QSMS 2021 위상 기하 가을 워크숍
- 일시: 10월 7일 목요일 ~ 10월 9일 토요일, 2021년
- 장소: 제주도 오션스위츠 호텔
10월 7일 목요일, 14:00 ~ 15:00 초청발표1 - 배영진 (인천대학교) 15:10 ~ 16:10 초청발표2 - 김유식 (부산대학교) 16:30 ~ 18:00 학생발표 - 김성호, 김경모, 노경민 (서울대학교) 10월 8일 금요일, 09:20 ~ 10:20 초청발표3 - 배영진 (인천대학교) 10:30 ~ 11:30 초청발표4 - 조윤형 (성균관대학교) 11:45 ~ 12:15 학생발표 - 이재혁 (포항공대) 14:00 ~ 18:00 토의 10월 9일 토요일, 09:00 ~ 09:30 초청발표5 - 좌동욱 (KIAS) 09:30 ~ 10:00 초청발표6 - 정원보 (서울대)
*스케쥴은 변경될 수 있습니다.
- 제목 및 초록:
Title: Weinstein Lefschetz fibrations and Legendrian Kirby diagrams.
We review a recipe of Casals-Murphy from affine Weinstein Lefsechtz fibrations to Legendrian front handlebodies. We apply this tool to several examples including certain Milnor fibers, and augmentation varieties.
Title : Rabinowitz Floer homology and negative line bundles
Rabinowitz Floer homology (RFH), a version of symplectic homology, is an invariant for hypersurfaces in symplectic manifolds. While RFH is invariant under the change of the “size” of a hypersurface for exact symplectic manifolds, we will see that this invariance property breaks down beyond the exact case, particularly for complex line bundles.
Title:Covariant Tannakian differential graded categories
The Tannaka-Krein duality states that a compact group G can be recovered from the category Rep(G) of its finite dimensional complex representations.
In fact, T. Tannaka and M. G. Krein characterized all categories which arise as the representation category of some compact group G. A. Grothendieck suggested and N. Saavedra Rivano showed in his thesis that analogous results hold true for affine group schemes over a field. P. Deligne gave further development of the work of Saavedra Rivano, which is the theory of Tannakian categories.
Motivated by rational homotopy theory, we present the differential graded, dual version of this story which we call as covariant Tannakian differential graded categories. In this talk, we explain an alternative method of recovering the group which is valid over an arbitrary commutative ring R.
We also give a proof of the analogous duality theorems when we are merely given a Lax-tensorial fiber functor. This is a joint work with Jae-Suk Park.
Speaker: 김경모, 노경민
Title: Mirror Symmetry Correspondence between Indecomposable Cohen-Macaulay Modules over Degenerate Cusps and Immersed Lagrangians on Surfaces
Burban and Drozd (2017) classified all indecomposable maximal Cohen-Macaulay modules over degenerate cusps. For the degenerate cusp defined by xyz, its mirror is given by a pair of pants (Abouzaid, Auroux, Efimov, Katzarkov and Orlov). We find explicit objects in the Fukaya category of a pair of pants, which correspond to every indecomposable Cohen-Macaulay modules in Burban and Drozd's list under the localized mirror functor. This is a joint work in progress with Cheol-Hyun Cho, Wonbo Jeong and Kyoungmo Kim.