BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ryushi GOTO (Osaka University) DTSTART:20210712T010000Z DTEND:20210712T015000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/1 DESCRIPTION:Title: Scalar curvature and moment map in Generalized Kähler geometry\nby Ryushi GOTO (Osaka University) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nWe introduce a notion of s calar curvature of a twisted generalized Kähler manifold in terms of pure spinors formalism. A moment map framework on an arbitrary compact twisted generalized Kähler manifold is provided and then it turns out that a mom ent map is given by the scalar curvature under the certain condition\, whi ch is a generalization of the result of the scalar curvature as a moment m ap in the ordinary Kähler geometry\, due to Fujiki and Donaldson. A nonco mmutative compact Lie group G does not have any Kähler structure. Howev er\, we show that a compact Lie group has a family of generalized Kähler structures twisted by the Cartan 3-form\, which is constructed by the act ion of the real Pin group of the double of Cartan subalgebra. Then we show that an arbitrary compact Lie group admits generalized Kähler structures with constant scalar curvature. In particular\, generalized Kähler struc tures with constant scalar curvature on the standard Hopf surface are expl icitly given.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Byunghee AN (Kyungpook National University) DTSTART:20210712T021000Z DTEND:20210712T030000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/2 DESCRIPTION:Title: Augmentations and ruling polynomials for Legendrian graphs\nb y Byunghee AN (Kyungpook National University) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nIn this talk\, we will show the equivalence between two Legendrian isotopy invariants of Leg endrian graphs: (i) augmentation number via point-counting over a finite f ield for the augmentation variety of the associated Chekanov-Eliashberg DG A\, and (ii) the ruling polynomial via combinatorics of the decompositions of the associated front projections. This is a joint work with Youngjin B ae(Incheon National University) and Tao Su(Yau Mathematical Sciences Cente r\, Tsinghua University).\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Youngjin Bae (Incheon National University) DTSTART:20210713T003000Z DTEND:20210713T012000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/3 DESCRIPTION:Title: Seeds many Lagrangian fillings for Legendrian links\nby Young jin Bae (Incheon National University) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nI will introduce Legendria n links of finite and affine Dynkin diagrams\, and then argue that there a re at least as many Lagrangian fillings as seeds in the corresponding clus ter structure. The main ingredients are N-graphs developed by Casals-Zaslo w\, and cluster structures by Fomin-Zelevinsky. This is a joint work with Byung Hee An and Eunjeong Lee.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Huai-Liang CHANG (Hong Kong University of Science and Technology) DTSTART:20210713T013500Z DTEND:20210713T022500Z DTSTAMP:20260404T131155Z UID:2021PRCSG/4 DESCRIPTION:Title: Structure of high genus Gromov Witten invariants\nby Huai-Lia ng CHANG (Hong Kong University of Science and Technology) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nGromov Witten invariants Fg encodes the numbers of genus g curves in Calabi Yau threefolds and play an important role in enumerative geometry. In 1993\, B ershadsky\, Cecotti\, Ooguri\, Vafa exhibited a hidden ``Feynman structure ” governing all Fg’s at once\, using path integral methods. The counte rpart in mathematics has been missing for many years. After a decades of s earch\, in 2018\, a mathematical approach: Mixed Spin P field (MSP) moduli \, is finally developed to provide the wanted ``Feynman structure”\, for quintic CY 3fold. Instead of enumerating curves in the quintic 3fold\, MS P enumerate curves in a large N dimensional singular space with quintic-3- fold boundary. The “P fields” and “cosections” are used to formula te counting in the singular space via a Landau Ginzburg type construction. In this talk\, I shall focus on geometric ideas behind the MSP moduli. Th e results follows from a decade of joint works with Jun Li\, Shuai Guo\, Y oung Hoon Kiem\, Weiping Li\, Melissa C.C. Liu\, Jie Zhou\, and Yang Zhou. \n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Hisashi KASUYA (Osaka University) DTSTART:20210713T024000Z DTEND:20210713T033000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/5 DESCRIPTION:Title: Non-invariant deformations of left-invariant complex structures o n compact Lie groups\nby Hisashi KASUYA (Osaka University) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nI t is known that every compact Lie group of even dimension admits left-inva riant complex structures. We study deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are non -invariant. We compute cohomology of vector bundles for such non-invariant complex structures and see the difference between invariant complex struc tures and non-invariant complex structures. This talk is a joint work with Hiroaki Ishida (Kagoshima).\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Hyungryul Baik (Korea Advanced Institute of Science and Technology ) DTSTART:20210714T010000Z DTEND:20210714T015000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/6 DESCRIPTION:Title: Limits of canonical metrics in low-dimensions\nby Hyungryul B aik (Korea Advanced Institute of Science and Technology) as part of 2021 P acific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nFor a t ower of finite normal covers of graphs or surfaces\, one can consider a se quence of metrics on the base given by pull-back of canonical metrc of the covers. We show that such a sequence has a limit and it depends only on t he cover approximated by the tower up to scaling. The case of compact Riem ann surface where the tower approximates the universal cover is due to Kaz hdan. In this talk\, we will mostly focus on the surface case and explain how the L^2-theory can be applied. This talk is based on a joint work with Farbod Shokrieh and Chenxi Wu.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ziyu ZHANG (ShanghaiTech University) DTSTART:20210714T021000Z DTEND:20210714T030000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/7 DESCRIPTION:Title: Degenerations of Hilbert schemes of points on K3 surfaces\nby Ziyu ZHANG (ShanghaiTech University) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nIt is a widely open proble m to understand the degenerations of higher dimensional hyperkähler manif olds. The simplest case would be the degenerations of Hilbert schemes of p oints on K3 surfaces. Given a simple degeneration family of K3 surfaces\, there are two existing constructions of the degenerations of the Hilbert s chemes of its fibers in the literature\, due to Nagai and Gulbrandsen-Hall e-Hulek respectively. I will compare the two constructions with an emphasi s on the geometry of the latter. Based on joint work with M.G.Gulbrandsen\ , L.H.Halle and K.Hulek.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ngoc Cuong Nguyen (Korea Advanced Institute of Science and Technol ogy) DTSTART:20210715T003000Z DTEND:20210715T012000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/8 DESCRIPTION:Title: Continuous solutions to Monge-Amp ere equations on Hermitian mani folds for measures dominated by capacity\nby Ngoc Cuong Nguyen (Korea Advanced Institute of Science and Technology) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nWe prove the exist ence of a continuous quasi-plurisubharmonic solution to the Monge-Amp ere equation on a compact Hermitian manifold for a very general measre on the right hand side. We admit measures dominated by capacity in a certain mann er\, in particular\, moderate measures studied by Dinh-Nguyen-Sibony. As a consequence\, we give a characterization of measures admitting Holder con tinuous quasi-plurisubharmonic potential\, inspired by the work of Dinh-Ng uyen. This is joint work with S lawomir Ko lodziej.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Peng WU (Fudan University) DTSTART:20210715T013500Z DTEND:20210715T022500Z DTSTAMP:20260404T131155Z UID:2021PRCSG/9 DESCRIPTION:Title: Complex structures on Einstein four-manifolds of positive scalar curvature\nby Peng WU (Fudan University) as part of 2021 Pacific Rim C omplex & Symplectic Geometry Conference\n\n\nAbstract\nThe question that w hen a four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian\, LeBrun\, r espectively. Tian classified Kahler-Einstein four-manifolds with positive scalar curvature\, LeBrun classified Hermitian\, Einstein four-manifolds o f positive scalar curvature. In this talk we consider the inverse problem\ , that is\, when a simply connected four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We wil l show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Ryosuke TAKAHASHI (Kyushu University) DTSTART:20210716T010000Z DTEND:20210716T015000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/10 DESCRIPTION:Title: Some geometric flow approaches for deformed Hermitian-Yang-Mills equation\nby Ryosuke TAKAHASHI (Kyushu University) as part of 2021 Pa cific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nOn SYZ m irror symmetry\, a deformed Hermitian-Yang-Mills (dHYM) metric is a fiber metric on a holomorphic line bundle\, which is the mirror object to a spec ial Lagrangian section of the dual torus fibration. As a parabolic analogu e\, Jacob-Yau introduced the Line Bundle Mean Curvature Flow (LBMCF) as th e mirror of the Lagrangian Mean Curvature Flow. In this talk\, we explore some geometric flow approaches for dHYM metrics: (A) On K\\”ahler surfac es\, it is known that the existence of dHYM metrics is equivalent to a K\\ ”ahler condition for a certain cohomology class. We relax this condition and study how the LBMCF blows up. (B) Recently\, Collins-Yau discovered a new variational characterization for dHYM metrics. Motivated by this\, we introduce a new geometric flow which is designed to deform a given metric to a dHYM one. Then we show that this new flow potentially has more globa l existence and convergence properties than the LBMCF.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyeongsu CHOI (Korea Institute for Advanced Study) DTSTART:20210716T021000Z DTEND:20210716T030000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/11 DESCRIPTION:Title: Translators of the Gauss curvature flow\nby Kyeongsu CHOI (K orea Institute for Advanced Study) as part of 2021 Pacific Rim Complex & S ymplectic Geometry Conference\n\n\nAbstract\nWe begin by reviewing the blo w-up analysis for the minimal surfaces at isolated singularities\, and wil l quickly discuss about some related recent developments in the singularit y analysis for the mean curvature flow. Then\, we will classify the transl ating surfaces under the flows by sub-affine-critical powers of the Gauss curvature\, which is a Liouville theorem for a class of Monge-Ampere equat ions. We will put an emphasis on the divergence free property of the linea rized operator of the Monge-Ampere equation. This is a joint work with Beo mjun Choi and Soojung Kim.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Genki HOSONO (Tohoku University) DTSTART:20210715T024000Z DTEND:20210715T033000Z DTSTAMP:20260404T131155Z UID:2021PRCSG/12 DESCRIPTION:Title: On Berndtsson-Lempert's proof of optimal $L^2$ extension theorem and extension from non-reduced varieties\nby Genki HOSONO (Tohoku Uni versity) as part of 2021 Pacific Rim Complex & Symplectic Geometry Confere nce\n\n\nAbstract\nI'd like to talk about the proof of an optimal version of the Ohsawa-Takegoshi $L^2$ extension theorem and its application to an extension theorem from non-reduced varieties.\n LOCATION:https://stable.researchseminars.org/talk/2021PRCSG/12/ END:VEVENT END:VCALENDAR