YeungNam Seminar on Algebraic Geometry X
(2023 Spring)

Organizers

• 김영락 (부산대학교)

• 주정훈 (부산대학교)

Invited Speakers

• 김호성 (창원대학교)

• 박현준 (KIAS)

Participants

• 김영락 (부산대학교)

• 김호성 (창원대학교)

• 박경동 (경상국립대학교)

• 박현준 (KIAS)

• 이완석 (부경대학교)

• 정기룡 (경북대학교)

• 조민서 (부산대학교)

• 조용화 (IBS-CCG)

• 주정훈 (부산대학교)

• 최영욱 (영남대학교)

• 최진성 (부산대학교)

• 한강진 (DGIST)

• 허석문 (성균관대학교)

• 황동선 (IBS-CCG)

Title & Abstract

• 김호성 (창원대학교)
  Title : Lagrangian fibration structure on cotangent bundle
  
  Abstract : The cotangent bundle of a complex projective manifold carries a natural holomorphic symplectic 2-form. The structure of Lagrangian fibration structure on these non-compact complex manifolds has not been studied very much. In the first talk, I will introduce well-known facts about compact Lagrangian fibrations based on the results of Hwang, Oguiso and Matsushita. In the second talk, I will present some non-compact Lagrangian fibrations defined on cotangent bundles and compare their fibration structure with that of compact Lagrangian fibrations.
  
  

• 박현준 (KIAS)
  Title : Virtual fundamental cycles and shifted symplectic forms
  
  Abstract : Modern enumerative geometry studies invariants defined thorugh the virtual fundamental cycles on moduli spaces. Examples include the Gromov-Witten invariants and Donaldson-Thomas invariants. These virtual enumerative invariants have been studied intensively in the last three decades, and rich structures have been discovered.
  
  Moduli spaces of sheaves on algebraic varieties are fundamental objects that reflect many properties of the given varieties. For instance, there are symplectic structures on the moduli space of sheaves on K3 surfaces. A far-reaching generalization is the existence of shifted symplectic structures on moduli spaces of sheaves on higher-dimensional Calabi-Yau varieties. Here the moduli spaces are not smooth, but the hidden smoothness is the derived structure which allows us to consider shifted differential forms.
  
  In this talk, I will give an introduction to the virtual fundamental cycles and shifted symplectic forms. In particular, I will introduce the Donaldson-Thomas theory of Calabi-Yau 4-folds, which is based on a new type of virtual cycles for (-2)-shifted symplectic derived schemes. 

Past Meetings

• YeungNam Seminar on Algebraic Geometry I (2016년 11월, 영남대)

• YeungNam Seminar on Algebraic Geometry II (2017년 4월, 영남대)

• The 3rd Yeongnam workshop on algebraic geometry (2017년 12월, 포항 IBS-CGP) https://cgp.ibs.re.kr/conferences/the_3rd_yeongnam_workshop_on_algebraic_geometry/

• 4th YeungNam Workshop on Alegebraic Geometry (2018년 11월, DGIST) https://sites.google.com/view/ywag4th/

• YeungNam Seminar on Algebraic Geometry V (2019년 5월, 부경대)

• YeungNam Seminar on Algebraic Geometry VI (2019년 10월, 경북대) https://sites.google.com/site/ynseminarag/

• 영남 대수기하 워크샵 (2021년 10월, 대구) https://sites.google.com/view/21fall-yn-ag-workshop

• 영남대수기하학회 VIII (2022년 5월, 울산대) https://sites.google.com/view/ynseminarag2022

• 영남대수기하학회 IX (2022년 10월, 진주) https://sites.google.com/view/ynseminarag2022autumn