Engineering-Research-Activity2015｜SHINSHU UNIV.

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SuzukiLabMycurrentresearchinterestisthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithazerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.AkitoSuzuki,AssociateProfessorResearchInterests:MathematicalPhysics,SpectralAnalysisKeywords:QuantumFieldTheory,DiscreteLaplacianMathematical Physics :Mathematics sheds light on physical phenomenaThestructureofsuchamaterialismathematicallydescribedbyagraphcomposedofasetofverticesandedges.Atomsinthematerialaredescribedbytheverticesandatomicbondsbytheedges.ThentheLaplaceoperatoronthegraphbecomestheHamiltonianofanelectronmovinginthematerial.ThespectrumofthisHamiltoniancorrespondstotheenergyoftheelectron.Thephysicalpropertieslikeelectricalconductivityareanalyzedviaspectralanalysisusingmathematicssuchasfunctionalanalysis,operatortheory,andgraphtheory.Tostudythespectraofelectronsisanimportantsubjectinmathematicalphysics.Mathematics OkamotoLabNonlinear Partial Differential EquationsManyphysical,chemical,andbiologicalphenomenacanbemodeledusingdifferentialequations,whichareinmanycasesnonlinear.But,itisdifficulttofindasolutionoftheCauchyproblem(initialvalueproblem)fornonlinearpartialdifferentialequations(PDEs)becauseofitsnonlinearity.Well-posednessoftheCauchyproblemthereforeisimportantandafirststepofstudyfornonlinearPDEs.Here,well-posednessmeansthattheexistenceofasolution,uniqueness,andcontinuousdependenceofinitialdata.MamoruOkamotoAssistantProfessorHereceiveddoctor'sdegreeofsciencefromKyotoUniversity.Hisresearchinterestisnonlinearpartialdifferentialequations.Ouraimistoobtainlowregularitywell-posednessoftheCauchyproblemfornonlinearpartialdifferentialequations(PDEs),especiallynonlineardispersiveandwaveequations.Ifnonlinearpartshavesymmetry,namelyisinvariantundersometransformations,onecanexpectthattheworstinteractioniscancelledout.ConstructionofatheoryforthesecancellationpropertiesisourgoalandthatwillcontributetheevolutionofawiderangeofnonlinearPDEs.Inordertomoreadvancedresearch,somegraduatedstudentsofourlaboratoryenteragraduateschool.Otherstudentsfindajobincompanies.In a seminar, not only understanding a theory of mathmatics but also good presentation skills are important.Mathematics In the FutureAfter Graduation69

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