Views 1402 Votes 0 Comment 0
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
Extra Form
일정시작 2023-08-21
일정종료 2023-08-23
배경색상 #7164D0

QSMS SUMMER SCHOOL 2023

 

DATE: 8/21 Mon  ~  8/23 Wed (3 days, 2 Lectures/day) 총 6강

PLACE:  129-104(Seoul National University)

SPEAKER; 오정석 (Imperial College London) 

TITLE:  Gromov-Witten invariants and mirror symmetry

ABSTRACT:  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.


REGISTRATION:  Link 


 


List of Articles
No. Subject Author Date Views
36 QSMS 2024 Summer School on Representation Theory file qsms 2024.03.22 1274
35 School on Lie theoretical methods in symplectic geometry and mirror symmetry file qsms 2024.03.22 929
34 2024 Algebra Camp file qsms 2024.01.05 1671
33 Workshop on torus actions on symplectic and algebraic geometry qsms 2023.10.06 1252
32 East Asian Symplectic Conference 2023 file qsms 2023.09.04 1801
» [Symplectic Geometry] QSMS SUMMER SCHOOL 2023 qsms 2023.07.17 1402
30 The 3rd International Undergraduate Mathematics Summer School file qsms 2023.07.11 1404
29 2023 Summer School on Number Theory file qsms 2023.07.11 1505
28 QSMS 2023 Summer Workshop on Representation theory file qsms 2023.07.11 1385
27 Cluster algebras and related topics in East Asia file qsms 2023.05.15 2004
26 Combinatorics on flag varieties and related topics 2023 file qsms 2023.02.13 1771
25 [Series of lectures 2/21, 2/23, 2/28] An introduction to geometric representation theory and 3d mirror symmetry qsms 2023.02.02 1212
24 QSMS Workshop on symplectic geometry and related topics (2023 Winter) file qsms 2023.01.06 1649
23 QSMS 2023 Winter workshop on number theory and representation theory file qsms 2023.01.06 1569
22 서울대학교 수리과학부 Rookies Workshop 2022 file qsms 2022.10.30 1474
21 2022 Summer School on Number Theory file qsms 2022.07.21 1651
20 QSMS 2022 summer workshop on representation theory file qsms 2022.07.04 1938
19 Mini-workshop on deformed W-algebras and q-characters II qsms 2022.06.03 1589
18 Mini-workshop on deformed W-algebras and q-characters I qsms 2022.05.15 1661
17 SYMPLECTIC GEOMETRY AND BEYOND (PART I) file qsms 2022.01.27 1752
Board Pagination Prev 1 2 Next
/ 2