2023.07.17 14:07

# [Symplectic Geometry] QSMS SUMMER SCHOOL 2023

조회 수 2800 추천 수 0 댓글 0
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

#### 단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
일정시작 2023-08-21 2023-08-23 #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.

 제목+내용제목내용댓글이름닉네임아이디태그
1. ### [QSMS 2022 Winter School] Workshop on Representation Theory

Date2022.01.07 Byqsms Views3517
2. ### [Series of lectures 2/21, 2/23, 2/28] An introduction to geometric representation theory and 3d mirror symmetry

Date2023.02.02 Byqsms Views2708
3. ### [Symplectic Geometry] QSMS SUMMER SCHOOL 2023

Date2023.07.17 Byqsms Views2800
4. ### [집중강연 2021.02.01~05] Auslander-Reiten translation and $\tau$-tilting theory

Date2020.11.18 Byqsms Views5024
5. ### 2021 Winter School on Number Theory

Date2021.12.13 Byqsms Views3217
6. ### 2022 Summer School on Number Theory

Date2022.07.21 Byqsms Views3189
7. ### 2023 Summer School on Number Theory

Date2023.07.11 Byqsms Views2915
8. ### 2024 Algebra Camp

Date2024.01.05 Byqsms Views3249
9. ### Cluster algebras and related topics

Date2021.05.07 Byqsms Views4544
10. ### Cluster algebras and related topics in East Asia

Date2023.05.15 Byqsms Views3493
11. ### Combinatorics on flag varieties and related topics 2023

Date2023.02.13 Byqsms Views3322
12. ### CONFERENCE ON ALGEBRAIC REPRESENTATION THEORY 2021

Date2021.10.04 Byqsms Views3272
13. ### East Asian Symplectic Conference 2023

Date2023.09.04 Byqsms Views3316
14. ### Mini-workshop on deformed W-algebras and q-characters I

Date2022.05.15 Byqsms Views3182
15. ### Mini-workshop on deformed W-algebras and q-characters II

Date2022.06.03 Byqsms Views3036
16. ### One Day Workshop on the Arithmetic Theory of Quadratic Forms

Date2021.10.05 Byqsms Views3050
17. ### QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 1)

Date2021.01.13 Byqsms Views16800
18. ### QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 2)

Date2021.01.13 Byqsms Views3672