2023.07.17 14:07

# [Symplectic Geometry] QSMS SUMMER SCHOOL 2023

Views 3234 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
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.

 Subject+ContentSubjectContentCommentUser NameNick NameUser IDTag
1. [QSMS 2022 Winter School] Workshop on Representation Theory

2. No Image 02Feb
by qsms
2023/02/02 by qsms
Views 3118

[Series of lectures 2/21, 2/23, 2/28] An introduction to geometric representation theory and 3d mirror symmetry

3. No Image 17Jul
by qsms
2023/07/17 by qsms
Views 3234

[Symplectic Geometry] QSMS SUMMER SCHOOL 2023

4. No Image 18Nov
by qsms
2020/11/18 by qsms
Views 5501

[집중강연 2021.02.01~05] Auslander-Reiten translation and $\tau$-tilting theory

5. No Image 13Dec
by qsms
2021/12/13 by qsms
Views 3693

2021 Winter School on Number Theory

6. 2022 Summer School on Number Theory

7. 2023 Summer School on Number Theory

8. 2024 Algebra Camp

9. No Image 20Aug
by qsms
2024/08/20 by qsms
Views 40

2024 Summer School on Number Theory

10. No Image 07May
by qsms
2021/05/07 by qsms
Views 4972

Cluster algebras and related topics

11. Cluster algebras and related topics in East Asia

12. Combinatorics on flag varieties and related topics 2023

13. No Image 04Oct
by qsms
2021/10/04 by qsms
Views 3712

CONFERENCE ON ALGEBRAIC REPRESENTATION THEORY 2021

14. East Asian Symplectic Conference 2023

15. No Image 15May
by qsms
2022/05/15 by qsms
Views 3604

Mini-workshop on deformed W-algebras and q-characters I

16. No Image 03Jun
by qsms
2022/06/03 by qsms
Views 3446

Mini-workshop on deformed W-algebras and q-characters II

17. No Image 05Oct
by qsms
2021/10/05 by qsms
Views 3484

One Day Workshop on the Arithmetic Theory of Quadratic Forms

18. No Image 13Jan
by qsms
2021/01/13 by qsms
Views 17256

QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 1)

19. No Image 13Jan
by qsms
2021/01/13 by qsms
Views 4104

QSMS 20/21 Winter mini-school on Mirror symmetry and related topics (Part 2)

20. No Image 13Jan
by qsms
2021/01/13 by qsms
Views 4006

QSMS 20/21 Winter School on Representation Theory

Board Pagination Prev 1 2 Next
/ 2