# Schedule for: 22w5065 - Topology in Dimension 4.5

Beginning on Sunday, October 30 and ending Friday November 4, 2022

All times in Banff, Alberta time, MDT (UTC-6).

Sunday, October 30
16:00 - 17:30 Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.
(Vistas Dining Room)
20:00 - 22:00 Informal gathering (TCPL Foyer)
Monday, October 31
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
08:45 - 09:00 Introduction and Welcome by BIRS Staff
A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.
(TCPL 201)
09:00 - 10:00 Seungwon Kim: Mini-series A - surfaces in 4-manifolds
Speakers: Anthony Conway, Seungwon Kim, Patrick Naylor, Arunima Ray.
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 12:00 Arunima Ray: Mini-Series A - surfaces in 4-manifolds
Speakers: Anthony Conway, Seungwon Kim, Patrick Naylor, Arunima Ray.
(TCPL 201)
11:30 - 13:00 Lunch
Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
13:00 - 14:00 Guided Tour of The Banff Centre
Meet in the PDC front desk for a guided tour of The Banff Centre campus.
(PDC Front Desk)
14:00 - 14:20 Group Photo
Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!
(TCPL Foyer)
14:30 - 14:55 Isaac Sundberg: A non-detection result in Khovanov homology
Picture this!
(TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:20 Mark Powell: Mapping class groups of simply connected compact 4-manifolds
I will describe the eponymous groups in the topological category. When the boundary is nonempty, the complete computation is new and joint with Patrick Orson. Then I will do some subset of: (i) make comparisons with the smooth category; (ii) mention applications to isotopy of surfaces; (iii) discuss possible avenues for generalisation to 4-manifolds with non-trivial fundamental group.
(TCPL 201)
16:30 - 17:20 Slava Krushkal: Topological pseudoisotopy of 4-manifolds
This talk will focus on work in progress, joint with Mark Powell, on pseudoisotopy theory for topological 4-manifolds. The goal is to extend Quinn's theorem, that a pseudoisotopy of a simply-connected 4-manifold is topologically isotopic to an isotopy, to 4-manifolds with good fundamental groups, provided that the Hatcher-Wagoner obstructions vanish. A part of the project is to establish what the relevant analogue of Hatcher-Wagoner's higher-dimensional obstructions should be in dimension 4. The talk will aim to explain these notions, problems, and our results.
(TCPL 201)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.
(Vistas Dining Room)
Tuesday, November 1
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
09:00 - 09:25 Alex Manchester: The Mazur pattern and concordance
Picture this!
(TCPL 201)
09:30 - 09:55 Terrin Warren: Diffeomorphisms and the Goeritz group of a trisection
Picture this!
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 10:55 Shintaro Fushida-Hardy: Pseudo bridge trisections
Picture this!
(TCPL 201)
11:00 - 11:25 Sally Collins: Satellite knots & Local Equivalence
Picture this!
(TCPL 201)
11:30 - 13:00 Lunch
Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
13:30 - 14:20 Nick Castro: Relative group trisections and open books
A relative trisection of a smooth 4-manifold with boundary induces an open book decomposition on the bounding 3-manifold, for which there is an algorithm to compute from the relative trisection diagram. In this talk I will discuss two works-in-progress which aim to better understand the relationship between trisections and open books. The first is to interpret a relative trisection as a commutative cubes of groups.  (joint with Jason Joseph and Patrick McFaddin); the second is obstructing destabilizations of relative trisections (joint with Thomas Kindred).
(TCPL 201)
14:30 - 14:55 Sarah Blackwell: Triple grid diagrams
Picture this!
(TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:20 Vincent Longo: An Infinite Family of Counterexamples to Batson's Conjecture
Batson's conjecture is a non-orientable version of Milnor's conjecture, which states that the 4-ball genus of a torus knot T(p,q) is equal to 1/2(p-1)(q-1). Batson's conjecture states that the nonorientable 4-ball genus is equal to the pinch number of a torus knot, i.e. the number of a specific type of (nonorientable) band surgeries needed to obtain the unknot. The conjecture was recently proved to be false by Lobb. We will show that Lobb's counterexample fits into an infinite family of counterexamples.
(TCPL 201)
16:30 - 17:20 Allison Miller: Strongly invertible knots and equivariant slice genera
A strong inversion of a knot K is an involution i of the 3-sphere that setwise fixes K and whose fixed set intersects K in exactly two points.The equivariant 4-genus of a (knot, inversion) pair (K, i) is defined to be the minimal genus of an embedded surface F in the 4-ball with boundary K and that is setwise fixed under some extension of i to an involution of the 4-ball. We give a new lower bound on the equivariant 4-genus in terms of the Blanchfield pairing, and discuss how this can be used to give many examples of knots with arbitrarily large equivariant 4-genus. In the process, we show that genus one strongly invertible knots with nontrivial Alexander polynomial are never equivariantly slice. This is joint work with Mark Powell.
(Online)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.
(Vistas Dining Room)
20:00 - 21:00 Robion Kirby: Gromov compactness by example
We will understand the Gromov Compactness Theorem by considering some examples.
(TCPL 201)
Wednesday, November 2
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
09:00 - 10:00 David Gabai: Mini-Series B: concordance of surfaces
Speakers: Dave Gabai, Michael Klug, Mark Powell, Rob Schneiderman.
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 12:00 Michael Klug: Mini-Series B: concordance of surfaces
Speakers: Dave Gabai, Michael Klug, Mark Powell, Rob Schneiderman.
(TCPL 201)
11:30 - 13:00 Lunch
Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
13:30 - 17:30 Free Afternoon (Banff National Park)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.
(Vistas Dining Room)
Thursday, November 3
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
09:00 - 10:00 Tadayuki Watanabe: Mini-Series C: diffeomorphism groups
Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 12:00 Mini-Series C: diffeomorphism groups
Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.
(TCPL 201)
10:30 - 12:00 Daniel Hartman: Mini-Series C: diffeomorphism groups
Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.
(TCPL 201)
11:30 - 13:00 Lunch
Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
13:30 - 14:20 Patrick Naylor: Doubles of Gluck twists
The Gluck twist of an embedded 2-sphere in the 4-sphere is a 4-manifold that is homeomorphic, but not obviously diffeomorphic to the 4-sphere. Despite considerable study, these homotopy spheres have resisted standardization except in special cases. In this talk, I will discuss some conditions that imply the double of a Gluck twist is standard, i.e., is diffeomorphic to the 4-sphere. This is based on joint work with Dave Gabai and Hannah Schwartz.
(TCPL 201)
14:30 - 14:55 Nicholas Cazet: Broken Sheet Diagrams of Knot Cobordisms
Picture this!
(TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:20 Kai Nakamura: Annulus twisting a disk: standard and exotic
We will discuss and compare two recent results of the author. First will be a family of homotopy 4-spheres constructed by Manolescu and Piccirillo by annulus twisting a ribbon disk. These we show are standard by visualizing the associated trace embedding by a Kirby diagram. To contrast this, we construct a family of exotic elliptic surfaces by annulus twisting an H-slice disk. This provides important evidence for the viability of the Manolescu-Piccirillo approach to disproving the smooth 4-dimensional Poincare conjecture by giving the first examples of their construction successfully producing exotic 4-manifolds.
(TCPL 201)
16:30 - 17:20 Irving Dai: The (2,1)-cable of the figure-eight knot is not smoothly slice
We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball. This answers a forty-year-old question posed by Kawauchi. (Joint with Sungkyung Kang, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.)
(TCPL 201)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.
(Vistas Dining Room)
Friday, November 4
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
09:00 - 09:50 Ryan Budney: How to show a barbell diffeomorphism is non-trivial
I will describe a few different scanning arguments, allowing one to show the non-triviality of some implanted barbell diffeomorphisms, as elements of the homotopy groups of Diff($S^1 \times D^{n-1}$) for $n\ge 4$.
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:00 Checkout by 11AM
5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.
(Front Desk - Professional Development Centre)
10:30 - 10:55 Peter Teichner: Isotopy classification of half-disks in 4-manifolds
Picture this!
(Online)
11:00 - 11:50 Danica Kosanović: A new approach to light bulb tricks
I will explain a new approach to settings with geometric dual spheres, which can not only classify isotopy classes of disks or spheres with such a dual, but also leads to some new insights into mapping class groups of 4-manifolds. This is joint work with Peter Teichner.
(Online)
12:00 - 13:30 Lunch from 11:30 to 13:30 (Vistas Dining Room)