조직위원: 조철현, 조윤형 연사; 오정석(Imperial College London) 일시: 8/21월 ~ 8/23수 ( 매일 14:00 ~ 15:15 Lecture, 15:15 ~ 15:45, Break, 15:45~ 17:00 Lecture) 장소: 서울대학교 (상산수리과학관 129 동 104호) 강연제목: Gromov-Witten invariants and mirror symmetry 초록: Mirror symmetry or its understanding seems to get better even at this moment. But on the other hand it makes it looks too diverse to follow other`s progress. In this talk I would like to introduce one old fashioned understanding in an enumerative geometer`s point of view, following the work of Bumsig Kim. The simplest version of mirror symmetry could be a symmetry of Hodge numbers of a pair of Calabi-Yau 3-folds. It says dimensions of tangent spaces of one`s K\"ahler moduli and the other`s complex moduli are the same. This predicts these two moduli spaces are isomorphic in local neighbourhoods. Over these two neighbourhoods, two different D-modules are naturally defined on each. Then an advanced version of mirror symmetry could be stated with an isomorphism between the two D-modules. These two define differential equations on the spaces of sections. Then mirror symmetry gives a relationship between the solutions, which are known as J and I-functions, respectively. The coefficients are generating functions of genus 0 Gromov-Witten invariants and period integrals, respectively. In the above story, the former is completely understood in terms of genus 0 Gromov-Witten theory. Hence it can be generalised beyond Calabi-Yau 3-folds and genus >0. The latter is hard for enumerative geometers to understand because it is not developed with moduli spaces. But interestingly I-function can be written as a generating function of genus 0 quasimap invariants (Givental and Ciocan-Fontanine--Kim) though it is not fully understood why. The relationship between J and I-functions can be understood as a wall-crossing phenomenon of moduli spaces (Givental, Ciocan-Fontanine--Kim and others). So it seems quasimap theory plays some role in mirror symmetry. Now quasimap theory defines a cohomological field theory for gauged linear sigma model (Favero--Kim). In other words, there is a curve counting theory for certain LG models, which can hopefully be connected to other progress in mirror symmetry.