All talks will take place in 4.102 in RLM (Robert Lee Moore)
Hall.
Friday, November 17
45PM

Registration

56PM

Josh Greene


Perspectives on Dehn surgery
Dehn surgery is one of the most popular themes in lowdimensional topology. I will survey its study, with an emphasis on the different perspectives that have been brought to bear on it from across the field: hyperbolic geometry, character varieties, sutured manifolds, combinatorial methods, and Floer homology. I will highlight some fascinating problems that have been solved and many that remain for the future.

67:30PM

Catered dinner in RLM

7:308:30PM

Jen Hom


Heegaard Floer homology and homology cobordism
Heegaard Floer homology is an invariant of closed threemanifolds. We consider threemanifolds up to a weaker notion of equivalence known as homology cobordism. Using additional data from the involutive Heegaard Floer homology package of Hendricks and Manolescu, we discuss applications of Heegaard Floer homology to homology cobordism. This is joint work with Kristen Hendricks and Tye Lidman.

Saturday, November 18
89AM

Registration

910AM

Jeremy Kahn


Surface Subgroups in Nonuniform Lattices
In 2009 the speaker and Vladimir Markovic constructed nearly geodesic surfaces in a given closed hyperbolic 3manifold M. The construction proceeded by taking all "good pants" in M and matching them at their boundaries to produce a closed surface. I will describe this construction, as well as a new construction with Alexander Wright, of a nearly geodesic surface in the case where M has a cusp. If time permits, I will discuss the potential applications of this construction to higher rank nonuniform lattices and mapping class groups.

10:0010:30AM

Break

10:3011:30AM

David Gay


Basic questions about trisections of 4manifolds.
Trisections are to 4manifolds as Heegaard splittings are to
3manifolds. I'll survey the subject with the aim of highlighting the
foundational questions that I think are most compelling and have the most
promise to shed light on smooth 4dimensional topology. Along the way I'll
present the basic results coming from my work with Kirby and subsequent work
of several others.

11:30AM1:30PM

Lunch break

1:302:30PM

Emmy Murphy


Graph Legendrians, contact homology, and SL_2 local systems
We will discuss some connections between framed SL_2 local systems on punctured surfaces and pseudoholomorphic curves in 5 dimensional contact manifolds. We will also discuss connections with planar graph colorings, representations of dg algebras, Lagrangian cobordisms, loose Legendrians, and maybe some other things.

2:302:45PM

Break

2:453:45PM

Dan Margalit


The Botany of Normal Subgroups of Mapping Class Groups
I'll give an overview of recent results that describe some of the different behaviors of normal subgroups of the mapping class group. For instance, we produce many normal subgroups that have automorphism group isomorphic to the extended mapping class group. On the other hand, we produce new normal subgroups that are isomorphic to infinitely generated rightangled Artin groups. Also, we give many new examples of mapping classes whose normal closure is the whole mapping class group, in particular answering a 30yearold question of Darren Long. This work is joint with Tori Akin, Tara Brendle, Matt Clay, Justin Lanier, and Johanna Mangahas.

3:454:15PM

Break

4:155:15PM

Josh Greene


Fibered simple knots
I will discuss joint work with John Luecke in which we classify the simple knots in lens spaces that fiber. The answer takes a peculiar and elementary number theoretic form.

6.30PM

Conference Banquet at The Clay Pit

Sunday, November 18
9:3010:30AM

Robert Lipshitz


Bordered Floer homology and compressible surfaces
After recalling some of the key properties of bordered Heegaard Floer homology, we will describe how it detects homologically essential compressing disks, and how borderedsutured Floer homology detects boundaryparallel tangles. Time permitting, we will also sketch an algorithm to compute borderedsutured Floer homology. This is joint work with Akram Alishahi, and uses earlier joint work with Peter Ozsváth and Dylan Thurston.

10:3011:00AM

Break

11:00AMnoon

Dani Wise


A graph coloring problem and its application towards virtual
algebraic fibering
I will first describe a simple graph coloring problem and survey
some examples of graphs for which the coloring problem has or has no
solution. I will then give a quick introduction to BestvinaBrady Morse
theory. Finally, I will describe the relationship between the coloring
problem and some amusing virtual algebraic fibering consequences for
geometric group theory and hyperbolic 4manifolds. This is joint work with
Kasia Jankiewicz and Sergey Norin.

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