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Reading Seminar on Heegaard Floer homology and related topics

Winter 2018

Time: Wednesdays, 3:00--4:30pm

Location: TBA Math

Description: We will read Hanselman-Rasmussen-Watson's work on Bordered Floer homology of manifolds with torus boundary.

Date

Speaker

Title

Jan 10 Yi Ni Sect 1-2 of Hanselman-Watson's paper
Jan 17    
     
     
     
     
     
     
     
     

 

 

Fall 2017

Time: Wednesdays, 3:00--4:30pm

Location: 104 Math

Description: We will read some papers about the naturality of Heegaard Floer homology.

Date

Speaker

Title

Oct 4 Yi Ni Sect 1-3 of Juhasz-Thurston's paper
Oct 11 Gahye Jeong Sect 4-5
Oct 18 Siqi He Sect 6
Oct 25 Juhyun Kim Sect 7
Nov 1 Yi Ni Sect 8
Nov 8 Cancelled  
Nov 15 Faramarz Vafaee  Sect 9
Nov 22 Cancelled  
Nov 29 Gahye Jeong Sect 1-5 of Zemke's paper
Dec 6 Juhyun Kim Sect 6-10

 

 

Spring 2017

Time: Wednesdays, 3:00--4:30pm

Location: 257 Sloan

Description: We will read some papers.

Date

Speaker

Title

Apr 5 Yi Ni Knot Floer homology and integer surgeries
Apr 12 Siqi He The Kobayashi--Hitchin correspondence
Apr 19 Gahye Jeong A product formula for Seiberg--Witten invariants
Apr 26 Faramarz Vafaee Integer surgery on links
May 3 Siqi He TBA
May 10 Juhyun Kim On the Floer homology of plumbed three-manifolds
May 17 Cancelled  
May 24 Gahye Jeong On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds, after Nemethi
May 31 Faramarz Vafaee Integer surgery on links, continued
Jun 7 Yi Ni Lattice cohomology of normal surface singularities, after Nemethi

 

 

 

Spring 2016

Time: Wednesdays, 3:00--4:30pm

Location: 257 Sloan

Description: We will read some papers of Kronheimer and Mrowka on instanton Floer homology.

Date

Speaker

Title

Apr 6 Yi Ni Khovanov homology is an unknot detector, after Kronheimer and Mrowka
Apr 13 Gahye Jeong Knots, sutures, and excision, after Kronheimer and Mrowka
Apr 20 Cancelled (special seminar by Lee)  
Apr 27 Siqi He Filtrations on instanton homology, after Kronheimer and Mrowka
May 4 Gahye Jeong Gauge theory and Rasmussen's invariant, after Kronheimer and Mrowka
May 11 Faramarz Vafaee Tait colorings, and an instanton homology for webs and foams, after Kronheimer and Mrowka
May 18 Cancelled (Candidacy exams of Gahye and Siqi)  
May 25 Cancelled  
Jun 1 Cancelled  
Jun 8, 2--3:30pm Siqi He Exact triangles for SO(3) instanton homology of webs, after Kronheimer and Mrowka

 

 

Winter 2016

Time: Wednesdays, 3:00--4:30pm

Location: 257 Sloan

Description: We will read some papers about Khovanov-Rozansky homology.

Date

Speaker

Title

Jan 20 Siqi He Khovanov-Rozansky homology, after Khovanov-Rozansky 1 and 2
Jan 27 Caili Shen Note on Khovanov link cohomology, after Gornik
Feb 3 Satoshi Nawata The superpolynomial for knot homologies, after Dunfield-Gukov-Rasmussen
Feb 10 Gahye Jeong Khovanov-Rozansky homology of two-bridge knots and links, after Rasmussen
Feb 17 Faramarz Vafaee Some differentials on Khovanov-Rozansky homology, after Rasmussen
Feb 24 Cancelled (Bonahon's NCG seminar at 3:30pm in 151)  
Mar 2 Gahye Jeong The s_N invariants, after Lobb and Lewark
Mar 9, 3--4pm Siqi He Nilpotent slices, Hilbert schemes, and the Jones polynomial, after Manolescu

 

 

 

Fall 2015

Time: Wednesdays, 3:10--4:30pm

Location: 153 Sloan

Description: We will read some papers about the concordance invariants in knot Floer homology.

Date

Speaker

Title

Sep 30 Faramarz Vafaee A combinatorial spanning tree model for knot Floer homology, after Baldwin-Levine
Oct 7 Siqi He Knot Floer homology and the four-ball genus, after Ozsvath-Szabo
Oct 14 Yi Ni Concordance homomorphisms from knot Floer homology, after Ozsvath-Stipsicz-Szabo
Oct 21 Gahye Jeong Unoriented knot Floer homology and the unoriented four-ball genus, after Ozsvath-Stipsicz-Szabo
Oct 28 Cancelled  
Nov 4 Faramarz Vafaee Bordered Heegaard Floer homology and the tau-invariant of cable knots, after Hom
Nov 11 Yi Ni The knot Floer complex and the smooth concordance group, after Hom
Nov 18 Siqi He An infinite-rank summand of topologically slice knots, after Hom
Nov 25 Gahye Jeong The four-genus of connected sums of torus knots, after Livingston-Van Cott

 

Spring 2015

Time: Wednesdays, 3:00--4:30pm

Location: 257 Sloan

Description: We will read some basic papers about combinatorial knot Floer homology.

Date

Speaker

Title

Apr 1 Yi Ni A combinatorial description of knot Floer homology, after Manolescu-Ozsvath-Sarkar
Apr 8 Faramarz Vafaee On combinatorial link Floer homology, after Manolescu-Ozsvath-Szabo-Thurston
Apr 15 Cancelled, special seminar by McCoy  
Apr 22 Gahye Jeong Floer homology and singular knots, after Ozsvath-Stipsicz-Szabo
Apr 29 Siqi He Khovanov-Rozansky homology, after Khovanov-Rozansky 1 and 2
May 6 Cancelled  
May 13 Caili Shen A cube of resolutions for knot Floer homology, after Ozsvath-Szabo
May 20 Siqi He An untwisted cube of resolutions for knot Floer homology, after Manolescu
May 27 Gahye Jeong An unoriented skein exact triangle for knot Floer homology, after Manolescu and Manolescu-Ozsvath
June 3 Cancelled A combinatorial spanning tree model for knot Floer homology, after Baldwin-Levine

 

 

Winter 2015

Time: Wednesdays, 3:20--4:50pm

Location: 153 Sloan

Description: We continue to read Manolescu's work on Seiberg--Witten stable homotopy types.

Date

Speaker

Title

Jan 7 Yi Ni Pin(2)-Equivarient Seiberg--Witten Floer homology and the Triangulation Conjecture, after Manolescu
Jan 14 Yi Ni continued
Jan 21 Yi Ni continued
Jan 28 Cancelled  
Feb 4 Cancelled  
Feb 11 Siqi He Periodic Floer pro-spectra from the Seiberg-Witten equations, after Kronheimer-Manolescu

 

 

 

Fall 2014

Time: Wednesdays, 3:00--4:30pm

Location: 151 Sloan

Description: The goal of this quarter is to understand Manolescu's work on Seiberg--Witten stable homotopy types.

Date

Speaker

Title

Oct 15 Yi Ni Seiberg-Witten equations on cylinders
Oct 22 Yi Ni Seiberg-Witten equations on cylinders, continued
Oct 29 Cancelled, special seminar by Zhou Zhang  
Nov 5 Cancelled, Barry Simon retirement party  
Nov 12 Faramarz Vafaee Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0, afterManolescu, see also the errata
Nov 19 Cancelled  
Nov 26 Faramarz Vafaee continued
Dec 3 Siqi He A gluing theorem for the relative Bauer-Furuta invariants, after Manolescu

 

 

Spring 2014

Time: Wednesdays, 2:30--3:30pm

Location: 151 Sloan

Description: The goal of this quarter is to understand stable homotopy types in Khovanov homology and Floer homology.

Date

Speaker

Title

Apr 2 Yi Ni The Cohen-Jones-Segal construction (following Cohen-Jones-Segal 1 and 2)
Apr 9 Nakul Dawra Khovanov spectrum: the construction (following Lipshitz-Sarkar)
Apr 16 Nakul Dawra Khovanov spectrum: the construction, continued (following Lipshitz-Sarkar)
Apr 23 Caili Shen Khovanov spectrum: invariance and properties (following Lipshitz-Sarkar)
Apr 30 Caili Shen Khovanov spectrum: invariance and properties, continued (following Lipshitz-Sarkar)
May 7 Siqi He A Steenrod Square on Khovanov Homology (following Lipshitz-Sarkar)
May 14 Siqi He A Steenrod Square on Khovanov Homology, continued (following Lipshitz-Sarkar)
May 21 Nakul Dawra A refinement of Rasmussen's s-invariant (following Lipshitz-Sarkar)
May 28 Yi Ni The Bauer-Furuta invariant (following Bauer-Furuta)

 

 

Fall 2013

Time: Wednesdays, 2--3:30pm

Location: 153 Sloan

Description: The goal of this quarter is to understand John Pardon's recent work

An algebraic approach to virtual fundamental cycles on moduli spaces of J-holomorphic curves.

Date

Speaker

Title

Oct 9 Yi Ni Technical introduction
Oct 16 Yi Ni Technical introduction, continued
Oct 23 Cancelled  
Oct 30 Nakul Dawra Homological algebra
Nov 6 Nakul Dawra/Caili Shen Homological algebra/ Implicit atlas
Nov 13 Caili Shen Virtual cochain complexes
Nov 20 Cancelled,

Masbaum and Andersen's seminars 3-5:30pm

 
Nov 27 Cancelled  
Dec 4 Zhiyu Tian Fundamental class/Gromov-Witten invariants

 

 

Spring 2013

Time: Wednesdays, 2--3:30pm

Location: 257 Sloan

Description: The goal of this quarter is to understand the topological aspect of Instanton Floer homology,

without focusing too much on its analytical aspect. More specifically, we wish to discuss Kronheimer and

Mrowka's result that Khovanov homology is an unknot-detector, as well as some related results. A master

class on this topic given by Mrowka at Aarhus can be viewed here.

Date

Speaker

Title

April 3 Yi Ni A brief introduction to instanton Floer homology, I, (following Donaldson's book)
April 10 Yi Ni A brief introduction to instanton Floer homology, II, (following Donaldson's book)
April 17 Zhongtao Wu Knot homology groups from instantons, I, (after Kronheimer and Mrowka)
April 24 Nakul Dawra Knot homology groups from instantons, II, (after Kronheimer and Mrowka)
May 1 Yi Ni Sutures, excision, and instanton Floer homology, (after Kronheimer and Mrowka)
May 8 Liling Gu Instanton Floer homology and the Alexander polynomial, (after Kronheimer and Mrowka)
May 15 Caili Shen Dehn surgery, the fundamental group and SU(2), (after Kronheimer and Mrowka)
May 22 Zhongtao Wu Khovanov homology is an unknot-detector, I, (after Kronheimer and Mrowka)
May 29 Nakul Dawra Khovanov homology is an unknot-detector, II
June 6 Liling Gu Khovanov homology is an unknot-detector, III

 

Winter 2013

Time: Thursdays, 2—3:30pm

Location: the conference room in 253 Sloan

Date

Speaker

Title

     Jan 17 Yi Ni The Heegaard Floer correction terms
     Jan 24

Liling Gu

Small Seifert-fibered Dehn surgery on hyperbolic knots, (after Dean)

    Jan 31 Hongbin Sun Small dilatation pseudo-Anosovs and 3-manifolds, (after Farb-Leininger-Margalit)
     Feb 7

Nakul Dawra

On the Floer homology of plumbed three-manifolds, (after Ozsvath-Szabo)

   Feb 14

Cancelled

 

    Feb 21

Caili Shen

Naturality and mapping class groups in Heegaard Floer homology, (after Juhasz-Thurston)

    Feb 28

Yi Ni

Teichmuller Polynomials, (after McMullen)

     Mar 7

Zhongtao Wu

Product formulae for Ozsváth–Szabó 4–manifold invariants, (after Jabuka-Mark)

     Mar 14

Liling Gu

Some constructions related to Dehn surgery

 

Fall 2012

Time: Wednesdays, 2pm—3:30pm

Location: 153 Sloan

Description: We will continue reading Manolescu and Ozsváth’s link surgery formula.

Date

Speaker

Title

     Oct 10

Nakul Dawra

Statement of the surgery theorem

     Oct 17

Liling Gu

Truncation

     Oct 24

Zhongtao Wu

Truncation, continued

     Oct 31

Nakul Dawra

Beyond the surgery theorem

     Nov 7

Liling Gu

On the infinity flavor of Heegaard Floer homology and the integral triple cohomology ring,

(after Tye Lidman)

Nov 14 Canceled

   

     Nov 21

Zhongtao Wu

Heegaard Floer homology and triple cup products, (after Tye Lidman)

     Nov 28

Nakul Dawra

Framed Floer homology, (after Tye Lidman)

 

Spring 2012

Date

Speaker

Title

   Apr 2

Liling Gu

Knot Floer homology and integer surgeries

   Apr 9

Nakul Dawra  

On the Heegaard Floer homology of branched double-covers

   Apr 16

Cancelled

 

    Apr 23

Yi Ni

Integer surgery on links: Introduction

   Apr 30

Zhongtao Wu

Knot Floer homology and rational surgeries

   May 7

Nakul Dawra

Hyperboxes of chain complexes and compression

   May 14

Liling Gu

Generalized Heegaard Floer complexes for links

May 23, 159 Sloan

Yi Ni

Quasi-stabilizations

May 29, 159 Sloan

Zhongtao Wu

Hyperboxes of Heegaard diagrams

     June 11

Nakul Dawra

Statement of the surgery theorem

 

 

Winter 2012

Time: Wednesdays, 4pm—5:30pm

Location: 153 Sloan

Date

Speaker

Title

   Jan 11

Yi Ni

Sutured manifolds and Heegaard Floer homology

   Jan 18

Liling Gu

Knot Floer homology of Whitehead doubles (after Hedden)

Jan 24(Tuesday)

1:30pm3pm

257 Sloan

Nakul Dawra

Pseudo holomorphic curves in symplectic manifolds (after Gromov)

   Feb 1

Yi Ni

Sutured manifolds and Heegaard Floer homology, II

   Feb 8

Liling Gu

Knot Floer homology of Whitehead doubles, II

   Feb 15

Nakul Dawra

Pseudo holomorphic curves in symplectic manifolds, II

Feb 22 Cancelled

 

 

   Feb 29

Liling Gu

On Floer homology and Cabling (after Hedden)

   Mar 7

Nakul Dawra

Concordance invariants from higher order covers (after Jabuka)

   Mar 14

Yi Ni

Some open problems