Enumerative Geometry And String Theory

Perhapsthemostfamousexampleofhowideasfrommodernphysicshaverevolutionizedmathematicsisthewaystringtheoryhasledtoanoverhaulofenumerativegeometry,anareaofmathematicsthatstartedintheeighteenhundreds.Century-oldproblemsofenumeratinggeometricconfigurationshavenowbeensolvedusingnewanddeepmathematicaltechniquesinspiredbyphysics!Thebookbeginswithaninsightfulintroductiontoenumerativegeometry.Fromthere,thegoalbecomesexplainingthemoreadvancedelementsofenumerativealgebraicgeometry.Alongtheway,therearesomecrashcoursesonintermediatetopicswhichareessentialtoolsforthestudentofmodernmathematics,suchascohomologyandothertopicsingeometry.Thephysicscontentassumesnothingbeyondafirstundergraduatecourse.Thefocusisonexplainingtheactionprincipleinphysics,theideaofstringtheory,andhowthesedirectlyleadtoquestionsingeometry.Oncethesetopicsareinplace,theconnectionbetweenphysicsandenumerativegeometryismadewiththeintroductionoftopologicalquantumfieldtheoryandquantumcohomology.