Confirmed Speakers:

Román Aranda (Binghamton)

Sarah Blackwell (Georgia)

Gabe Islambouli (UC Davis)

Rob Kirby (Berkeley)

Peter Lambert-Cole (Georgia)

Maggie Miller (Stanford)

Laura Starkston (UC Davis)

Tuesday, June 28:

8:30-9am Breakfast

9am-10am Laura Starkston

Symplectic manifolds meet trisections

10am-10:30am Break

10:30am-11:30am Peter Lambert-Cole

TBA

11:30am-1pm Lunch

1pm-3pm Work in Groups

3pm-3:30pm Break

3:30pm-5pm Work in Groups

Thursday, June 30:

8:30-9am Breakfast

9am-10am Maggie Miller

What can you do with bridge trisections?

10am-10:30am Break

10:30am-11:30am Román Aranda

Bounds for L-invariants of knotted surfaces

11:30am-1pm Lunch

1pm-3pm Work in Groups

3pm-3:30pm Break

3:30pm-5pm Work in Groups

Abstracts:

1. Trisections of 4-manifolds with boundary (Rob Kirby)

Different perspective than Castro et al. This may be a rather elementary talk, but perhaps good for an introduction to those who are not deeply immersed in trisections. I hope there are some of those in the audience!

2. Symplectic manifolds meet trisections (Laura Starkston)

I'll give an introduction to symplectic 4-manifolds and ways in which they can interact well with trisections. I'll try to explain what we know so far, and some questions we still have in this area.

3. TBA (Peter Lambert-Cole)

TBA

4. An introduction to multisections of 4-manifolds (Gabe Islambouli)

We will give a gentle introduction to multisections of 4-manifolds, which are straightforward generalizations of trisections into decompositions with more than three pieces. We highlight the new phenomena that appear, such as cut and paste procedures of sectors, and explore a connection between multisections and loops of Morse functions on a surface.

5. Group Trisections and Smoothly Knotted Surfaces (Sarah Blackwell)

I’ll give an introduction to group trisections, with the endgame of talking about my joint project with Rob Kirby, Michael Klug, Vince Longo, and Ben Ruppik, in which we give a formulation of group trisections for groups of knotted surfaces in 4-manifolds. One aspect of our work that I really like is that we show algorithmically how to produce diagrams from a trisection; I plan to carefully go through this procedure. Stallings folding, a technique that translates between surjections between free groups and directed graphs, guides the algorithm.

6. What can you do with bridge trisections? (Maggie Miller)

I’ll show how to do some basic things with triplane diagrams of surfaces in the 4-sphere, e.g. describe a bounded 3-manifold, compute the complement fundamental group or peripheral subgroup, or compute Euler number (with some fun convincing ourselves of what “positive” means). This is joint work with Jason Joseph, Jeffrey Meier, and Alexander Zupan.

7. Bounds for L-invariants of knotted surfaces (Román Aranda)

Take two 3-dimensional handlebodies with the same boundary surface. One can tell them apart by studying the curves on the boundary surface bounding disks on each handlebody. Hempel studied Heegaard splittings of closed 3-manifolds by comparing these disk sets in the curve complex. For trisections, one can measure the length of loops in some complex passing through the disk set of each 3-dimensional handlebody. Kirby and Thompson used cut systems this way to define the L-invariant of a trisection of a closed 4-manifold. Other authors extended this definition for relative trisections and bridge trisections. Naturally, L is hard to compute. We will discuss lower bounds for (b,c)-bridge trisections of closed surfaces. This is joint work with Pongtanapaisan and Zhang.