited sites are represented using a small set of measurable
descriptors?such as lengths, angles, distances, branching patterns,
and
crossings?to identify structural features associated with editing efficiency
and
specificity. In parallel, structural information from ADAR?RNA complexes is used
to extract three-dimensional constraints including base-flipping geometry,
enzyme approach direction, and accessibility from major or minor grooves,
which
are essential for formulating practical design rules for guide RNAs or guide
nucleic acids.
In this presentation, I will first provide a brief overview of the biological
background of A-to-I RNA editing and ADAR enzymes. I will then introduce
our
ongoing efforts to assemble structural data around edited sites and to compress
structural “shape” into a small number of interpretable descriptors.
Finally, I will
discuss how collaboration with geometry and topology can enable new
mathematical descriptions and design strategies for understanding and
engineering RNA editing.
・Kazutoshi Inoue
Title: Lattice Defects Described by Difference Discrete Geometry
Abstract:
Deformations of continua have long been formulated through dif erential geometry,
where dislocations are characterized by curvature and torsion. In
parallel, differe-
nce discrete geometry on lattices has been developed as a discrete
counterpart of
differential geometry. In this talk, we discuss an approach to representing one-dim-
ensional lattice defects, namely dislocations, within the framework
of difference
discrete geometry.
・Toru Kajigaya
Title: Geometry of discrete harmonic maps
Abstract:
A piecewise smooth map from a fi nite graph to a Riemannian manifold
is called
a discrete harmonicmap when it is a critical point of the discrete
Dirichlet energy.
This notion is a natural extension ofgeodesics, but the geometry it
captures is
richer than that of geodesics. Many properties of harmonic maps between
smooth
manifolds extend to the graph setting, while atthe same time various phenomena
and issues specifi c to the discrete setting also appear.
In this talk, I will introduce what is currently known about discrete
harmonic maps
and what istechnically possible, through several mathematical results.
・Naoyuki Koike
Title: Research progress for 2025 and Proposal for future research
plan
Abstract:
First we explain the research progress for 2025 in ``Division of Joint
Research of
Geometry and Natural Science''. In more detail, we recall the original
research plan
and state the overview of research process of the following three
researches:
I. Effect of the local geometric structure of RNA to A-to-I editing;
II. The method to control the shape of the grain boundary;
III. The construction of the geometric model of the quantum walks
on
the graphs equipped with weight and color.
Next we propose the future research plan for each research thema in this
division of research.
Program:
9:50ー10:40
Speaker: Naoyuki Koike (Department of Mathematics, Faculty of Science
Division I, Tokyo University of Science)
Title: Research progress for 2025 and Proposal for future research
plan
10:40ー10:50 Q & A
11:00ー11:50
Speaker: Toru Kajigaya (Department of Mathematics, Faculty of Science
Division I, Tokyo University of Science)
Title: Geometry of discrete harmonic maps
11:50ー12:00 Q & A
Lunch
14:00ー14:50
Speaker: Kazutoshi Inoue (Advanced Institute for Materials Research,
Tohoku University)
Title: Lattice Defects Described by Difference Discrete Geometry
14:50ー15:00 Q & A
15:10ー16:00
Speaker: Masayuki Sakurai (Research Institute for Biomedical Sciences,
Tokyo University of Science)
Title:
16:00ー16:10 Q & A
16:20ー17:10
Speaker: Katsuhiko Suzuki (Department of Physics, Faculty of Science
Division I, Tokyo University of Science)
Title: Quantum-Walk description of quantum eff ects on the classical
motion
of Dirac particles
17:10ー17:20 Q & A