9:15-10:00 Breakfast in JWB lounge

10:00-10:50 Agol

11:10-12:00 Goffer

2-2:50 Le

3-3:50 Minahan

4:20 - 5:15 Lightning talks

Conference Dinner

Sunday

9:15-10:00 Breakfast in JWB lounge

10:00-10:50 Verberne

11:10-12:00 Zelerowicz

Speaker: **Becky Eastman**

Title: Separable homology of graphs and the Whitehead
complex

Abstract: Given a finite-type surface Σ and a collection
𝒞 of curves on Σ, a natural question to ask is, do lifts of
curves in 𝒞 generate the homology of every finite cover of
Σ? Versions of this question have been studied by numerous
authors (Farb-Hensel '16, Koberda-Satharoubane '16,
Malestein-Putman '19, Klukowski '23, Boggi-Putman-Salter
'23). Our version of this question is: let Γ be a finite
regular cover of the rose. We identify the fundamental group of
the rose with a finite-rank free group. Is the fundamental
group of Γ generated by lifts of elements in a proper free
factor of the free group? We define a locally infinite
1-complex **Wh**(Γ) called the Whitehead complex of Γ which
is connected if and only if the answer to this question is
yes. Interestingly, if Γ represents a characteristic
subgroup or Γ is the rose, **Wh**(Γ) admits an action of **Out**(**F**_{n})
by isometries. Every component of **Wh**(Γ) has
infinite diameter, and the Whitehead complex of the rose is
nonhyperbolic.

Speaker: **Brian Udall**

Title: Combinations of parabolically geometrically
finite groups

Abstract: We consider the set of parabolically
geometrically finite subgroups of mapping class groups of closed
surfaces, a collection containing all finitely generated Veech
groups and convex cocompact groups. In this talk, we'll discuss
a combination theorem for these groups, motivated by and
generalizing the combination theorem of Leininger-Reid for Veech
groups. In particular, we establish that Leininger-Reid surface
groups are parabolically geometrically finite.

Speaker: **Carlos Ospina**

Title: Real rel flow

Abstract: I will explain what the real rel flow is
in the setting of translation surfaces with two cone angles.

Title: Projective Structures on the Circle

Abstract: In this talk we will describe the topological
space of projective structures on the circle.

Speaker: **Leslie Mavrakis**

Title: Branched Manifolds and Thurston's Geometries

Abstract: In joint work with Daryl Cooper and Priyam
Patel we prove that for every model geometry, G, there is a
compact branched manifold, W(G), with the property that
a closed 3-manifold M has a G-structure if and only if there
is an immersion of M into W(G). In this talk, I will give some
background on branched manifolds and describe W(G) when G is
S^3.

Speaker: **Michael Zshornack**

Title: Arithmetic with Mickey Mouse

Abstract: "Bending" is a way of deforming
representations of surface groups to new ones with more
interesting properties. For instance, it is one way of
constructing quasi-Fuchsian groups from Fuchsian ones. An
oft overlooked aspect of this deformation is its
underlying arithmetic nature, but this perspective has
proven especially useful in studying higher Teichmüller
spaces, whose arithmetic properties have interesting
relations to higher-rank lattices. In this talk, I'll
outline the general idea behind this deformation and how
its arithmetic nature has been useful in studying the
Hitchin component, one example of a higher Teichmüller
space. This is partially based on joint work with Jacques
Audibert.

Speaker: **Rebecca Rechkin**

Title: Normal Stalling's Completion

Abstract: A group G is residually finite if for every
nontrivial element g, there exists a finite quotient of G
where g is not in the kernel of the quotient. Stallings
completion provides a geometric algorithm for finding a
finite index subgroup of the rank n free group that does not
contain a specific word g by constructing an appropriate
cover of the wedge of n circles. However, the algorithm does
not usually construct a normal cover of the wedge of
circles. In this talk I will give a new algorithm that
produces a normal subgroup of the rank n free group that
does not contain a specific word g by constructing normal
covers of the rose. This work is motivated by a body of
research dedicated to quantifying residual finiteness for
certain classes of groups.

Speaker: **Ryan Dickmann**

Title: Mapping class groups of surfaces with
noncompact boundary

Abstract: We will talk about sliced Loch Ness monsters,
disks with handles, and the classification of surfaces
with noncompact boundary due to Brown and Messer. We will
also see some general theorems on the mapping class groups
of surfaces that were made possible through understanding
the Brown and Messer classification.

Speaker: **Thomas Hill**

Title: Large-Scale Geometry of Pure Mapping Class
Groups of Infinite-Type Surfaces

Abstract: The work of Mann and Rafi gives a
classification surfaces Σ when Map(Σ) is globally CB,
locally CB, and CB generated under the technical
assumption of tameness. We restrict our study to the pure
mapping class group and give a complete classification
without additional assumptions. In stark contrast with the
rich class of examples of Mann–Rafi, we prove that PMap(Σ)
is globally CB if and only if Σ is the Loch Ness monster
surface, and locally CB or CB generated if and only if Σ
has finitely many ends and is not a Loch Ness monster
surface with (nonzero) punctures.

Speaker: **Vivian He**

In this talk, I will delve into the superlinear divergence property, as well as its geometric consequences that led to the theory of random walks on groups containing superlinear divergent quasi-geodesics. This is based on joint work with Kunal Chawla, Inhyeok Choi, and Kasra Rafi.

Title: Random walks on groups and superlinear
divergent quasi-geodesics

Abstract: When studying random walks on a group, a
natural question is how far is the n-th step from the
origin. The central limit theorem says that,
asymptotically, it follows a normal distribution. We
proved this for groups containing superlinar divergent
quasi-geodesics. The advantage of this setting compared
to previous versions of CLT is that it is invariant
under quasi-isometry.

In this talk, I will delve into the superlinear divergence property, as well as its geometric consequences that led to the theory of random walks on groups containing superlinear divergent quasi-geodesics. This is based on joint work with Kunal Chawla, Inhyeok Choi, and Kasra Rafi.

Speaker: **Wiktor Mogilski**

Title: A discrete four vertex theorem for
hyperbolic polygons

Abstract: There are many four vertex type
theorems appearing in the literature, coming in both
smooth and discrete flavors. The most familiar of these
is the classical theorem in differential geometry, which
states that the curvature function of a simple smooth
closed curve in the plane has at least four extreme
values. This theorem admits a natural discretization to
Euclidean polygons due to O. Musin. In this talk we
adapt the techniques of Musin and provea discrete four
vertex theorem for convex hyperbolic polygons.

Speaker: **Ziqiang Li**

Title: Winding Number for the Spherical Point-in-Polygon Problem

Abstract: We revisit the spherical point-in-polygon problem and discuss how the winding number could be made sense of, for a very practical subclass of spherical polygons: boundary antipode-excluding spherical polygons.

Title: Winding Number for the Spherical Point-in-Polygon Problem

Abstract: We revisit the spherical point-in-polygon problem and discuss how the winding number could be made sense of, for a very practical subclass of spherical polygons: boundary antipode-excluding spherical polygons.