Engineering Core Engineering Core 64Mycurrentresearchinterestfocusesonthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithzerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.Partialdifferentialequationshaveappearedinvariousfieldsofphysicsandengineeringsuchasfluidmechanicsandnonlinearwavestheoryasamathematicalmodelfordescribingnaturalphenomena,andtheirapplicationrangeisverywide.Throughmathematicalanalysisonpartialdifferentialequations,wecangainnewinsightsthatcannotbeobtainedfromexperiments.OuraimofthislaboratoryistodevelopstudentswhocanplayanactiveroleinavariousfieldsbyapplyingmathematicalInaddition,wealsostudyawiderangeofperipheralfieldsanddevelopabird's-eyeviewabilitytolookatengineeringfromvariousperspectives.Thestructureofismathematicallydescribedbyagraphthatiscomposedofthesetofverticesandedges.Atomsinthematerialaredescribedbytheverticesandatomicbondsbytheedges.ThentheLaplaceoperatoronthegraphbecomestheHamiltonianofanelectronmovinginthematerial.ThespectrumofthisHamiltoniancorrespondstotheenergyoftheelectron.Thephysicalpropertieslikeelectricalconductivityareanalyzedbymathematicssuchasfunctionalanalysis,operatortheoryandgraphtheory.Tostudythespectraofelectronsisanimportantprobleminmathematicalphysics.In the FutureAfter Graduationsuchamaterialanalysisviaspectralthinking.Recentlypublishedacademicpaper.Thisstudywashighlyevaluatedbymanymathematiciansataninternationalresearchconference.Thisisamathematicsseminar.IgavearesearchpresentationinEnglishwhenIstayedatZhejiangUniversityinChina.AkitoSuzukiInourLaboratory,westudynonlinearpartialdifferentialequationsfromatheoreticalaspect.Amongthem,wearemainlyengagedinmathematicalanalysisfordifferentialequationsthatappearinnonlinearwavetheoryandrelatedproblems.Inparticular,weareinterestedinhowtheshapeofthewavechangeswithtime,andwedealwiththeanalysisofthelargetimebehaviorofthesolutions.Themathematicalstudyofpartialdifferentialequationsprovidesusaunifiedunderstandingthatgoesbeyondindividualphenomena.IkkiFukudaAssociateProfessorResearchInterests:MathematicalPhysics,SpectralAnalysisKeywords:QuantumFieldTheory,DiscreteLaplacianLecturerDoctor of Science (Hokkaido University, March, 2020)Research Field:Nonlinear Partial Differential Equations Mathematical Physics : Mathematics sheds light on physical phenomenaTheory of Nonlinear Partial Differential Equations
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