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:20260404T111006Z UID:IBSCGP/1 DESCRIPTION:Title: Mirror symmetry for Berglund-Hübsch Milnor fibers\nby Benjamin Gammage (Harvard) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nAf ter recalling some joint work with Jack Smith proving homological Berglund -Hübsch mirror symmetry\, we explain the calculation of the Fukaya catego ry of a Berglund-Hübsch Milnor fiber\, proving a conjecture of Yankı Lek ili and Kazushi Ueda. The strategy of proof involves deforming the Fukaya category of an open ("very affine") subset\, by calculating a contribution from disks passing through an affine normal crossings divisor.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenji Fukaya (Simon Center for Geometry and Physics) DTSTART:20210315T010000Z DTEND:20210315T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/2 DESCRIPTION:Title: Virtual fundamental chain in gauge theory\nby Kenji Fukaya (Simo n Center for Geometry and Physics) as part of IBS-CGP weekly zoom seminar\ n\n\nAbstract\nThe virtual fundamental chain technique is developed to stu dy moduli space of pseudoholomorphic curve. In the case of moduli space ap pearing in gauge theory\, the singularity appearing in the compactificatio n is harder to work with and existing theory such as Kuranishi structure d oes not work. In this talk I explain certain stratified version of Kuranis hi structure which works to find virtual fundamental chain in some easy ca se of gauge theory. This is a part of project I am working with A. Daemi a nd the motivation is to apply it to study certain SO(3) version of Atiyah Floer conjecture.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanwool Bae (Seoul National University) DTSTART:20210322T010000Z DTEND:20210322T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/3 DESCRIPTION:Title: Peterson conjecture via Lagrangian correspondences and wonderful com pactifications\nby Hanwool Bae (Seoul National University) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nLet $G$ be a compact simply-con nected semisimple Lie group and let $T$ be a maximal torus subgroup of $G$ . Peterson conjecture says that the homology of the based loop space of $G $ and the quantum cohomology of the full flag variety $G/T$ are isomorphic as rings after a localization. In a joint work with Naichung Conan Leung\ , we found a geometric proof of the conjecture using Floer theoretic techn iques. In this talk\, I will first introduce the moment Lagrangian corresp ondence from the cotangent bundle of $G$ to the square $(G/T)^2$ of the fl ag variety $G/T$. Then I will discuss how to compute an $A$-infinity homom orphism associated to the Lagrangian correspondence and show that it induc es the desired isomorphism.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuan Gao (USC) DTSTART:20210329T010000Z DTEND:20210329T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/4 DESCRIPTION:Title: The Rabinowitz Fukaya category and applications\nby Yuan Gao (US C) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nThe goal of the t alk is to introduce the Rabinowitz (wrapped) Fukaya category\, as an open- string analogue of Rabinowitz Floer homology of (the boundary at infinity of) a Liouville manifold\, which is a categorical invariant of exact cylin drical Lagrangians whose cohomology morphisms measure the failure of wrapp ed Floer cohomology to satisfy Poincare duality. The main result\, answeri ng a conjecture of Abouzaid\, relates this category to the usual wrapped F ukaya category by a canonical algebraic formula\, in terms of the categori cal formal punctured neighborhood of infinity introduced by Efimov. As an application\, we shall see a few new computations in Floer theory via homo logical mirror symmetry. In addition\, we are going to explore the open-cl osed string relationship and derive structural and computational results i n both Rabinowitz Floer homology and symplectic cohomology. This is based on joint work with Sheel Ganatra and Sara Venkatesh.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Mclean (Stony Brook) DTSTART:20210405T010000Z DTEND:20210405T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/5 DESCRIPTION:Title: Floer Cohomology and Arc Spaces\nby Mark Mclean (Stony Brook) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nLet f be a polynomial over the 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 spac e 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 dth power of the Milnor monodromy map is isomorphic to compactly su pported cohomology of the dth contact locus. This answers a question of Pa ul Seidel and it also proves a conjecture of Nero Budur\, Javier Fernánde z de Bobadilla\, Quy Thuong Lê and Hong Duc Nguyen. The key idea of the p roof is to use a jet space version of the PSS map together with a filtrati on argument.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Smith (Cambridge) DTSTART:20210419T080000Z DTEND:20210419T090000Z DTSTAMP:20260404T111006Z UID:IBSCGP/6 DESCRIPTION:Title: Fukaya categories of quasihomogeneous polynomials\nby Jack Smith (Cambridge) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nBerglun d-Hübsch mirror symmetry predicts that for certain 'transpose' pairs of q uasihomogeneous polynomials\, the Fukaya-Seidel category of one is equival ent to a category of matrix factorisations of the other. The difficulty in proving this is that the natural types of objects to consider on the two sides do not match up with each other. I will introduce an enlarged versio n of the Fukaya-Seidel category that contains the missing objects\, and ou tline how this allows one to prove B-H mirror symmetry. This is joint work in progress with Benjamin Gammage.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgios Dimitroglou Rizell (Uppsala) DTSTART:20210426T080000Z DTEND:20210426T090000Z DTSTAMP:20260404T111006Z UID:IBSCGP/7 DESCRIPTION:Title: Lagrangian Poincaré Recurrence via pseudoholomorphic foliations \nby Georgios Dimitroglou Rizell (Uppsala) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nFor any Hamiltonian displaceable closed curve insid e a closed symplectic surface\, there is a bound on the number of pairwise disjoint Hamiltonian isotopic copies of the curve that one can produce. T his phenomenon is called Lagrangian Poincaré Recurrence\, and it was only shown very recently by Polterovich and Shelukhin that there exist displac eable Lagrangians in higher dimension that satisfy the analogous property. In this work in progress joint with E. Opshtein\, we use the technique of pseudoholomorphic foliations to show that the bound on the number of disj oint copies in the surface persists after increasing the dimension by the following stabilisation: take the cartesian product of the symplectic surf ace with a sufficiently small symplectic annulus\, and take the product of the curve with the with the core of the annulus to produce a Lagrangian t orus.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Wei Fan (UC Berkerley) DTSTART:20210607T010000Z DTEND:20210607T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/8 DESCRIPTION:Title: Shifting numbers in triangulated categories\nby Yu-Wei Fan (UC B erkerley) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nOne can co nsider endofunctors of triangulated categories as dynamical systems\, and study their long term behaviors under large iterations. There are (at leas t) three natural invariants that one can associate to endofunctors from th e dynamical perspective: categorical entropy\, and upper/lower shifting nu mbers. We will recall some background on categorical dynamical systems and categorical entropy\, and introduce the notion of shifting numbers\, whic h measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category. The shifting numbers are analogou s to Poincare translation numbers. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of auto equivalences. Joint work with Simion Filip.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hansol Hong (Yonsei) DTSTART:20210412T010000Z DTEND:20210412T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/9 DESCRIPTION:Title: Scattering diagrams from blowups of toric surfaces\nby Hansol Ho ng (Yonsei) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nGross-Ha cking-Keel has shown that any cluster variety can be obtained by a sequenc e of (nontoric) blow-ups and blow-downs starting from a toric variety. Mot ivated by this\, we study the effect of blowup on the Lagrangian torus fib ration 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 resu lting fibration on the blowup produces a scattering diagram that matches w ith the one constructed by Gross-Pandharipande-Siebert using algebraic cur ve counting. The talk is based on the work in progress jointly with Sam Ba rdwell-Evans\, Man-Wai Mandy Cheung and Yu-Shen Lin.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Nate Bottman (Max Planck) DTSTART:20210503T010000Z DTEND:20210503T020000Z DTSTAMP:20260404T111006Z 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)-category Symp\, which is currently under construction by myself and my collaborators\, is a 2-category-like structure whose objects are symplect ic manifolds and where hom(M\,N) := Fuk(M^- x N). Symp is a coherent algeb raic structure which encodes the functoriality properties of the Fukaya ca tegory. This talk will begin with the following question: what can say abo ut the part of Symp that knows only about a single symplectic manifold M\, and the diagonal Lagrangian correspondence from M to itself? We expect th at the answer to this question should be a chain-level algebraic structure on symplectic cohomology\, and in this talk I will present progress towar d confirming this. Specifically\, I will present a "simplicial version" of the 2-dimensional Fulton-MacPherson operad. If there is time\, I will dis cuss work-in-progress with Felix Janda and Paolo Salvatore that aims to co mplete this answer.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Renato Vianna (Rio de Janeiro) DTSTART:20210621T010000Z DTEND:20210621T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/11 DESCRIPTION:Title: Sharp Ellipsoid Embeddings and Toric Mutations\nby Renato Viann a (Rio de Janeiro) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nW e will show how to construct volume filling ellipsoid embeddings in some 4 -dimensional toric domain using mutation of almost toric compactification of those. In particular we recover the results of McDuff-Schlenk for the b all\, Fenkel-Müller for the product of symplectic disks and Cristofaro-Ga rdiner for E(2\,3)\, giving a more explicit geometric perspective for thes e results. To be able to represent certain divisors\, we develop the idea of symplectic tropical curves in almost toric fibrations\, inspired by Mik halkin's work for tropical curves. This is joint work with Roger Casals.\n Obs: The same result appears in "On infinite staircases in toric symplecti c four-manifolds"\, by Cristofaro-Gardiner -- Holm -- Mandini -- Pires. Bo th papers were posted simultaneously on arXiv.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Kwokwai Chan (CUHK) DTSTART:20210628T010000Z DTEND:20210628T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/12 DESCRIPTION:Title: An algebraic model for smoothing Calabi-Yau varieties and its appli cations\nby Kwokwai Chan (CUHK) as part of IBS-CGP weekly zoom seminar \n\n\nAbstract\nWe are interested in smoothing of a degenerate Calabi-Yau variety or a pair (degenerate CY\, sheaf). I will explain an algebraic fra mework 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 object is only an almost dg Lie algebra (or pre-dg Lie algebra)\, it is sufficient to prove unobstructedness of the associated Maurer-Cartan eq uation (a kind of Bogomolov-Tian-Todorov theorem) under suitable assumptio ns\, so the former can be regarded as a singular version of the Kodaira-Sp encer DGLA. Our framework applies to degenerate CY varieties previously st udied by Kawamata-Namikawa and Gross-Siebert\, as well as a more general c lass of varieties called toroidal crossing spaces (by the recent work of F elten-Filip-Ruddat). This talk is based on various joint works with Conan Leung\, Ziming Ma and Y.-H. Suen.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Egor Shelukhin (Montreal) DTSTART:20210510T010000Z DTEND:20210510T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/13 DESCRIPTION:Title: Lagrangian configurations and Hamiltonian maps\nby Egor Shelukh in (Montreal) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nWe stu dy configurations of disjoint Lagrangian submanifolds in certain low-dimen sional symplectic manifolds from the perspective of the geometry of Hamilt onian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere equipped with Hofer's metric\, showing in particular tha t this group is not quasi-isometric to a line. This answers a well-known q uestion of Kapovich-Polterovich from 2006. We show that these flats in Ham (S^2) stabilize to certain product four-manifolds\, prove constraints on L agrangian packing\, find new instances of Lagrangian Poincare recurrence\, and present a new hierarchy of normal subgroups of area-preserving homeom orphisms of the two-sphere. The technology involves Lagrangian spectral in variants in symmetric product orbifolds. This is joint work with Leonid Po lterovich.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Xujia Chen (IAS) DTSTART:20210517T010000Z DTEND:20210517T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/14 DESCRIPTION:Title: Lifting cobordisms and Kontsevich-type recursions for counts of rea l curves\nby Xujia Chen (IAS) as part of IBS-CGP weekly zoom seminar\n \n\nAbstract\nKontsevich's recursion\, proved in the early 90s\, is a recu rsion formula for the counts of rational holomorphic curves in complex man ifolds. For complex fourfolds and sixfolds with a real structure (i.e. a c onjugation)\, signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger's inv ariants as holomorphic disk counts in 2006 and proposed Kontsevich-type re cursions for them in 2007\, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds\, these recurs ions determine all invariants from basic inputs. We establish Solomon's re cursions by re-interpreting his disk counts as degrees of relatively orien ted pseudocycles from moduli spaces of stable real maps and lifting cobord isms from Deligne-Mumford moduli spaces of stable real curves (which is di fferent from Solomon's approach).\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeff Hicks (Cambridge) DTSTART:20210524T010000Z DTEND:20210524T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/15 DESCRIPTION:Title: Lagrangian Cobordism and Lagrangian Surgery\nby Jeff Hicks (Cam bridge) as part of IBS-CGP weekly zoom seminar\n\nLecture held in Zoom onl ine.\n\nAbstract\nA Lagrangian cobordism is a Lagrangian submanifold in X x C whose "ends" are Lagrangian submanifolds inside of X. We will show tha t the Lagrangian cobordisms associated to the Lagrangian surgery operation provide the building blocks for all Lagrangian cobordisms. Finally\, we w ill discuss some of the Floer theoretic implications of this decomposition \, extending previous work of Biran and Cornea. This is based on work from arxiv:2102.10197.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Jootae Kim (KIAS) DTSTART:20210531T010000Z DTEND:20210531T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/16 DESCRIPTION:Title: Real Lagrangian tori in monotone symplectic 4-manifolds\nby Joo tae Kim (KIAS) as part of IBS-CGP weekly zoom seminar\n\nLecture held in Z oom online.\n\nAbstract\nBy a real Lagrangian\, we mean the fixed point se t of an anti-symplectic involution in a symplectic manifold. In this talk\ , we explore the topology of real Lagrangian tori in monotone symplectic 4 -manifolds. They are very rare in the sense that all known exotic monotone Lagrangian tori cannot be real\, but they exist exactly when no topologic al obstructions occur. The disc potential plays an intriguing role in our voyage.\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Wonbo Jeong (SNU) DTSTART:20210614T010000Z DTEND:20210614T020000Z DTSTAMP:20260404T111006Z UID:IBSCGP/17 DESCRIPTION:Title: Noncompact description for Fukaya-Seidel categories of invertible c urve singularities\nby Wonbo Jeong (SNU) as part of IBS-CGP weekly zoo m seminar\n\nLecture held in Zoom online.\n\nAbstract\nFor given invertibl e polynomial W\, we consider two types of Fukaya category. One is the usua l Fukaya-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 q uantum cap action of monodromy orbit. In this talk\, we compare the equiva riant lift of the latter with the Fukaya-Seidel category and prove its der ived equivalence for invertible curve singularities. In particular\, direc tedness of the category is obtained from quantum cap action and related co nstructions. This talk is based on the joint work (in progress) with Cheol -hyun Cho (SNU) and Dongwook Choa (KIAS).\n LOCATION:https://stable.researchseminars.org/talk/IBSCGP/17/ END:VEVENT END:VCALENDAR