Engineering Core Engineering Core Engineering Core Engineering Core Inourlaboratory,westudyatheoryofnonlinearpartialdifferentialequations.Especially,wedealwithamathematicalanalysisofpartialdifferentialequationsthatappearinnonlinearwavetheoryandrelatedproblems.Inparticular,weareinterestedinhowthewaveshapechangesovertime,andweanalyzelargetimebehaviorofsolutions.Themathematicalstudyofpartialdifferentialequationsprovidesusaunifiedunderstandingthatgoesbeyondtheframeworkofindividualphenomena.Mycurrentresearchinterestfocusesonthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithzerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.Partialdifferentialequationshaveappearedinvariousfieldsofphysicsandengineeringsuchasfluidmechanicsandnonlinearwavestheoryasamathematicalmodelfordescribingnaturalphenomena,andtheirapplicationrangeisverywide.Throughmathematicalresearchonpartialdifferentialequations,wecangainnewinsightsthatcannotbeobtainedfromexperiments.OuraimofthislaboratoryistodevelopstudentswhocanplayanactiveroleinavariousfieldsInaddition,byapplyingmathematicalwealsostudyawiderangeofperipheralfieldsanddevelopabird's-eyeviewabilitytolookatengineeringfromvariousperspectives.suchamaterialThestructureofismathematicallydescribedbyagraphthatiscomposedofthesetofverticesandedges.Atomsinthematerialaredescribedbytheverticesandatomicbondsbytheedges.ThentheLaplaceoperatoronthegraphbecomestheHamiltonianofanelectronmovinginthematerial.ThespectrumofthisHamiltoniancorrespondstotheenergyoftheelectron.Thephysicalpropertieslikeelectricalconductivityareanalyzedbymathematicssuchasfunctionalanalysis,operatortheoryandgraphtheory.Tostudythespectraofelectronsisanimportantprobleminmathematicalphysics.viaspectralthinking.analysisRecentlypublishedacademicpapers.Thisresearchwashighlyevaluatedbymanyresearchersataninternationalresearchconference.Thisisamathematicsseminar.IgavearesearchpresentationinEnglishwhenIstayedatZhejiangUniversityinChina.AkitoSuzukiAssociateProfessorResearchInterests:MathematicalPhysics,SpectralAnalysisKeywords:QuantumFieldTheory,DiscreteLaplacianIkkiFukudaAssistantProfessorDoctor of Science (Hokkaido University, March, 2020)Research Field:Nonlinear Partial Differential Equations In the FutureAfter GraduationMathematical Physics : Mathematics sheds light on physical phenomenaTheory of Nonlinear Partial Differential Equations
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