The SGGTC seminar meets on Fridays in Math 407 at 1pm, unless noted otherwise (in red).

Previous semesters: Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007.

Our e-mail list.

Date |
Speaker |
Title |

Jan. 19 | Mark McLean (Stony Brook) |
Birational Calabi-Yau Manifolds have Isomorphic Hamiltonian Floer Algebras |

Jan. 26 1:15pm | Jen Hom (Georgia Tech) |
Knot concordance in homology cobordisms |

Feb. 2 | Michael Usher (University of Georgia) |
Symplectic embeddings of ellipsoids into polydisks |

Feb. 9 | Inbar Klang (Stanford) |
Hochschild invariants of Thom spectra |

Feb. 16 | Catherine Cannizzo (Berkeley) |
Homological mirror symmetry for the complex genus 2 curve |

Feb. 23 | Chris Scaduto (SCGP) |
Yang-Mills theory and definite intersection forms bounding homology 3-spheres |

Mar. 2 | Irving Dai (Princeton) |
TBA |

Mar. 9
10:30am Math 520 |
Ziva Myer (Duke) |
TBA |

Mar. 9 | Kristen Hendricks (Michigan State) |
TBA |

Mar. 23
10:30am Math 520 |
Marithania Silvero (Universidad de Catalunia) |
TBA |

Mar. 23 | John Etnyre (Georgia Tech) |
TBA |

Mar. 30
10:30am Math 520 |
Andy Manion (UCLA) |
TBA |

Mar. 30 | Diana Hubbard (University of Michigan) |
TBA |

Apr. 6 | ||

Apr. 13 | Bahar Acu (Northwestern University) |
TBA |

Apr. 20
10:30am Math 520 |
Andrew Lobb (Durham University) |
TBA |

Apr. 20 | Emmy Murphy (Northwestern University) |
TBA |

Apr. 27 | Ciprian Manolescu (UCLA) |
TBA |

# Abstracts

#### January 19, 2018: Mark McLean " Birational Calabi-Yau Manifolds have Isomorphic Hamiltonian Floer Algebras "

*Abstract:*
We show that any two birational projective Calabi-Yau manifolds admit
Hamiltonians with isomorphic Hamiltonian Floer cohomology algebras
after a certain change of Novikov rings. As a result, we show that
such Calabi-Yau manifolds have isomorphic small quantum cohomology
algebras over Novikov rings of any characteristic. The proof is
inspired by ongoing work of Borman and Sheridan and uses a version of
symplectic cohomology defined by Groman, Venkatesh and Varolgunes.

#### January 26, 2018: Jen Hom " Knot concordance in homology cobordisms "

*Abstract:*
The knot concordance group C consists of knots in S^3 modulo knots that bound smooth disks in B^4. We consider C_Z, the group of knots in homology spheres that bound homology balls modulo knots that bound smooth disks in a homology ball. Matsumoto asked if the natural map from C to C_Z is an isomorphism. Adam Levine answered this question in the negative by showing the map is not surjective. We show that the quotient of C_Z by the image of C is infinitely generated and contains elements of infinite order. The proof relies on Heegaard Floer homology. This is joint work with Adam Levine and Tye Lidman.

#### February 2, 2018: Michael Usher " Symplectic embeddings of ellipsoids into polydisks "

*Abstract:*
Work of Li-Li, McDuff, and others makes it possible to determine algorithmically whether a given rational four-dimensional ellipsoid E(1,a) symplectically embeds into a given rational polydisk P(b,c). Even so, the dependence of the answer on a, b, and c is sufficiently complicated that a number of features of the embedding capacity functions governing embeddings of ellipsoids into polydisks are not well-understood. I will describe a method for constructing families of exceptional spheres in blowups of CP^2 that give rise to sharp obstructions to embeddings of E(1,a) into dilates of P(1,b) for certain a and b, which collectively give rise to infinite staircases in the embedding capacity functions of certain irrational polydisks that are analogous to the infinite staircases found by McDuff and Schlenk for balls and Frenkel and Muller for cubes.

#### February 9, 2018: Inbar Klang " Hochschild invariants of Thom spectra "

*Abstract:*
Thom spectra of virtual bundles give important examples of ring spectra. I'll discuss a project describing Hochschild-type invariants of such ring spectra, and talk about what this has to do with Lagrangian immersions. This talk will include an introduction to factorization homology via labeled configuration spaces.

#### February 16, 2018: Catherine Cannizzo " Homological mirror symmetry for the complex genus 2 curve "

*Abstract:*
In this thesis talk, we will describe progress towards proving homological mirror symmetry (HMS) for the genus 2 curve in an abelian variety. HMS is known for the genus 2 surface as a symplectic manifold by work of Seidel. Here we consider it on the complex manifold side. We describe a fully faithful embedding of the bounded derived category of coherent sheaves on the genus 2 curve to the Fukaya-Seidel category of a generalized SYZ mirror constructed via methods described in Abouzaid-Auroux-Katzarkov’s paper on SYZ for hypersurfaces of toric varieties. HMS would be that these two categories are equivalent.

#### February 23, 2018: Chris Scaduto " Yang-Mills theory and definite intersection forms bounding homology 3-spheres "

*Abstract:*
Using Yang-Mills instanton Floer theory, we find new constraints on the possible definite intersection forms of smooth 4-manifolds that bound integer homology 3-spheres. We will give examples of 3-manifolds such that the set of all bounding negative definite lattices consists of essentially two distinct non-standard lattices. The methods used follow the work of Froyshov.

## Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups.