Some recent mathematical progress in enumerative geometry on a variety V is presented in the light of string theory, in its formulation as a topological field theory with target space V. Simple physical notions
Student Mathematical Library(共108册),这套丛书还有 《Galois Theory for Beginners》《Frames for Undergraduates》《Introduction to Topology》《Problems in Mathematical Analysis 1》《Classical Mechanics With Calculus of Variations and Optimal Control》等。 喜欢读"Enumerative Geometry And String Theory"的人也...
generality, although it does hold for every application we have of this theory. By general points s 1 , . . . , s k ∈ A 1 , we mean general in the sense of algebraic geometry: there is a non-empty open subset of the scheme A k consisting of points (s 1 , . . . , s k...
C Summary Classical enumerative geometry: examples Modern tools: Gromov-Witten invariants counts of holomorphic maps Insights from string theory: quantum cohomology: refinement of usual cohomology mirror symmetry formulas duality between symplectic/holomorphic structures integrality predictions for GW-...
Throughout its long history, algebraic geometry has been enriched by the influences of invariant theory, abstract algebra, number theory, topology, complex analysis, symplectic geometry, category theory and so on. One of the most recent influences came from string theory circa 1990 when a group ...
Hence, the purpose of these lectures was to provide the participants with a rather informal gateway to some of the applications of String Theory in the realm of the Enumerative Geometry problems. We would like to thank the organizers, especially Prof. Tanush Shaska for giving us an opportunity...
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as...
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as...
We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in symplectic cohomology which are mirror to Landau-Ginzburg potentials. We also treat the higher Maslov index versions of the...