researchseminars.org

Hiro Lee Tanaka (Texas State University)
2020-04-17 16:00 - 17:00 UTC | https://researchseminars.org/talk/WHSymplectic/1/
Title: Formalisms of gluing Fukaya categories (https://researchseminars.org/talk/WHSymplectic/1/)
by Hiro Lee Tanaka (Texas State University) as part of Western Hemisphere virtual symplectic seminar

Abstract
In the Weinstein setting, we know that wrapped Fukaya categories glue, so it behooves us to understand a general framework that captures the properties of this gluing. After explaining a few approaches of how to formalize gluing procedures in the 2-dimensional setting, we'll explain why we think a framework inspired by factorization homology seems most promising to capture the general behavior of local-to-global invariants of Weinstein sectors. Setting up this formalism sheds insights into things like the following: (a) We can classify all local-to-global invariants of 2-dimensional Liouville sectors. (b) We see that the Floer theory of Lagrangian cobordisms in R^oo recovers the higher K theory of the integers. (We have been unable to compute this higher K theory for decades, and a computation would yield powerful results in arithmetic.) (c) Wrapped Floer theory can shed insight into higher homotopy groups of Liouville embedding spaces.

Andrew Hanlon (Simons Center)
2020-04-17 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/2/
Title: On Fukaya-Seidel categories mirror to toric varieties (https://researchseminars.org/talk/WHSymplectic/2/)
by Andrew Hanlon (Simons Center) as part of Western Hemisphere virtual symplectic seminar

Abstract
We will discuss one way of defining a Fukaya-Seidel category mirror to a toric variety and use it to understand homological mirror symmetry in this setting. Along the way, we will see how this Fukaya-Seidel category relates to more traditional definitions. This is partly based on joint work in progress with Jeff Hicks.

Abigail Ward (Harvard)
2020-04-24 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/3/
Title: Homological mirror symmetry for elliptic Hopf surfaces (https://researchseminars.org/talk/WHSymplectic/3/)
by Abigail Ward (Harvard) as part of Western Hemisphere virtual symplectic seminar

Abstract
One can produce non-Kähler complex surfaces by performing logarithmic transformations on projective elliptic surfaces; for example, elliptic Hopf surfaces (including the classical Hopf surface $S^1 \times S^3$) can be obtained by performing such operations to the product of the projective plane with an elliptic curve. In situations where the original surface has a mirror symplectic space, one can ask if there is a "mirror operation" to the logarithmic transformation, i.e. a way of producing a mirror to the logarithmically transformed surface from the original mirror space. We will discuss an answer to this question in the case of elliptic Hopf surfaces. For each such surface $S$, we will produce a mirror "non-algebraic Landau-Ginzburg model" with an associated Fukaya category. We will relate objects of this Fukaya category to coherent analytic sheaves on $S$.

Yu Pan (MIT)
2020-04-24 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/4/
Title: Augmentations and exact Lagrangian surfaces (https://researchseminars.org/talk/WHSymplectic/4/)
by Yu Pan (MIT) as part of Western Hemisphere virtual symplectic seminar

Abstract
Augmentations are some algebraic invariants of Legendrians that are tightly related to both embedded and immersed exact Lagrangian fillings. We will talk about various relations between embedded and immersed exact Lagrangian surfaces using tools related to augmentations.

Tim Large (MIT)
2020-05-01 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/5/
Title: Floer K-theory and exotic Liouville manifolds (https://researchseminars.org/talk/WHSymplectic/5/)
by Tim Large (MIT) as part of Western Hemisphere virtual symplectic seminar

Abstract
In this talk, we will explain how to construct Liouville manifolds which have vanishing symplectic cohomology but non-vanishing symplectic K-theory. In particular, we construct an exotic symplectic structure on Euclidean space which is not distinguished by traditional Floer homology invariants. Instead, it is detected by a module spectrum for complex K-theory, built as a variant of Cohen-Jones-Segal’s Floer homotopy type. The proof involves passage through (wrapped) Fukaya categories with coefficients in a ring spectrum, rather than an ordinary ring; we will outline the construction of such "spectral Fukaya categories" in the setting of exact symplectic manifolds.

Jo Nelson (Rice) and Morgan Weiler (Berkeley)
2020-05-01 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/6/
Title: ECH of prequantization bundles and lens spaces (https://researchseminars.org/talk/WHSymplectic/6/)
by Jo Nelson (Rice) and Morgan Weiler (Berkeley) as part of Western Hemisphere virtual symplectic seminar

Abstract
In 2011, Farris provided an expected dictionary between counts of pseudoholomorphic cylinders and Z_2-graded embedded contact homology (ECH) of prequantization bundles over Riemann surfaces. We upgrade to a full Z-grading, and in combination with the domain dependent methods introduced by Farris in his thesis, make use of the direct limits for filtered ECH established in Hutchings-Taubes proof of the Arnold-Chord conjecture to extend the Morse-Bott methods for prequantization bundles to the realm of ECH. In particular, we establish that the ECH of a prequantization bundle over a Riemann surface is isomorphic to the exterior algebra of the homology of this base. We comment on future work, which relates the U map in ECH to Gromov-Witten invariants of the base, permitting computations of the associated ECH capacities and an expected stabilization result purely in the context of ECH.

Semon Rezchikov (Columbia)
2020-05-08 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/7/
Title: Generalizations of Hodge-de-Rham degeneration for Fukaya categories (https://researchseminars.org/talk/WHSymplectic/7/)
by Semon Rezchikov (Columbia) as part of Western Hemisphere virtual symplectic seminar

Abstract
Hodge theory shows that the Hodge-de-Rham spectral sequence associated to a compact Kahler manifold degenerates. Kaledin showed that the non-commutative Hodge-de-Rham spectral sequence associated to a smooth proper dg-category over a field of characteristic zero degenerates as well. When the category is just smooth or just proper, Kontsevich conjectured that certain weaker statements, which are true for smooth or proper varieties, should continue to hold in the categorical setting. Recently, counterexamples to Kontsevich's conjectures were found by Efimov. I will discuss the background to this story, and then I will explain why the conjectures of Kontsevich do hold, for analytic reasons, when the category is a Fukaya category. The argument suggests interesting directions to explore regarding the homological algebra of PROPs of surfaces.

Melissa Zhang (University of Georgia)
2020-05-08 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/8/
Title: An annular filtration on Sarkar-Seed-Szabó's spectral sequence (https://researchseminars.org/talk/WHSymplectic/8/)
by Melissa Zhang (University of Georgia) as part of Western Hemisphere virtual symplectic seminar

Abstract
Khovanov homology is a combinatorial invariant of links in the three-sphere borne from structures in representation theory. Nevertheless, there are many spectral sequences relating Khovanov homology to geometrically-defined invariants, such as Ozsváth-Szabó's Heegaard Floer homology. Seidel-Smith defined its geometric counterpart, symplectic Khovanov homology, which Abouzaid-Smith showed is indeed isomorphic to combinatorial Khovanov homology over characteristic 0. Inspired by symplectic Khovanov homology's O(2) action, Sarkar-Seed-Szabó extended Szabó's geometric spectral sequence, which is a combinatorial spectral sequence conjectured to be isomorphic to Ozsváth-Szabó's spectral sequence (from the Khovanov homology of a knot to the Heegaard Floer homology of the branched double cover of its mirror knot). A bifiltered version of this complex admits a family of Rasmussen-type link invariants.

In joint work with Linh Truong, we show that for links in a solid torus (i.e. annular links), Sarkar-Seed-Szabó's complex admits third filtration. This annular filtration allows us to define a 2-parameter family of annular concordance invariants s_{r,t} analogous to Grigsby-Licata-Wehrli's annular Rasmussen invariants d_t (from annular Khovanov-Lee theory). The two families share many properties, including applications to 3D contact geometry and smooth knot concordance.

Xujia Chen (Stony Brook University)
2020-05-15 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/9/
Title: Lifting cobordisms and Kontsevich-type recursions for counts of real curves (https://researchseminars.org/talk/WHSymplectic/9/)
by Xujia Chen (Stony Brook University) as part of Western Hemisphere virtual symplectic seminar

Abstract
Kontsevich's recursion, proved by Ruan-Tian in the early 90s, is a recursion formula for genus 0 Gromov-Witten invariants. For symplectic fourfolds and sixfolds with a real structure (i.e. an anti-symplectic involution, analogue of the usual conjugation map on C^n), signed invariant counts of real rational pseudo-holomorphic curves were defined by Welschinger in 2003. In 2006-07, Solomon re-interpreted Welschinger's invariants, proposed Kontsevich-type recursion formulas for them, and suggested a potential adaptation of the proof in the complex case for confirming them. For many symplectic fourfolds and sixfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by a different approach: lifting cobordisms from the moduli spaces of real domains to the moduli space of real maps and incorporating the wall-crossing corrections from the walls obstructing relative-orientability.

Jack Smith (Cambridge University)
2020-05-22 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/10/
Title: Towards Berglund-Hübsch mirror symmetry (https://researchseminars.org/talk/WHSymplectic/10/)
by Jack Smith (Cambridge University) as part of Western Hemisphere virtual symplectic seminar

Abstract
An $n \times n$ non-negative integer matrix encodes an $n$-term polynomial in $n$ variables, by using each column to define the exponents in one monomial. Berglund and Hübsch predicted that the polynomials associated to transpose matrices should have mirror Landau-Ginzburg models; precisely, the Fukaya-Seidel category of one polynomial should be equivalent to graded matrix factorisations of the other. I'll describe a new strategy for attacking this conjecture, based on joint work in progress with Benjamin Gammage.

Ko Honda (UCLA)
2020-05-22 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/11/
Title: Convex hypersurface theory in higher-dimensional contact topology (https://researchseminars.org/talk/WHSymplectic/11/)
by Ko Honda (UCLA) as part of Western Hemisphere virtual symplectic seminar

Abstract
Convex surface theory and bypasses are extremely powerful tools for analyzing contact 3-manifolds. In particular they have been successfully applied to many classification problems. After briefly reviewing convex surface theory in dimension three, we explain how to generalize many of their properties to higher dimensions. This is joint work with Yang Huang.

Oleg Lazarev (Columbia University)
2020-05-15 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/12/
Title: Weinstein geometry of cotangent bundles (https://researchseminars.org/talk/WHSymplectic/12/)
by Oleg Lazarev (Columbia University) as part of Western Hemisphere virtual symplectic seminar

Abstract
Although the cotangent bundle of a sphere $T^*S^n$ has very few closed exact Lagrangians (conjecturally only one), we will explain that it has many singular Lagrangians in the form of Weinstein subdomains. We first produce flexible subdomains of $T^*S^n$, which in high-dimensions yield exotic Weinstein presentations for $T^*S^n$ as the standard ball with a single handle attached along an exotic Legendrian knot. The algebraic side of the story for the wrapped Fukaya category is closely connected to a result of Thomason in algebraic K-theory. Then we discuss joint work with Z. Sylvan that associates to every finite collection of prime integers a (non-flexible) Weinstein subdomain of $T^*S^n$ whose Fukaya category is localized at those primes and show that the Fukaya category of any Weinstein subdomain is one of these prime localizations.

Ailsa Keating (Cambridge)
2020-05-29 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/13/
Title: Homological mirror symmetry for log Calabi-Yau surfaces (https://researchseminars.org/talk/WHSymplectic/13/)
by Ailsa Keating (Cambridge) as part of Western Hemisphere virtual symplectic seminar

Abstract
Given a log Calabi-Yau surface Y with maximal boundary D, I'll explain how to construct a mirror Landau-Ginzburg model, and sketch a proof of homological mirror symmetry for these pairs when (Y,D) is distinguished within its deformation class (this is mirror to an exact manifold). I'll explain how to relate this to the total space of the SYZ fibration predicted by Gross-Hacking-Keel, and, time permitting, explain ties with earlier work of Auroux-Katzarkov-Orlov and Abouzaid. Joint work with Paul Hacking.

Jeff Hicks (Cambridge)
2020-05-29 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/14/
Title: Lagrangian surgery and Lagrangian cobordis (https://researchseminars.org/talk/WHSymplectic/14/)
by Jeff Hicks (Cambridge) as part of Western Hemisphere virtual symplectic seminar

Abstract
Lagrangian cobordisms form an equivalence relation on Lagrangian submanifolds of a symplectic manifold X. In the monotone setting, the work of Biran and Cornea show that cobordant Lagrangian submanifolds have equivalent Floer homology. However, to date the only known 2-ended monotone Lagrangian cobordisms are those constructed as the suspension of a Hamiltonian isotopy. This talk will explain how Lagrangian cobordism can be decomposed into models based on Haug antisurgeries. I will also speculate about the relation between Biran and Cornea's work on iterated exact triangles and the Fukaya, Oh, Ohta, and Ono surgery exact triangle in the context of this decomposition.

Daniel Álvarez-Gavela (Princeton)
2020-06-05 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/15/
Title: The nearby Lagrangian conjecture from the K-theoretic viewpoint (https://researchseminars.org/talk/WHSymplectic/15/)
by Daniel Álvarez-Gavela (Princeton) as part of Western Hemisphere virtual symplectic seminar

Abstract
In this talk I will explain some connections between the nearby Lagrangian conjecture and the algebraic K-theory of spaces. These connections have opened up as a consequence of the recent existence result for (twisted) generating functions due to Abouzaid, Courte, Guillermou and Kragh. In work in progress joint with Abouzaid, Courte and Kragh we find that a certain geometric description of the splitting map for the algebraic K-theory of a point due to Waldhausen and Bökstedt gives a new restriction on the framed bordism class of nearby Lagrangians. In particular I will show that if L is any Lagrangian homotopy sphere in the cotangent bundle of the standard sphere, then the connected sum of L with itself bounds a parallelizable manifold. This extends known constraints for the possible class of L in the group of homotopy spheres modulo those which bound a parallelizable manifold. I will also touch on joint work with Igusa concerning the higher torsion of Legendrians in 1-jet spaces and make some speculations about the higher torsion of nearby Lagrangians.

Kristen Hendricks (Rutgers)
2020-06-05 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/16/
Title: A surgery exact triangle for involutive Heegaard Floer homology, and consequences (https://researchseminars.org/talk/WHSymplectic/16/)
by Kristen Hendricks (Rutgers) as part of Western Hemisphere virtual symplectic seminar

Abstract
We construct a surgery exact triangle in the involutive variant of Ozsvath and Szabo's Heegaard Floer homology, and give an application to the structure of the integer homology cobordism group. This is joint work in progress with J. Hom, M. Stoffregen, and I. Zemke.

Sushmita Venugopalan (IMS Chennai)
2020-06-12 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/17/
Title: Tropical Fukaya algebras (https://researchseminars.org/talk/WHSymplectic/17/)
by Sushmita Venugopalan (IMS Chennai) as part of Western Hemisphere virtual symplectic seminar

Abstract
A multiple cut operation on a symplectic manifold produces a collection of cut spaces, each containing relative normal crossing divisors. We explore what happens to curve count-based invariants when a collection of cuts is applied to a symplectic manifold. The invariant we consider is the Fukaya algebra of a Lagrangian submanifold that is contained in the complement of relative divisors. The ordinary Fukaya algebra in the unbroken manifold is homotopy equivalent to a `broken Fukaya algebra' whose structure maps count `broken disks' associated to rigid tropical graphs. Via a further degeneration, the broken Fukaya algebra is homotopy equivalent to a `tropical Fukaya algebra' whose structure maps are sums of products over vertices of tropical graphs. This is joint work with Chris Woodward.

Zhengyi Zhou (IAS)
2020-06-12 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/18/
Title: (RP^{2n-1}, xi_std) is not exactly fillable for n != 2^k (https://researchseminars.org/talk/WHSymplectic/18/)
by Zhengyi Zhou (IAS) as part of Western Hemisphere virtual symplectic seminar

Abstract
I will show that the 2n-1 dimensional real projective space with the standard contact structure is not exactly fillable when n is not a power of 2. Then I will prove that there exist strongly fillable but not exactly fillable contact manifolds in all dimensions greater than 3. Time permitting, I will explain how a similar approach can be used to obtain uni

Vera Vertesi (Universität Wien)
2020-06-19 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/19/
Title: Cut and paste techniques for open books (https://researchseminars.org/talk/WHSymplectic/19/)
by Vera Vertesi (Universität Wien) as part of Western Hemisphere virtual symplectic seminar

Abstract
Due to their combinatorial nature, open books have been one of the major tools of research for 3-dimensional contact manifolds. In this talk I will introduce a new technique to do cut and paste arguments for open books, and on the way I will introduce a generalisation for open books for contact 3-manifolds with a fixed characteristic foliation on their boundary. These objects are called foliated open books. I will explain that, although more complicated, foliated open books are still combinatorial. I will illustrate their use by proving a result about the additivity of the support norm for tight contact structures. I finish with another application, and show that foliated open books are the natural objects to define the contact invariant in bordered Floer homology. Some of the work presented are joint work with Akram Alishahi, Vikt\'oria F\”oldv\'ari, Kristen Hendricks, Joan Licata and Ina Petkova.

Kenji Fukaya (Simons Center)
2020-06-19 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/20/
Title: SYZ and KAM (https://researchseminars.org/talk/WHSymplectic/20/)
by Kenji Fukaya (Simons Center) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Ivan Smith (Cambridge)
2020-06-26 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/21/
Title: Fukaya categories of surfaces and the mapping class group (https://researchseminars.org/talk/WHSymplectic/21/)
by Ivan Smith (Cambridge) as part of Western Hemisphere virtual symplectic seminar

Abstract
I will explain how to build the classical mapping class group of a closed surface of genus at least two starting from the derived Fukaya category of the surface. The proof illustrates numerous different Floer-theoretic technologies in a concrete case. This talk reports on joint work with Denis Auroux.

Umut Varolgunes (Stanford)
2020-06-26 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/22/
Title: Mirror symmetry for symplectic cluster manifolds (https://researchseminars.org/talk/WHSymplectic/22/)
by Umut Varolgunes (Stanford) as part of Western Hemisphere virtual symplectic seminar

Abstract
I will start by explaining a general framework for constructing non-archimedean analytic mirrors of symplectic manifolds with a Lagrangian fibration using relative symplectic cohomology (including some expected concrete relationships of the A and B-sides). Then I will define symplectic cluster manifolds (conjecturally “half” hyperkahler rotations of smooth Looijenga interiors), which admit a Lagrangian fibration over a topological plane with only focus-focus singularities. These symplectic manifolds are open and geometrically bounded, but not necessarily exact or have contact boundary. Using a general locality result and computations for two local models, I will construct analytic mirrors of symplectic cluster manifolds. Finally, I will describe a conjecture reinterpreting these mirrors as analytifications of certain cluster varieties over the Novikov field (with the same seed data as the Looijenga interior). Joint work with Yoel Groman.

Roger Casals (UC Davis)
2020-07-03 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/23/
Title: Sharp Ellipsoid Embeddings and Toric Mutations (https://researchseminars.org/talk/WHSymplectic/23/)
by Roger Casals (UC Davis) as part of Western Hemisphere virtual symplectic seminar

Abstract
In this talk we will explain how to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in almost-toric varieties. The construction uniformly recovers the sharp embeddings in the Fibonacci Staircase of McDuff-Schlenk, the Pell Staircase of Frenkel-Muller and the Cristofaro-Gardiner-Kleinman's Staircase, and also adds new infinite sequences. I will explain the intuition behind this construction and introduce the two main ingredients for the proof: polytope mutations, following M. Symington and Akhtar-Coates-Galkin-Kasprzyk, and our study of symplectic tropical curves in almost-toric fibrations. This is joint work with R. Vianna.

Dan Cristofaro-Gardiner (UCSC)
2020-07-03 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/24/
Title: Obstructing infinite staircases (https://researchseminars.org/talk/WHSymplectic/24/)
by Dan Cristofaro-Gardiner (UCSC) as part of Western Hemisphere virtual symplectic seminar

Abstract
A landmark result, due to McDuff and Schlenk, asserts that in determining when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional ball, the answer is given by an “infinite staircase” determined by the odd-index Fibonacci numbers and the Golden Mean. There has recently been considerable interest in better understanding this phenomenon for more general embedding problems. I will explain a theorem showing that for any four-dimensional convex toric domain of finite type, if an infinite staircase occurs, then its singular points must accumulate at a unique point, characterized by an explicit quadratic equation. I will then explain how to apply this theorem to prove that when the target is a rational ellipsoid, there is an infinite staircase in precisely three cases -- when the target has "eccentricity" 1, 2, or 3/2; interestingly, in each of these cases, the corresponding embeddings can be constructed explicitly using polytope mutation. Part of this is joint work with Holm, Mandini and Pires, but will not overlap with their talk.

Aliakbar Daemi (WUSTL)
2020-07-10 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/25/
Title: SO(3)-instantons and the Atiyah-Floer Conjecture (https://researchseminars.org/talk/WHSymplectic/25/)
by Aliakbar Daemi (WUSTL) as part of Western Hemisphere virtual symplectic seminar

Abstract
A useful tool to study a 3-manifold is the space of representations of its fundamental group into a Lie group. Any 3-manifold can be decomposed as the union of two handlebodies. Thus representations of the 3-manifold group into a Lie group can be obtained by intersecting representation varieties of the two handlebodies. Casson utilized this observation to define his celebrated invariant. Later Taubes introduced an alternative approach to define Casson invariant using more geometrical objects. By building on Taubes' work, Floer refined Casson invariant into a 3-manifold invariant which is known as instanton Floer homology. The Atiyah-Floer conjecture states that Casson's original approach can be also used to define a graded vector space and the resulting invariant of 3-manifolds is isomorphic to instanton Floer homology. In this talk, I will discuss a variation of the Atiyah-Floer conjecture, which states that framed Floer homology (defined by Kronheimer and Mrowka) is isomorphic to symplectic framed Floer homology (defined by Wehrheim and Woodward). I will explain how the closed-open string map is related to framed Floer homology. Finally I comment on how earlier works of Seidel and Smith might provide useful computational tools for framed Floer homology. This talk is based on a joint work with Kenji Fukaya and Maksim Lipyanskyi.

Xin Jin (Boston College)
2020-07-10 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/26/
Title: Microlocal sheaf categories and the J-homomorphism (https://researchseminars.org/talk/WHSymplectic/26/)
by Xin Jin (Boston College) as part of Western Hemisphere virtual symplectic seminar

Abstract
The theory of microlocal sheaves, developed by Kashiwara--Schapira, has found many applications in the study of symplectic topology. For a smooth Lagrangian L in a cotangent bundle of a smooth manifold and a commutative ring spectrum k, one can associate a sheaf of microlocal categories, which is locally constant with fiber equivalent to Mod(k). It admits a classifying map L--->BPic(k). We will show that the classifying map factors through the Gauss map L--->U/O and the delooping of the J-homomorphism U/O--->BPic(S), where S is the sphere spectrum. As an application, combining with previous results of Guillermou, we show that if L is a compact smooth exact Lagrangian, then the classifying map is homotopically trivial, recovering a result of Abouzaid--Kragh.

Jagna Wiśniewska (ETH Zurich)
2020-07-17 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/27/
by Jagna Wiśniewska (ETH Zurich) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Cheuk Yu Mak (Cambridge)
2020-07-17 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/28/
Title: Symplectic annular Khovanov homology (https://researchseminars.org/talk/WHSymplectic/28/)
by Cheuk Yu Mak (Cambridge) as part of Western Hemisphere virtual symplectic seminar

Abstract
Annular Khovanov homology is an invariant of annular links (links in a solid torus) introduced by Asaeda-Przytycki-Sikora as an analogue of Khovanov homology for links. Auroux-Grigsby-Wehrli showed that the first piece of the annular Khovanov homology can be identified with the Hochschild homology of the Fukaya-Seidel category of A_n Milnor fibers with coefficients in braid bimodules. In this talk, we will introduce a symplectic version of annular Khovanov homology using Hochschild homology of the Fukaya-Seidel category of more general type A nilpotent slices. Building on the work of Abouzaid-Smith and Beliakova-Putyra-Wehrli, we show that the symplectic version is isomorphic to the ordinary version. Finally, we will explain how to derive a spectral sequence from the symplectic annular Khovanov homology to the symplectic Khovanov homology directly using symplectic geometry. This is based on a joint work with Ivan Smith.

Eva Miranda (Universitat Politècnica de Catalunya)
2020-07-24 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/29/
Title: The singular Weinstein conjecture (https://researchseminars.org/talk/WHSymplectic/29/)
by Eva Miranda (Universitat Politècnica de Catalunya) as part of Western Hemisphere virtual symplectic seminar

Abstract
The purpose of this talk is to present some recent results concerning Reeb dynamics on a $b^m$-contact manifolds. b-Contact manifolds (and more generally b^m´-contact manifolds) are the odd-dimensional counterpart to $b^m$-symplectic manifolds which have been a center of attention in Poisson Geometry. The study of $b^m$-Reeb dynamics is motivated by well-known problems in fluid dynamics (Beltrami fields) and celestial mechanics, where those geometric structures naturally appear.

The first part of the talk will focus on the singular Weinstein conjecture following https://arxiv.org/abs/2005.09568 (joint work with Cédric Oms). We prove that in dimension 3 there are always infinite periodic orbits on the critical set (if compact). In particular, we will prove that the dynamics on positive energy level-sets in the restricted planar circular three-body problem are described by the Reeb vector field of a $b^3$-contact form that admits an infinite number of periodic orbits at the critical set. This investigation goes hand-in-hand with the Weinstein conjecture on non-compact manifolds having compact ends of convex type. In particular, we extend Hofer's arguments to open overtwisted contact manifolds that are $\R^+$-invariant in the open ends, obtaining as a corollary the existence of periodic $b^m$-Reeb orbits away from the critical set.

At the end of the talk, we will focus on singular Reeb orbits (joint work with Cédric Oms and Daniel Peralta-Salas). Inspired by Poincaré's orbits going to infinity in the (restricted) three-body problem, we investigate the existence of singular Reeb orbits emanating from/going to the critical set and we prove their existence for generic Melrose b-contact structures. In the proof, we use the correspondence between b-Beltrami vector fields and b-contact structures.

Egor Shelukhin (University of Montreal)
2020-07-24 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/30/
Title: Smith theory in filtered Floer homology and Hamiltonian diffeomorphisms (https://researchseminars.org/talk/WHSymplectic/30/)
by Egor Shelukhin (University of Montreal) as part of Western Hemisphere virtual symplectic seminar

Abstract
We describe how Smith theory applies in the setting of Hamiltonian Floer homology filtered by the action functional, and provide applications to questions regarding Hamiltonian diffeomorphisms, including the Hofer-Zehnder conjecture on the existence of infinitely many periodic points.

Chris Woodward (Rutgers)
2020-10-09 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/31/
Title: Towards a Lagrangian minimal model program (https://researchseminars.org/talk/WHSymplectic/31/)
by Chris Woodward (Rutgers) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Yusuf Barış Kartal (Princeton)
2020-10-23 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/32/
Title: Iterates of symplectomorphisms and p-adic analytic actions (https://researchseminars.org/talk/WHSymplectic/32/)
by Yusuf Barış Kartal (Princeton) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Yuhan Sun (Rutgers)
2020-11-06 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/33/
Title: Some computations of relative symplectic cohomology (https://researchseminars.org/talk/WHSymplectic/33/)
by Yuhan Sun (Rutgers) as part of Western Hemisphere virtual symplectic seminar

Abstract
Relative symplectic cohomology, constructed by U.Varolgunes, provides a useful tool to study topological and dynamical properties of closed subsets in a symplectic manifold. I will discuss several computational aspects about it, with a focus on index bounded Liouville domains in Calabi-Yau manifolds. In particular, a spectral sequence will be defined in this case. If time permits, some thought of the homologically index bonded case will also be explained.

Ben Wormleighton (Washington University)
2020-11-13 20:00 - 21:00 | https://researchseminars.org/talk/WHSymplectic/34/
Title: Asymptotics of ECH capacities via algebraic positivity (https://researchseminars.org/talk/WHSymplectic/34/)
by Ben Wormleighton (Washington University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Artem Kotelskiy (Indiana)
2020-10-30 19:00 - 20:00 | https://researchseminars.org/talk/WHSymplectic/35/
Title: Khovanov homology via immersed curves (https://researchseminars.org/talk/WHSymplectic/35/)
by Artem Kotelskiy (Indiana) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Mohan Swaminathan (Princeton)
2020-11-20 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/36/
Title: Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds (https://researchseminars.org/talk/WHSymplectic/36/)
by Mohan Swaminathan (Princeton) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Cecilia Karlsson (Oslo)
2020-12-11 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/37/
Title: Legendrian contact homology for Weinstein handle attachments in higher dimensions (https://researchseminars.org/talk/WHSymplectic/37/)
by Cecilia Karlsson (Oslo) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Shira Tanny (Tel-Aviv University)
2021-01-29 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/38/
by Shira Tanny (Tel-Aviv University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Penka Georgieva (Jussieu Institute of Mathematics)
2021-02-05 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/39/
Title: Klein TQFT and real Gromov-Witten invariants (https://researchseminars.org/talk/WHSymplectic/39/)
by Penka Georgieva (Jussieu Institute of Mathematics) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Yu-Shen Lin (Boston University)
2021-02-12 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/40/
Title: SYZ Mirror Symmetry on P^2 and Enumerative Geometry (https://researchseminars.org/talk/WHSymplectic/40/)
by Yu-Shen Lin (Boston University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Honghao Gao (Michigan State University)
2021-02-19 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/41/
Title: Augmentations, fillings, and clusters (https://researchseminars.org/talk/WHSymplectic/41/)
by Honghao Gao (Michigan State University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Simon Allais (ENS Lyon)
2021-02-26 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/42/
Title: Periodic points of Hamiltonian diffeomorphisms and generating functions (https://researchseminars.org/talk/WHSymplectic/42/)
by Simon Allais (ENS Lyon) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Arnav Tripathy (Harvard University)
2021-03-05 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/43/
Title: K3 metrics and disk counting (https://researchseminars.org/talk/WHSymplectic/43/)
by Arnav Tripathy (Harvard University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Orsola Capovilla-Searle / Angela Wu (Duke / UCL)
2021-03-12 17:00 - 18:00 | https://researchseminars.org/talk/WHSymplectic/44/
Title: Weinstein handlebodies for complements of smoothed toric divisors (https://researchseminars.org/talk/WHSymplectic/44/)
by Orsola Capovilla-Searle / Angela Wu (Duke / UCL) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Melissa Liu (Columbia University)
2021-04-02 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/45/
Title: Topological Recursion and Crepant Transformation Conjecture (https://researchseminars.org/talk/WHSymplectic/45/)
by Melissa Liu (Columbia University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Heather Lee (University of Washington)
2021-04-30 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/46/
by Heather Lee (University of Washington) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Olga Plamenevskaya (Stony Brook University)
2021-05-07 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/47/
by Olga Plamenevskaya (Stony Brook University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Yael Karshon (Toronto University)
2021-02-26 20:00 - 21:00 | https://researchseminars.org/talk/WHSymplectic/48/
by Yael Karshon (Toronto University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Susan Tolman (Illinois)
2021-04-09 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/50/
Title: Beyond semitoric (https://researchseminars.org/talk/WHSymplectic/50/)
by Susan Tolman (Illinois) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Bulent Tosun (Alabama)
2021-04-23 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/51/
Title: On embedding problems for 3-manifolds in 4-space (https://researchseminars.org/talk/WHSymplectic/51/)
by Bulent Tosun (Alabama) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Francisco Presas (ICMAT)
2021-03-26 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/52/
Title: The homotopy type of the contactomorphism group of a contact $3$-fold (https://researchseminars.org/talk/WHSymplectic/52/)
by Francisco Presas (ICMAT) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Tobias Ekholm (Uppsala)
2021-04-16 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/53/
Title: Skein module curve counts and recursion (https://researchseminars.org/talk/WHSymplectic/53/)
by Tobias Ekholm (Uppsala) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Noémie Legout (Uppsala)
2021-03-19 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/54/
Title: A-infinity category of Lagrangian cobordisms (https://researchseminars.org/talk/WHSymplectic/54/)
by Noémie Legout (Uppsala) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Yoel Groman (Hebrew University)
2021-06-11 15:00 - 16:00 | https://researchseminars.org/talk/WHSymplectic/55/
Title: Torsion of non-exact embeddings of Liouville domains (https://researchseminars.org/talk/WHSymplectic/55/)
by Yoel Groman (Hebrew University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Eleny Ionel (Stanford University)
2021-06-18 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/56/
Title: Counting embedded curves in 3-folds (https://researchseminars.org/talk/WHSymplectic/56/)
by Eleny Ionel (Stanford University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Marco Castronovo (Rutgers University)
2021-06-25 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/57/
Title: Fukaya category of Grassmannians: bootstrap and mutation (https://researchseminars.org/talk/WHSymplectic/57/)
by Marco Castronovo (Rutgers University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Kai Cieliebak (Universität Augsburg)
2021-07-09 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/58/
Title: Sullivan's relation in Rabinowitz Floer homology and loop space homology (https://researchseminars.org/talk/WHSymplectic/58/)
by Kai Cieliebak (Universität Augsburg) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Dusa McDuff (Columbia University), Nicki Magill (Cornell University), and Morgan Weiler (Rice University)
2021-07-30 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/59/
Title: Recursive staircase patterns in Hirzebruch surfaces (https://researchseminars.org/talk/WHSymplectic/59/)
by Dusa McDuff (Columbia University), Nicki Magill (Cornell University), and Morgan Weiler (Rice University) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Sobhan Seyfaddini (Jussieu)
2021-07-23 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/60/
Title: The algebraic structure of groups of area-preserving homeomorphisms (https://researchseminars.org/talk/WHSymplectic/60/)
by Sobhan Seyfaddini (Jussieu) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA

Mina Aganagic (UC Berkeley)
2021-07-16 16:00 - 17:00 | https://researchseminars.org/talk/WHSymplectic/61/
Title: Knot homologies from mirror symmetry (https://researchseminars.org/talk/WHSymplectic/61/)
by Mina Aganagic (UC Berkeley) as part of Western Hemisphere virtual symplectic seminar

Abstract: TBA
