BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benjamin Gammage (Harvard) DTSTART:20210308T010000Z DTEND:20210308T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/1 DESCRIPTION:Title: M irror symmetry for Berglund-Hübsch Milnor fibers\nby Benjamin Gammage (Harvard) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nAfter rec alling some joint work with Jack Smith proving homological Berglund-Hübsc h mirror symmetry\, we explain the calculation of the Fukaya category of a Berglund-Hübsch Milnor fiber\, proving a conjecture of Yankı Lekili and Kazushi Ueda. The strategy of proof involves deforming the Fukaya categor y of an open ("very affine") subset\, by calculating a contribution from d isks passing through an affine normal crossings divisor.\n LOCATION:https://researchseminars.org/talk/IBSCGP/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenji Fukaya (Simon Center for Geometry and Physics) DTSTART:20210315T010000Z DTEND:20210315T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/2 DESCRIPTION:Title: V irtual fundamental chain in gauge theory\nby Kenji Fukaya (Simon Cente r for Geometry and Physics) as part of IBS-CGP weekly zoom seminar\n\n\nAb stract\nThe virtual fundamental chain technique is developed to study modu li space of pseudoholomorphic curve. In the case of moduli space appearing in gauge theory\, the singularity appearing in the compactification is ha rder to work with and existing theory such as Kuranishi structure does not work. In this talk I explain certain stratified version of Kuranishi stru cture which works to find virtual fundamental chain in some easy case of g auge theory. This is a part of project I am working with A. Daemi and the motivation is to apply it to study certain SO(3) version of Atiyah Floer c onjecture.\n LOCATION:https://researchseminars.org/talk/IBSCGP/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanwool Bae (Seoul National University) DTSTART:20210322T010000Z DTEND:20210322T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/3 DESCRIPTION:Title: P eterson conjecture via Lagrangian correspondences and wonderful compactifi cations\nby Hanwool Bae (Seoul National University) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nLet $G$ be a compact simply-connected semisimple Lie group and let $T$ be a maximal torus subgroup of $G$. Peter son conjecture says that the homology of the based loop space of $G$ and t he quantum cohomology of the full flag variety $G/T$ are isomorphic as rin gs after a localization. In a joint work with Naichung Conan Leung\, we fo und a geometric proof of the conjecture using Floer theoretic techniques. In this talk\, I will first introduce the moment Lagrangian correspondence from the cotangent bundle of $G$ to the square $(G/T)^2$ of the flag vari ety $G/T$. Then I will discuss how to compute an $A$-infinity homomorphism associated to the Lagrangian correspondence and show that it induces the desired isomorphism.\n LOCATION:https://researchseminars.org/talk/IBSCGP/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuan Gao (USC) DTSTART:20210329T010000Z DTEND:20210329T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/4 DESCRIPTION:Title: T he Rabinowitz Fukaya category and applications\nby Yuan Gao (USC) as p art of IBS-CGP weekly zoom seminar\n\n\nAbstract\nThe goal of the talk is to introduce the Rabinowitz (wrapped) Fukaya category\, as an open-string analogue of Rabinowitz Floer homology of (the boundary at infinity of) a L iouville manifold\, which is a categorical invariant of exact cylindrical Lagrangians whose cohomology morphisms measure the failure of wrapped Floe r cohomology to satisfy Poincare duality. The main result\, answering a co njecture of Abouzaid\, relates this category to the usual wrapped Fukaya c ategory by a canonical algebraic formula\, in terms of the categorical for mal punctured neighborhood of infinity introduced by Efimov. As an applica tion\, we shall see a few new computations in Floer theory via homological mirror symmetry. In addition\, we are going to explore the open-closed st ring relationship and derive structural and computational results in both Rabinowitz Floer homology and symplectic cohomology. This is based on join t work with Sheel Ganatra and Sara Venkatesh.\n LOCATION:https://researchseminars.org/talk/IBSCGP/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Mclean (Stony Brook) DTSTART:20210405T010000Z DTEND:20210405T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/5 DESCRIPTION:Title: F loer Cohomology and Arc Spaces\nby Mark Mclean (Stony Brook) as part o f IBS-CGP weekly zoom seminar\n\n\nAbstract\nLet f be a polynomial over th e complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally\, this corresponds to the space of d- jets of holomorphic disks in complex affine space whose boundary ‘wraps ’ around the singularity d times. We show that Floer cohomology of the d th power of the Milnor monodromy map is isomorphic to compactly supported cohomology of the dth contact locus. This answers a question of Paul Seide l and it also proves a conjecture of Nero Budur\, Javier Fernández de Bob adilla\, Quy Thuong Lê and Hong Duc Nguyen. The key idea of the proof is to use a jet space version of the PSS map together with a filtration argum ent.\n LOCATION:https://researchseminars.org/talk/IBSCGP/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Smith (Cambridge) DTSTART:20210419T080000Z DTEND:20210419T090000Z DTSTAMP:20260422T225758Z UID:IBSCGP/6 DESCRIPTION:Title: F ukaya categories of quasihomogeneous polynomials\nby Jack Smith (Cambr idge) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nBerglund-Hübs ch mirror symmetry predicts that for certain 'transpose' pairs of quasihom ogeneous polynomials\, the Fukaya-Seidel category of one is equivalent to a category of matrix factorisations of the other. The difficulty in provin g this is that the natural types of objects to consider on the two sides d o not match up with each other. I will introduce an enlarged version of th e Fukaya-Seidel category that contains the missing objects\, and outline h ow this allows one to prove B-H mirror symmetry. This is joint work in pro gress with Benjamin Gammage.\n LOCATION:https://researchseminars.org/talk/IBSCGP/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgios Dimitroglou Rizell (Uppsala) DTSTART:20210426T080000Z DTEND:20210426T090000Z DTSTAMP:20260422T225758Z UID:IBSCGP/7 DESCRIPTION:Title: L agrangian Poincaré Recurrence via pseudoholomorphic foliations\nby Ge orgios Dimitroglou Rizell (Uppsala) as part of IBS-CGP weekly zoom seminar \n\n\nAbstract\nFor any Hamiltonian displaceable closed curve inside a clo sed symplectic surface\, there is a bound on the number of pairwise disjoi nt Hamiltonian isotopic copies of the curve that one can produce. This phe nomenon is called Lagrangian Poincaré Recurrence\, and it was only shown very recently by Polterovich and Shelukhin that there exist displaceable L agrangians in higher dimension that satisfy the analogous property. In thi s work in progress joint with E. Opshtein\, we use the technique of pseudo holomorphic foliations to show that the bound on the number of disjoint co pies in the surface persists after increasing the dimension by the followi ng stabilisation: take the cartesian product of the symplectic surface wit h a sufficiently small symplectic annulus\, and take the product of the cu rve with the with the core of the annulus to produce a Lagrangian torus.\n LOCATION:https://researchseminars.org/talk/IBSCGP/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Wei Fan (UC Berkerley) DTSTART:20210607T010000Z DTEND:20210607T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/8 DESCRIPTION:Title: S hifting numbers in triangulated categories\nby Yu-Wei Fan (UC Berkerle y) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nOne can consider endofunctors of triangulated categories as dynamical systems\, and study t heir long term behaviors under large iterations. There are (at least) thre e natural invariants that one can associate to endofunctors from the dynam ical perspective: categorical entropy\, and upper/lower shifting numbers. We will recall some background on categorical dynamical systems and catego rical entropy\, and introduce the notion of shifting numbers\, which measu re the asymptotic amount by which an endofunctor of a triangulated categor y translates inside the category. The shifting numbers are analogous to Po incare translation numbers. We additionally establish that in some example s the shifting numbers provide a quasimorphism on the group of autoequival ences. Joint work with Simion Filip.\n LOCATION:https://researchseminars.org/talk/IBSCGP/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hansol Hong (Yonsei) DTSTART:20210412T010000Z DTEND:20210412T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/9 DESCRIPTION:Title: S cattering diagrams from blowups of toric surfaces\nby Hansol Hong (Yon sei) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nGross-Hacking-K eel has shown that any cluster variety can be obtained by a sequence of (n ontoric) blow-ups and blow-downs starting from a toric variety. Motivated by this\, we study the effect of blowup on the Lagrangian torus fibration on a toric surface. In particular\, we will see that if the blowup points lie over the codimension one strata of the toric variety\, the resulting f ibration on the blowup produces a scattering diagram that matches with the one constructed by Gross-Pandharipande-Siebert using algebraic curve coun ting. The talk is based on the work in progress jointly with Sam Bardwell- Evans\, Man-Wai Mandy Cheung and Yu-Shen Lin.\n LOCATION:https://researchseminars.org/talk/IBSCGP/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nate Bottman (Max Planck) DTSTART:20210503T010000Z DTEND:20210503T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/10 DESCRIPTION:Title: The symplectic (A-infinity\,2)-category and a simplicial version of the 2D Fulton-MacPherson operad\nby Nate Bottman (Max Planck) as part of IBS -CGP weekly zoom seminar\n\n\nAbstract\nThe symplectic (A-infinity\,2)-cat egory Symp\, which is currently under construction by myself and my collab orators\, is a 2-category-like structure whose objects are symplectic mani folds and where hom(M\,N) := Fuk(M^- x N). Symp is a coherent algebraic st ructure which encodes the functoriality properties of the Fukaya category. This talk will begin with the following question: what can say about the part of Symp that knows only about a single symplectic manifold M\, and th e diagonal Lagrangian correspondence from M to itself? We expect that the answer to this question should be a chain-level algebraic structure on sym plectic cohomology\, and in this talk I will present progress toward confi rming this. Specifically\, I will present a "simplicial version" of the 2- dimensional Fulton-MacPherson operad. If there is time\, I will discuss wo rk-in-progress with Felix Janda and Paolo Salvatore that aims to complete this answer.\n LOCATION:https://researchseminars.org/talk/IBSCGP/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Renato Vianna (Rio de Janeiro) DTSTART:20210621T010000Z DTEND:20210621T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/11 DESCRIPTION:Title: Sharp Ellipsoid Embeddings and Toric Mutations\nby Renato Vianna (Rio de Janeiro) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nWe will show how to construct volume filling ellipsoid embeddings in some 4-dimens ional toric domain using mutation of almost toric compactification of thos e. In particular we recover the results of McDuff-Schlenk for the ball\, F enkel-Müller for the product of symplectic disks and Cristofaro-Gardiner for E(2\,3)\, giving a more explicit geometric perspective for these resul ts. To be able to represent certain divisors\, we develop the idea of symp lectic tropical curves in almost toric fibrations\, inspired by Mikhalkin' s work for tropical curves. This is joint work with Roger Casals.\nObs: Th e same result appears in "On infinite staircases in toric symplectic four- manifolds"\, by Cristofaro-Gardiner -- Holm -- Mandini -- Pires. Both pape rs were posted simultaneously on arXiv.\n LOCATION:https://researchseminars.org/talk/IBSCGP/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Kwokwai Chan (CUHK) DTSTART:20210628T010000Z DTEND:20210628T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/12 DESCRIPTION:Title: An algebraic model for smoothing Calabi-Yau varieties and its applications \nby Kwokwai Chan (CUHK) as part of IBS-CGP weekly zoom seminar\n\n\nA bstract\nWe are interested in smoothing of a degenerate Calabi-Yau variety or a pair (degenerate CY\, sheaf). I will explain an algebraic framework for solving such smoothability problems. The idea is to glue local dg Lie algebras (or dg Batalin-Vilkovisky algebras)\, coming from suitable local models\, to get a global object. The key observation is that while this ob ject is only an almost dg Lie algebra (or pre-dg Lie algebra)\, it is suff icient to prove unobstructedness of the associated Maurer-Cartan equation (a kind of Bogomolov-Tian-Todorov theorem) under suitable assumptions\, so the former can be regarded as a singular version of the Kodaira-Spencer D GLA. Our framework applies to degenerate CY varieties previously studied b y Kawamata-Namikawa and Gross-Siebert\, as well as a more general class of varieties called toroidal crossing spaces (by the recent work of Felten-F ilip-Ruddat). This talk is based on various joint works with Conan Leung\, Ziming Ma and Y.-H. Suen.\n LOCATION:https://researchseminars.org/talk/IBSCGP/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Egor Shelukhin (Montreal) DTSTART:20210510T010000Z DTEND:20210510T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/13 DESCRIPTION:Title: Lagrangian configurations and Hamiltonian maps\nby Egor Shelukhin (Mon treal) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nWe study conf igurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian m aps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofer's metric\, showing in particular that this group is not quasi-isometric to a line. This answers a well-known question of Kapovich-Polterovich from 2006. We show that these flats in Ham(S^2) s tabilize to certain product four-manifolds\, prove constraints on Lagrangi an packing\, find new instances of Lagrangian Poincare recurrence\, and pr esent a new hierarchy of normal subgroups of area-preserving homeomorphism s of the two-sphere. The technology involves Lagrangian spectral invariant s in symmetric product orbifolds. This is joint work with Leonid Polterovi ch.\n LOCATION:https://researchseminars.org/talk/IBSCGP/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Xujia Chen (IAS) DTSTART:20210517T010000Z DTEND:20210517T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/14 DESCRIPTION:Title: Lifting cobordisms and Kontsevich-type recursions for counts of real curve s\nby Xujia Chen (IAS) as part of IBS-CGP weekly zoom seminar\n\n\nAbs tract\nKontsevich's recursion\, proved in the early 90s\, is a recursion f ormula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugat ion)\, signed invariant counts of real rational holomorphic curves were de fined by Welschinger in 2003. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursion s for them in 2007\, along with an outline of a potential approach of prov ing them. For many symplectic fourfolds and sixfolds\, these recursions de termine all invariants from basic inputs. We establish Solomon's recursion s by re-interpreting his disk counts as degrees of relatively oriented pse udocycles from moduli spaces of stable real maps and lifting cobordisms fr om Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon's approach).\n LOCATION:https://researchseminars.org/talk/IBSCGP/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeff Hicks (Cambridge) DTSTART:20210524T010000Z DTEND:20210524T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/15 DESCRIPTION:Title: Lagrangian Cobordism and Lagrangian Surgery\nby Jeff Hicks (Cambridge) as part of IBS-CGP weekly zoom seminar\n\nLecture held in Zoom online.\n\ nAbstract\nA Lagrangian cobordism is a Lagrangian submanifold in X x C who se "ends" are Lagrangian submanifolds inside of X. We will show that the L agrangian cobordisms associated to the Lagrangian surgery operation provid e the building blocks for all Lagrangian cobordisms. Finally\, we will dis cuss some of the Floer theoretic implications of this decomposition\, exte nding previous work of Biran and Cornea. This is based on work from arxiv: 2102.10197.\n LOCATION:https://researchseminars.org/talk/IBSCGP/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jootae Kim (KIAS) DTSTART:20210531T010000Z DTEND:20210531T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/16 DESCRIPTION:Title: Real Lagrangian tori in monotone symplectic 4-manifolds\nby Jootae Kim (KIAS) as part of IBS-CGP weekly zoom seminar\n\nLecture held in Zoom onl ine.\n\nAbstract\nBy a real Lagrangian\, we mean the fixed point set of an anti-symplectic involution in a symplectic manifold. In this talk\, we ex plore the topology of real Lagrangian tori in monotone symplectic 4-manifo lds. They are very rare in the sense that all known exotic monotone Lagran gian tori cannot be real\, but they exist exactly when no topological obst ructions occur. The disc potential plays an intriguing role in our voyage. \n LOCATION:https://researchseminars.org/talk/IBSCGP/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Wonbo Jeong (SNU) DTSTART:20210614T010000Z DTEND:20210614T020000Z DTSTAMP:20260422T225758Z UID:IBSCGP/17 DESCRIPTION:Title: Noncompact description for Fukaya-Seidel categories of invertible curve si ngularities\nby Wonbo Jeong (SNU) as part of IBS-CGP weekly zoom semin ar\n\nLecture held in Zoom online.\n\nAbstract\nFor given invertible polyn omial W\, we consider two types of Fukaya category. One is the usual Fukay a-Seidel category from Lefschetz fibration structure of W. For the maximal symmetry group G of W\, we can construct the other Fukaya category of the pair (W\,G) from wrapped Fukaya category of the Milnor fiber and quantum cap action of monodromy orbit. In this talk\, we compare the equivariant l ift of the latter with the Fukaya-Seidel category and prove its derived eq uivalence for invertible curve singularities. In particular\, directedness of the category is obtained from quantum cap action and related construct ions. This talk is based on the joint work (in progress) with Cheol-hyun C ho (SNU) and Dongwook Choa (KIAS).\n LOCATION:https://researchseminars.org/talk/IBSCGP/17/ END:VEVENT END:VCALENDAR