## Schedule, 2024

Lectures will be in 253 Malott Hall (Campus Map). Plenary talks are scheduled for 50 minutes plus 10 minutes for questions, and workshop talks for 25 minutes plus 5 minutes for questions. Breakfasts, lunches, coffee etc. will be provided in the Malott Hall fifth floor lounge (MLT 532). All times are ET.

### Friday, 3 May 2024

—— Check-in, Malott Hall fifth floor lounge from 10:30 —— | |

11:30–12:00 | Brannon Basilio, University of Illinois at Urbana Champaign, Workshop talk
Foundations of 3-Manifolds and Essential Surfaces
▾ We give a basic introduction to the field of 3-manifolds and in particular the role that surfaces play. We cover a fundamental notion of decomposing a 3-manifold, a few important early results including the loop theorem, and mention a recent result resolving the Virtual Haken conjecture. If time permits, we introduce the idea of normal surfaces and its connection to essential surfaces. |

12:05–12:35 | Tomas Mejia Gomez, Johns Hopkins University, Workshop talk
The Eckmann-Hilton argument in homotopy groups and 2 categories
▾ The Eckman-Hilton argument arises in topological or algebraic situations where two operations are present which interact well with each other, in a sense. Basic examples are the various ways to concatenate two representatives of the homotopy group \pi_nX of a space X for n>=2, or the two ways to compose higher morphisms in a 2-category. We will make a tour of these examples and the precise conditions we ask from our operations: compatibility, strict vs. weak, etc. In the process we use the argument to get nice results such as the commutativity of \pi_nX. |

—— Lunch —— | |

2:00–2:30 | Colby Kelln, Cornell University, Workshop talk
Tools for Constructions in Geometric Topology and Geometric Group Theory ▾ There are many different ways to think about a torus--we will advocate for "a square with opposite sides identified in a certain way." We will start here and introduce other techniques that are useful when trying to construct examples of spaces of interest to geometric topologists and geometric group theorists, working up to the definition of a hyperbolic orbifold. |

2:35–3:05 | Jeremy West, University of Oklahoma, Workshop talk
Houghton Groups and the Brown-Lee Complex
▾ For each natural number n, one can consider the set of
n-many copies of $\mathbb{N}$, and the group of permutations on this
set which are eventual translations: for each permutation, in each
copy of $\mathbb{N}$, there is some point beyond which the permutation
is just a translation. Brown showed that the Houghton group $H_n$ is
of type $F_{n-1}$, but not of type F_{n}. If one replaces
"permutation" with "almost surjective injection", one obtains a monoid
$M_n$ which serves as vertex set of a cube complex. Lee proved that
this complex is CAT(0), and derived an exponential upper bound on the
Dehn function of $H_n$ for $n \geq 3$. |

—— Break —— | |

4:00–5:00 | Martin Bridson, Oxford University, Opening plenary talk of the conference and final Oliver Club (Department Colloqioum) of the year
Profinite rigidity, Grothendieck Pairs, and finiteness properties
▾ A finitely generated, residually finite group G is said to be profinitely rigid if the only finitely generated, residually finite groups with the same
set of finite quotients as G are those that are isomorphic to G. More generally, one wants to know which properties P of groups are profinite invariants,
i.e. if G has P and H has the same finite quotients as G, does H have P? For example, if G is a 3-manifold group, is H? If G is torsion-free, is H? |

### Saturday, 4 May 2024

—— Breakfast from 8:30 —— | |

9:00–10:00 | Bruno Martelli, Università di Pisa, Plenary talk
Negatively curved spaces obtained via branched coverings over a torus
▾ In his seminal paper on hyperbolic groups, Gromov tries to extend a beautiful construction of Thurston from dimension 3 to arbitrary n: he builds of a non-positively curved manifold as a branched covering over the n-torus, ramified along codimension-2 subtori. This is particularly interesting in odd dimension n, because every generic fibration of the n-torus lifts to a fibration of the branched cover. |

10:10–11:10 | Viktor Ginzburg, University of California, Santa Cruz, Plenary talk
Topological Entropy of Hamiltonian Systems and Persistence Modules
▾ Topological entropy is a fundamental invariant of a dynamical system, measuring its complexity. In this talk, we will discuss connections between the topological entropy of a Hamiltonian system, e.g., a geodesic flow, and the underlying filtered Morse or Floer homology viewed as a persistence module in the spirit of Topological Data Analysis. We will introduce barcode entropy — a Morse/Floer theoretic counterpart of topological entropy — and show that barcode entropy is closely related to topological entropy and that, in low dimensions, these invariants agree. For instance, for a geodesic flow on any closed surface the barcode entropy is equal to the topological entropy. The talk is based on joint work with Erman Cineli, Basak Gurel and Marco Mazzucchelli. |

—— Coffee —— | |

11:40–12:40 | Eugenia Cheng, School of the Art Institute of Chicago and City, University of London, Plenary talk
The Eckmann–Hilton argument in higher dimensional category theory
▾ The Eckmann–Hilton argument gives us circumstances in which commutativity arises from having two binary operations that interact in certain coherent ways. The argument is used to show that all higher homotopy groups are Abelian, but can be stated in generality as a piece of algebra: if a set is equipped with two monoid structures satisfying a type of interchange, then the two binary operations coincide and are commutative. |

—— Lunch —— | |

1:40–2:40 | Rhiannon Griffiths, Cornell University, Plenary talk
The Homotopy Types of Higher Categories
▾ Grothendieck’s Homotopy Hypothesis states that homotopy n-types are modeled by n-groupoids, and by extension, that spaces are modeled by $\infty$-groupoids. Moreover, this equivalence is induced by the homotopy groups of both constructions. |

—— Break —— | |

3:10–4:40 | Panel discussion |

—— Picnic at Stewart Park, large pavilion from 5:30 —— |

### Sunday, 5 May 2024

—— Breakfast from 8:30 —— | |

9:00–10:00 | Morgan Weiler, Cornell University, Plenary talk
Anchored symplectic embeddings of four-dimensional toric domains
▾ Symplectic geometry is a generalization of classical mechanics, in which position and momentum coordinates are paired. Mathematically, a symplectic manifold is an even-dimensional manifold carrying a "symplectic form" – a closed, nondegenerate 2-form. In two dimensions, symplectic geometry is equivalent to volume-preserving geometry, but in higher dimensions, Gromov proved in 1985 that an embedding from a finite-volume ball into an infinite-volume cylinder can only preserve the symplectic form if the ball embeds via the identity. Symplectic geometers have studied generalizations of Gromov's result ever since. In this talk, we will show that in many four-dimensional examples, requiring the complement of the embedding to contain a symplectic surface with fixed boundary conditions (the so-called "anchor") provides an even stronger restriction than the symplectic form alone. Our examples have a toric structure, and when symplectic embeddings between them are anchored we show they must also be toric. The main tool is the interplay between the action filtration and intersection number in embedded contact homology, which we will review. Joint work with Michael Hutchings, Agniva Roy, and Yuan Yao. |

10:10–11:10 | Ina Petkova, Dartmouth, Plenary talk
Spectral GRID invariants and Lagrangian cobordisms
▾ Knot Floer homology is a powerful invariant of knots and links, developed by Ozsvath and Szabo in the early 2000s. Among other properties, it detects the genus, detects fiberedness, and gives a lower bound to the 4-ball genus. The original definition involves counting homomorphic curves in a high-dimensional manifold, and as a result the invariant can be hard to compute. In 2007, Manolecu, Ozsvath, and Sarkar came up with a purely combinatorial description of knot Floer homology for knots in the 3-sphere, called grid homology. Soon after, Ozsvath, Szabo, and Thurston defined invariants of Legendrian knots using grid homology. We show that the filtered version of these GRID invariants, and consequently their associated invariants in a certain spectral sequence for grid homology, obstruct decomposable Lagrangian cobordisms in the symplectization of the standard contact structure, strengthening a result of Baldwin, Lidman, and Wong. This is joint work with Jubeir, Schwartz, Winkeler, and Wong. |

—— Coffee —— | |

11:40–12:40 | Kasia Jankiewicz, University of California Santa Cruz, Plenary talk
Profinite properties of Artin groups
▾ Artin groups are a family of groups that generalize braid groups, and can be defined and studied from various perspectives: topologically, algebraically, and combinatorially. They are mysterious - a lot of basic questions about them remain unanswered. Artin groups are given by simple looking group presentations, are closely related to Coxeter groups, and arise as the fundamental groups of certain complex hyperplane arrangements. In this talk, I will focus on profinite properties of Artin groups. Informally, those properties tell us if the geometry and algebra of the group can be approximated by its finite quotients. I will mention some joint work with Kevin Schreve. |

—— Lunch (Graduate and Speakers Student Luncheon in the Big Red Barn) —— | |

2:00–3:00 | Noel Brady, University of Oklahoma, Plenary talk
Isoperimetric inequalities and pushing fillings
▾ Suppose that a finitely presented group H is a normal subgroup of a hyperbolic group with free quotient. By a result of Gersten and Short the group H has a polynomial isoperimetric inequality. This is established by starting with a geometrically controlled disk filling in the ambient hyperbolic group of a loop in H and then pushing this filling into H. We describe other situations where one can push fillings with respect to height functions on spaces and give applications to subgroups of right-angled Artin groups and to Houghton groups. |

—— Break —— | |

3:30–4:30 | Nathan Dunfield, University of Illinois Urbana-Champaign, Plenary talk
Counting essential surfaces in 3-manifolds
▾ Counting embedded curves on a surface as a function of their length has been much studied by Mirzakhani and others. I will discuss analogous questions about counting surfaces in a 3-manifold, with the key difference that now the surfaces themselves have more intrinsic topology. As there are only finitely many essential surfaces of bounded Euler characteristic up to isotopy in an atoroidal 3-manifold, it makes sense to ask how the number of isotopy classes grows as a function of the Euler characteristic. Using Haken’s normal surface theory, we can characterize not just the rate of growth but show the exact count is a quasi-polynomial. Moreover, our method allows for explicit computations in reasonably complicated examples. |