• Abstract:  A fundamental problem in quantitative symplectic geometry is to understand in which ways a Hamtilonian flow can "squeeze" phase space. The special case of ellipsoids has been a great source of motivation for the last several decades, in many ways mirroring various important developments in the field (e.g. Gromov-Witten theory, Floer homology, symplectic field theory, embedded contact homology, and more). In this talk, I will survey some new developments in the study of high dimensional symplectic embeddings, and in particular the recent resolution of the so-called stabilized ellipsoid conjecture. Our framework sets up a bridge between quantitative symplectic geometry and the classical study of singular algebraic curves, studying the latter using tools from log Calabi-Yau mirror symmetry. I will not assume familiarity with any of this background. 

• Speaker: Kyler Siegel (University of Southern California & 서울대)

• Time & Location: 9월 5일 금요일, 오전 11-13시, 서울대학교 상산수리과학관 309호

• Abstract: We introduce and develop the theory of spectral networks in real contact and symplectic topology. First, we establish the existence and pseudoholomorphic characterization of spectral networks for Lagrangian fillings in the cotangent bundle of a smooth surface. These are proven via analytic results on the adiabatic degeneration of Floer trajectories and the explicit computation of continuation strips. Second, we construct a Family Floer functor for Lagrangian fillings endowed with a spectral network and prove its equivalence to the non-abelianization functor. In particular, this implies that both the framed 2d-4d BPS states and the Gaiotto-Moore-Neitzke non-abelianized parallel transport are realized as part of the A∞-operations of the associated 4d partially wrapped Fukaya categories. To conclude, we present a new construction relating spectral networks and Lagrangian fillings using Demazure weaves, and show the precise relation between spectral networks and augmentations of the Legendrian contact dg-algebra. 

• Speaker: 노윤재

• Time & Location: 8월 8일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract: 지난 두 번의 세미나(김종명 박사님, 유필상 교수님 발표)에서 stability condition에 관해 논의하였습니다. 이번 세미나에서는 symplectic geometry와 stablity condition이 어떻게 연결되는지 살펴보려 합니다. 

구체적으로는 Joyce의 conjecture를 소개하고, Joyce가 왜/어떻게 holomorphic volume form, special Lagrangian과 같은 기하학의 object들을 stability condition이라는 대수적인 object와 연결시켰는지 살펴보려 합니다. 

• Speaker: 이상진 (KIAS)

• Time & Location: 8월 1일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Notes

• Abstract: Abstract: In their 2023 survey, Lekili and Segal proposed a conjecture relating equivariant Lagrangian Floer theory to the Floer theory of a singular symplectic reduction. In this talk, I will present their conjecture, discuss a broad class of supporting evidence they provided, and explain why and how it is expected to hold. 

• Speaker: 좌동욱 (충북대학교)

• Time & Location: 7월 25일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract: Various types of duality results in both symplectic and algebraic geometry are well-known to be related to Calabi-Yau structures on the relevant categories. In this talk, I'll discuss an abstract approach, as a categorical analogue to Beilinson-Tate residue theory, to provide ingredients for constructing Calabi-Yau structures on dg/A-infinity categories that are not necessarily proper. Applications include duality type results for Rabinowitz Fukaya categories, singularity categories, and so on.

• Speaker: Yuan Gao (Nanjing University)

• Time & Location: 7월 9일 수요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract: In this talk, I will introduce the recent result of Lekili-Ueda. They conjectured HMS for Rabinowotz Fukaya category of Milnor fibers of invertible polynomials and proved it for Brieskorn-Pham singularities which are not of Calabi-Yau type. If time permits, I will explain its application for a calculation of the Rabinowitz Floer homology of the Milner fiber. 

• Speaker: 정원보 (서강대학교)

• Time & Location: 7월 4일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract: In this expository talk, we will review the notions of t-structures and torsion theories, with an emphasis on an explicit example. We will then introduce the notion of a 3-Calabi–Yau category via a quiver with potential, and revisit torsion theories in terms of the quiver data. Time permitting, we will discuss the correspondence between quiver mutations and surface triangulations. 

• Speaker: 유필상(서울대학교)

• Time & Location: 6월 27일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 301호

• Abstract:  I will talk about the basics of Bridgeland stability conditions and a conjectural description of the spaces of stability conditions as (almost) Frobenius manifolds. 

• Speaker: 김종명(QSMS)

• Time & Location: 6월 13일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract:  We introduce a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. As a consequence, we prove that any two closed exact Lagrangians that are isomorphic in the Fukaya category of a Weinstein manifold are simple homotopy equivalent, under the assumption that one of them is homotopy equivalent to the ambient symplectic manifold. This generalizes Abouzaid-Kragh's result for cotangent bundles to general Weinstein manifolds. 

• Speaker: 김용환(MIT)

• Time & Location: 6월 10일 화요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Abstract: Fukaya categories of smooth surfaces can be defined topologically, which makes them easier to compute with. Through their formal generators, topological Fukaya categories (TFC) can be related to a certain class of graded algebras, called (graded) gentle algebras. Conversely, derived categories of gentle algebras are realized as TFCs of some smooth surfaces. In this talk, I will generalize TFC construction to Z/2Z-orbifold surfaces, which introduces a new class of algebras, semi-gentle algebras. Also, we will see how to use this result to show the class of semi-gentle algebras is closed under derived equivalence. This talk is based on the joint work with Cheol-Hyun Cho and ongoing project with Severin Barmeier, Cheol-Hyun Cho, Kyungmin Rho, Sibylle Schroll, and Zhengfang Wang. 

• Speaker: 김경모 (퀼른대학교)

• Time & Location: 6월 2일 월요일, 오후 3-5시, 서울대학교 상산수리과학관 309호

• Abstract: Rabinowitz Floer homology is a Floer homology theory for contact hypersurfaces in symplectic manifolds. Recently, Ganatra-Gao-Venkatesh introduced its categorification, called the Rabinowitz Fukaya category. In this talk, I will discuss its construction and some examples. If time permits, I will explain that for any Weinstein manifold, its Rabinowitz Fukaya category is quasi-equivalent to the categorical formal punctured neighborhood of infinity of the wrapped Fukaya category.

• Speaker: 배한울 (QSMS)

• Time & Location: 5월 9일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Notes

• Abstract:  이번 발표에서는 지난 발표에서 정의한 topological Fukaya category의 hall algebra에 대해 공부하고 그 Hall algebra가 derived Skein relation을 만족한다는 Cooper-Samuelson의 결과(https://arxiv.org/abs/1708.00889)를 소개하려 합니다. Cooper-Samuelson은 local-to-global approach를 사용하여 Hall algebra를 연구하였고 이와 관련된 conjecture를 제시하였습니다. 이번 발표는 local-to-global approach를 소개하는 것으로 시작하여 이를 이용하여 어떻게 derived Skein relation을 증명할 수 있는지 간략하게 살펴보려 합니다. 

• Speaker: 이상진(고등과학원)

• Time & Location: 4월 18일 금요일, 오전 10-12시, 서울대학교 상산수리과학관 309호

• Notes

• Abstract:  Skein algebra is an algebra assigned to a surface that carries interesting information, such as quantum group actions or cluster algebra structures. It is conjectured and partially proven by Cooper-Samuelson and others that the skein algebra of a surface has a deep relation with the hall algebra of the Fukaya category of the surface. The expository talk will start with motivational questions about the conjectured relation and will discuss the result of Cooper-Samuelson with examples.  

• Speaker: 이상진(고등과학원)

• Time & Location: 4월 11일 금요일, 오후 1-3시, 서울대학교 상산수리과학관 309호

• Notes

• Abstract: A Hall algebra is an invariant of a category that encodes extension data between objects. In this expository talk, we will introduce the Hall algebra associated to a "finite" category and present Ringel's theorem, which reveals a striking relationship between Hall algebras and quantum groups. If time permits, we will also discuss how this framework extends beyond the classical setting. 

• Speaker: 유필상(서울대학교)

• Time & Location: 4월 4일 금요일, 오후 1-3시, 서울대학교 상산수리과학관 309호