GT GAPS is an online seminar (via Zoom) for graduate students and postdoctoral scholars studying geometric topology. In Spring 2024, we meet **Fridays 9 am PT/ 12pm EDT/ 5pm CET/ 9:30pm IST**.

Each week, someone (a student or postdoc) gives a talk by Zoom that lasts about one hour. Many talks are expository and very informal. Participants are encouraged to ask many questions and potentially break into discussion, depending on the speaker's preference.

The organizers of this seminar are Clair Xinle Dai, Vivian He, and Aru Mukherjea. You can email us if you have any questions. Check out the current or old calendars to get an idea of potential topics.

If you are interested in getting reminder emails on Thursdays with the Zoom info, please sign up here!

**Speaker**: Jaewon Chang (Harvard)

Title: Canonical basis of the wrapped Floer cohomology

Abstract: Beginning from the observation made by physicists that Calabi-Yau manifolds come in pairs of "mirror dual" families, the mirror symmetry conjectures were proposed as a way to formulate the intricate connection between symplectic geometry on a space and algebraic geometry on its dual. One version of this is the homological mirror symmetry conjecture, which implies a correspondence between Lagrangian Floer chain complexes and corresponding Hom spaces in the category of coherent sheaves.

Studying these chain complexes and their homology groups can be challenging due to the multiple ways to calculate or describe them. In particular, while there are vast studies and predictions of canonical bases of the cohomology rings on the algebraic side, the descriptions of Lagrangian Floer cohomology rings often fail to give a distinguished basis.

In this talk, I will discuss the case of certain Lagrangians in (C*)², and describe distinguished bases of their (wrapped) Floer cohomology. Under mirror symmetry, this will also give distinguished bases of the ring of functions on P¹ minus 4 points.

Date and Time: April 12**, 9 am PT/ 12pm EDT/ 5pm CET/ 9:30pm IST**.

Date | Speaker | Title |
---|---|---|

Dec 7 | Oğuz Şavk (Boğaziçi) | Classical and new plumbings bounding contractible manifolds and homology balls |

Nov 30 | Sarah Blackwell (UGA) | Triple Knot Grid Diagrams |

Nov 23 | Jonathan Johnson (Oklahoma State) | Bi-Orderability and Pretzel Knots |

Nov 16 | Lisa Lokteva (Glasgow) | Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls |

Nov 9 | Shintaro Fushida-Hardy (Stanford) | Chopping up 4-manifolds to study embedded surfacesTuesday |

Nov 2 | Charles Stine (Brandeis) | Shake-Slice Knots and the Levine-Tristram Signature |

Oct 26 | William Stagner (Rice) | Filling links in 3-manifolds |

Oct 19 | Khánh Le (Temple) | Left orderability and Dehn surgery |

Oct 12 | Julian Chaidez (Princeton) | Surface diagrams and quantum invariants in low dimensions |

Oct 5 | Jonathan Zung (Princeton) | Universal circles for foliations |

Aug 17 | Ethan Dlugie (UC Berkeley) | Geometry, Topology, and Wallpaper Groups |

Aug 10 | Hyun Ki Min (Georgia Tech/MIT) | Symplectic topology and property R |

Aug 3 | Casandra Monroe (UT Austin) | Deformations of hyperbolic structures on manifolds |

Jul 27 | Seraphina Lee (Chicago) | Finite order elements of mapping class groups |

Jul 20 | Dionne Ibarra (George Washington) | On framings of links in 3-manifolds |

Jul 13 | Shawn Williams (Rice) | Higher Order Alexander Modules |

Jun 29 | Agniva Roy (Georgia Tech) | Legendrian Contact Homology and Flow Trees |

May 13 | Ben Ruppik (MPIM) | Homotopy classification of 4-manifolds whose fundamental group is dihedral |

May 6 | Nicole Yamzon (UIUC) | Binomial ideals of domino tilings |

Apr 22 | Ceren Kose (UT Austin) | 3-manifolds that admit exotic fillings |

Apr 15 | John Chae (UC Davis) | Knot complement, series invariants and categorification |

Apr 8 | Sally Collins (Georgia Tech) | Bordered Floer Homology via Immersed Curves |

Apr 1 | Paula Truöl (ETH Zurich) | Positive 3-braid knots, their upsilon invariants and alternation numbers |

Mar 25 | Aaron Calderon (Yale) | Building random hyperbolic surfaces (after Mirzakhani) |

Mar 18 | Carmen Galaz-García (UCSB) | Anosov representations and symmetric spaces |

Mar 11 | Mac Krumpak (Brandeis) | Monopoles and the Froyshov h invariant |

Mar 4 | Seppo Niemi-Colvin (Duke) | Invariance Result for Knot Lattice Homology |

Feb 25 | Beibei Liu (Georgia Tech) | Some applications of Heegaard Floer homology to links in the three-sphere |

Feb 18 | Tam Cheetham-West (Rice) | Some remarks on 4-dimensional geometries |

Feb 11 | Braeden Reinoso (Boston College) | Capping off open books and fractional Dehn twist coefficients |

Feb 4 | Irving Dai (MIT) | Instantons and Homology Cobordism |

Date | Speaker | Title |
---|---|---|

Dec 3 | Oğuz Şavk (Boğaziçi) | Brieskorn spheres, homology cobordism and homology balls |

Nov 19 | Agnese Barbensi (Oxford) | Knotoids and knotted proteins |

Nov 12 | Maggie Miller (MIT) | Stong's Kervaire-Milnor invariant |

Nov 5 | Lvzhou (Joe) Chen (UT Austin) | Quasimorphisms and group actions |

Oct 29 | Ludovico Battista (Pisa) | A Hyperbolic 4-Manifold with a Perfect Circle-Valued Morse Function |

Oct 22 | Patrick Naylor (Waterloo) | Gluck twists of some roll spun knots are standard (with Hannah Schwartz) |

Oct 8 | Seungwon Kim (IBS CGP Korea) | Turaev genus |

Oct 1 | Onkar Singh Gujral (Duke) | Khovanov homology and cobordisms between split links (with Adam Levine) |

Sep 24 | Clayton McDonald (Boston College) | Doubly slice links (with Duncan McCoy) |

Sep 17 | Ben Lowe (Princeton) | Totally geodesic planes in hyperbolic 3-manifolds |

Sep 10 | Tyrone Ghaswala (UQAM) | The Meyer signature cocycle |

Aug 27 | Luya Wang (UC Berkeley) | ECH, HF and open book decompositions |

Aug 20 | Terrin Warren (UGA) | Slice knots and an interestingly uninteresting example (Piccirillo) |

Aug 13 | Adam Howard (Montana) | Some Examples of Knotted Tori (Boyle) |

Aug 6 | Robin Gaudreau (Toronto) | A direct proof that classical braid groups inject in virtual braid groups |

Jul 30 | Nickolas Castro (Arkansas) | Future Directions of Relative Trisections |

Jul 23 | Puttipong Pongtanapaisan (U Iowa) | Bridge distance of a knot in a 3-manifold |

Jul 16 | Vitalijs Brejevs (Glasgow) | 3-braid closures and rational balls (Simone) |

Jul 9 | Daniel Hartman (UGA) | Morse 2-functions to Kirby diagrams |

Jul 2 | Josh Wang (Harvard) | Floer and Khovanov homologies of band sums |

Jun 18 | Maggie Miller (Princeton/MIT) | Handle-ribbon knots (some joint work with Alex Zupan) |

Jun 11 | Vincent Longo (UNL) | Infinite family of counterexamples to Batson's conjecture |

Jun 4 | Anubhav Mukherjee (Georgia Tech) | Exotic cap on 3-manifolds |

May 21 | Tam Cheetham-West (Rice) | Identifying a hyperbolic 3-manifold via finite quotients (Wilton-Zalesskii) |

May 14 | Shruthi Sridhar (Princeton) | Kontsevich invariants |

May 7 | Patrick Naylor (Waterloo) | Diffeomorphisms of 4D 1- handlebodies (Laudenbach-Poenaru) |

Apr 30 | Charles Stine (Brandeis) | Closed oriented 4-manifolds embed in CP^3 (Ghanwat--Pancholi) |

Apr 23 | Hannah Schwartz (MPIM) | Isotopies of 2-spheres in S^2 x S^2 |

Apr 16 | Tanushree Shah (Glasgow) | Classification of contact structures on certain 3-manifolds |

Apr 9 | Antonio Alfieri (UBC) | Symplectic foliations of higher-dimensional manifolds |

Apr 2 | Ben Ruppik (MPIM) | Deeply slice knots |

Mar 26 | Sarah Blackwell (UGA/MPIM) | My (at the moment) fav proof (concerning Legendrian knots) |

Mar 19 | Maggie Miller (Princeton) | Dehn's Lemma |

Mar 12 | Gabriel Islambouli (Waterloo) | Multisections of 4-manifolds |

Mar 5 | Irving Dai (MIT) | Corks + involutive Floer homology |

Feb 27 | Maggie Miller (Princeton) | Knots branched covers bounding rational balls |

Feb 13 | Danica Kosanović (MPIM) | Budney-Gabai (obstruction) |

Feb 6 | Clayton McDonald (Boston College) | Budney-Gabai's non-isotopic 3-balls in S^4 (construction) |

Jan 30 | Puttipong Pongtanapaisan (U Iowa) | Additivity of Morse-Novikov (Ken Baker) |

Jan 23 | Oliver Singh (Durham) | The cork theorem |

Jan 16 | Jason Joseph (UGA/MPIM) | Unknotting numbers of 2-knots in S^4 |

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