Engineering-Research-Activity2016｜SHINSHU UNIV.

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SuzukiLabMycurrentresearchinterestisthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithazerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.AkitoSuzukiAssociate ProfessorResearch Interests:Mathematical Physics, Spectral AnalysisKeywords:Quantum Field Theory,Discrete Laplacian.Mathematical 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.MamoruOkamotoAssistant ProfessorHe received doctor's degree of science from Kyoto University.His research interest is nonlinear partial differential equations.Ouraimistoobtainlowregularitywell-posednessoftheCauchyproblemfornonlinearpartialdifferentialequations(PDEs),especiallynonlineardispersiveandwaveequations.Ifnonlinearpartshavesymmetry,namelyisinvariantundersometransformations,onecanexpectthattheworstinteractioniscancelledout.ConstructionofatheoryforthesecancellationpropertiesisourgoalandthatwillcontributetheevolutionofawiderangeofnonlinearPDEs.Inordertomoreadvancedresearch,somegraduatedstudentsofourlaboratoryenteragraduateschool.Otherstudentsfindajobincompanies.In a seminar, not only understanding a theory of mathmaticsbut also good presentation skills are important.Mathematics In the FutureAfter Graduation68

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