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.
2025
DateDecember 20, 2025
PlaceTokyo University of Science, Kagurazaka Campus, 242 room, 4-th floor, Building No.2
Speaker
Katsuhiko Suzuki
Masayuki Sakurai
Kazutoshi Inoue
Toru Kajigaya
Naoyuki Koike
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
SpeakerNaoyuki Koike (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleResearch progress for 2025 and Proposal for future research plan 10:40ー10:50 Q & A 11:00ー11:50
SpeakerToru Kajigaya (Department of Mathematics, Faculty of Science Division I, Tokyo University of Science)
TitleGeometry of discrete harmonic maps 11:50ー12:00 Q & A Lunch 14:00ー14:50
SpeakerKazutoshi Inoue (Advanced Institute for Materials Research, Tohoku University)
TitleLattice Defects Described by Difference Discrete Geometry 14:50ー15:00 Q & A 15:10ー16:00
SpeakerMasayuki Sakurai (Research Institute for Biomedical Sciences, Tokyo University of Science)
Title16:00ー16:10 Q & A 16:20ー17:10
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 17:10ー17:20 Q & A List of Geometry Seminars RIST Division of Joint Research of Geometry and Natural Science