Research results report meeting 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.
2026
DateDecember 12, 2026
PlaceTokyo University of Science, Kagurazaka Campus, 242 room, 4-th floor, Building No.2
Speaker
Shogo Tanimura (Nagoya University) Katsuhiko Suzuki (Tokyo University of Science) Masayuki Sakurai (Tokyo University of Science) Masashi Mizuno (Nihon University) Kazutoshi Inoue (Tohoku University) Naoyuki Koike (Tokyo University of Science) Yuto Nagatsuka (Tokyo University of Science)
Shogo Tanimura
TitleTBAAbstractTBA
Katsuhiko Suzuki
TitleTBAAbstractTBA
Masayuki Sakurai
TitleTBAAbstractTBA
Masashi Mizuno
TitleLong-time behavior of the dissipation function for non-linear
Fokker-Planck equations with spatially inhomogeneous diffusionAbstractGiven a free energy with spatial inhomogeneity, we derive a diffusion equation based on the law of energy dissipation. We call this diffusion equation a nonlinear Fokker-Planck equation, since it is related to stochastic differential equations. We will theoretically and numerically investigate the long-time behavior of the dissipation function, which determines the dissipation rate of the free energy. If time permits, I will explain the reason why we introduce the spatial inhomogeneity. This talk is based on joint work with Kouta Araki (Graduate School of Science and Technology, Nihon University).
Kazutoshi Inoue
TitleTBAAbstractTBA
Naoyuki Koike
TitleResearch progress for 2026 and Proposal for future research planAbstractFirst 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.
Yuto Nagatsuka
TitleTBAAbstractTBA
Program
9:50ー10:20 Q & A 10:20ー10:30
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)TitleResearch progress for 2026 and Proposal for future research plan
10:40ー11:00 Q & A 11:00ー11:10
SpeakerYuto Nagatssuka (Tokyo University of Science, M2)
TitleTBA
11:20ー11:50 Q & A 11:50ー12:10
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
TitleTBA
14:00ー14:30 Q & A 14:30ー14:40
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleTBA
14:50ー15:20 Q & A 15:20ー15:30
SpeakerMasashi Mizuno (Faculty of Science and Technology, Nihon University)
TitleLong-time behavior of the dissipation function for non-linear Fokker-Planck equations with spatially inhomogeneous diffusion
15:40ー16:10 Q & A 16:10ー16:20
SpeakerKatsuhiko Suzuki (Department of Physics, Faculty of Science Division I, Tokyo University of Science)
TitleTBA
16:20ー17:10 Q & A 17:10ー17:20
SpeakerShogo Tanimura (Graduate School of Informatics, Nagoya University)
TitleTBA
2025
DateDecember 20, 2025PlaceTokyo University of Science, Kagurazaka Campus, 242 room, 4-th floor, Building No.2Speaker
Katsuhiko Suzuki (Tokyo University of Science) Masayuki Sakurai (Tokyo University of Science) Kazutoshi Inoue (Tohoku University) Toru Kajigaya (Tokyo University of Science) Naoyuki Koike (Tokyo University of Science)
Katsuhiko Suzuki
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particlesAbstractIt 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
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing EnzymesAbstractRNA 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
TitleLattice Defects Described by Difference Discrete GeometryAbstractDeformations 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
TitleGeometry of discrete harmonic mapsAbstractA 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
TitleResearch progress for 2025 and Proposal for future research planAbstractFirst 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
9:40ー10:30 Q & A 10:30ー10:40
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleResearch progress for 2025 and Proposal for future research plan
10:50ー11:40 Q & A 11:40ー11:50
SpeakerToru Kajigaya (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleGeometry of discrete harmonic maps
14:00ー14:50 Q & A 14:50ー15:00
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleLattice Defects Described by Difference Discrete Geometry
15:10ー16:00 Q & A 16:00ー16:10
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing Enzymes
16:20ー17:10 Q & A 17:10ー17:20
SpeakerKatsuhiko Suzuki (Department of Physics, Faculty of Science Division I, Tokyo University of Science)
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particles
Shogo Tanimura
TitleTBA
AbstractTBA
Katsuhiko Suzuki
TitleTBA
AbstractTBA
Masayuki Sakurai
TitleTBA
AbstractTBA
Masashi Mizuno
TitleLong-time behavior of the dissipation function for non-linear
Fokker-Planck equations with spatially inhomogeneous diffusion
AbstractGiven a free energy with spatial inhomogeneity, we derive a diffusion equation based on the law of energy dissipation. We call this diffusion equation a nonlinear Fokker-Planck equation, since it is related to stochastic differential equations. We will theoretically and numerically investigate the long-time behavior of the dissipation function, which determines the dissipation rate of the free energy. If time permits, I will explain the reason why we introduce the spatial inhomogeneity. This talk is based on joint work with Kouta Araki (Graduate School of Science and Technology, Nihon University).
Kazutoshi Inoue
TitleTBA
AbstractTBA
Naoyuki Koike
TitleResearch progress for 2026 and Proposal for future research plan
AbstractFirst 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.
Yuto Nagatsuka
TitleTBA
AbstractTBA
Program
9:50ー10:20 Q & A 10:20ー10:30
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleResearch progress for 2026 and Proposal for future research plan
10:40ー11:00 Q & A 11:00ー11:10
SpeakerYuto Nagatssuka (Tokyo University of Science, M2)
TitleTBA
11:20ー11:50 Q & A 11:50ー12:10
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
TitleTBA
14:00ー14:30 Q & A 14:30ー14:40
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleTBA
14:50ー15:20 Q & A 15:20ー15:30
SpeakerMasashi Mizuno (Faculty of Science and Technology, Nihon University)
TitleLong-time behavior of the dissipation function for non-linear Fokker-Planck equations with spatially inhomogeneous diffusion
15:40ー16:10 Q & A 16:10ー16:20
SpeakerKatsuhiko Suzuki (Department of Physics, Faculty of Science Division I, Tokyo University of Science)
TitleTBA
16:20ー17:10 Q & A 17:10ー17:20
SpeakerShogo Tanimura (Graduate School of Informatics, Nagoya University)
TitleTBA
2025
DateDecember 20, 2025
PlaceTokyo University of Science, Kagurazaka Campus, 242 room, 4-th floor, Building No.2
Speaker
Katsuhiko Suzuki (Tokyo University of Science) Masayuki Sakurai (Tokyo University of Science) Kazutoshi Inoue (Tohoku University) Toru Kajigaya (Tokyo University of Science) Naoyuki Koike (Tokyo University of Science)
Katsuhiko Suzuki
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particlesAbstractIt 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
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing EnzymesAbstractRNA 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
TitleLattice Defects Described by Difference Discrete GeometryAbstractDeformations 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
TitleGeometry of discrete harmonic mapsAbstractA 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
TitleResearch progress for 2025 and Proposal for future research planAbstractFirst 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
9:40ー10:30 Q & A 10:30ー10:40
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleResearch progress for 2025 and Proposal for future research plan
10:50ー11:40 Q & A 11:40ー11:50
SpeakerToru Kajigaya (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleGeometry of discrete harmonic maps
14:00ー14:50 Q & A 14:50ー15:00
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleLattice Defects Described by Difference Discrete Geometry
15:10ー16:00 Q & A 16:00ー16:10
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing Enzymes
16:20ー17:10 Q & A 17:10ー17:20
SpeakerKatsuhiko Suzuki (Department of Physics, Faculty of Science Division I, Tokyo University of Science)
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particles
Katsuhiko Suzuki
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particles
AbstractIt 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
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing Enzymes
AbstractRNA 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
TitleLattice Defects Described by Difference Discrete Geometry
AbstractDeformations 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
TitleGeometry of discrete harmonic maps
AbstractA 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
TitleResearch progress for 2025 and Proposal for future research plan
AbstractFirst 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
9:40ー10:30 Q & A 10:30ー10:40
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleResearch progress for 2025 and Proposal for future research plan
10:50ー11:40 Q & A 11:40ー11:50
SpeakerToru Kajigaya (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleGeometry of discrete harmonic maps
14:00ー14:50 Q & A 14:50ー15:00
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleLattice Defects Described by Difference Discrete Geometry
15:10ー16:00 Q & A 16:00ー16:10
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
TitleGeometry-guided Interpretation of Nucleic Acids and A-to-I RNA Editing Enzymes
16:20ー17:10 Q & A 17:10ー17:20
SpeakerKatsuhiko Suzuki (Department of Physics, Faculty of Science Division I, Tokyo University of Science)
TitleQuantum-Walk description of quantum eff ects on the classical motion of Dirac particles