Matt Zaremsky – SUNY Albany

 The Boone-Higman conjecture (1973) predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. The “if” direction is true and easy, but the “only if” direction has been open for over 50 years. The conjecture is known to hold for various families of groups, perhaps most prominently the groups GL_n(Z) (due to work of Scott in 1984), and hyperbolic groups (due to work of Belk, Bleak, Matucci, and myself in 2023). In this talk I will discuss some recent work joint with Belk, Fournier-Facio, and Hyde establishing the conjecture for Aut(Fn), the group of automorphisms of the free group Fn. I will also highlight an interesting sufficient condition for satisfying the conjecture, which just amounts to finding an action of the group with certain properties, with no need to actually deal with simple groups. 

Host: Denis Osin

Matt Zaremsky – SUNY Albany

The Boone-Higman conjecture (1973) predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. The “if” direction is true and easy, but the “only if” direction has been open for over 50 years. The conjecture is known to hold for various families of groups, perhaps most prominently the groups GL_n(Z) (due to work of Scott in 1984), and hyperbolic groups (due to work of Belk, Bleak, Matucci, and myself in 2023). In this talk I will discuss some recent work joint with Belk, Fournier-Facio, and Hyde establishing the conjecture for Aut(Fn), the group of automorphisms of the free group Fn. I will also highlight an interesting sufficient condition for satisfying the conjecture, which just amounts to finding an action of the group with certain properties, with no need to actually deal with simple groups. 

Host: Denis Osin

Leonardo Abbrescia, Georgia Tech

A Lorentzian manifold-with-boundary where causality breaks down due to shock singularities

We present a novel example of a Lorentzian manifold-with-boundary featuring a dramatic degeneracy in its deterministic and causal properties known as “causal bubbles” along its boundary. These issues arise because the regularity of the Lorentzian metric is below Lipschitz and fit within the larger framework of low regularity Lorentzian geometry. Although manifolds with causal bubbles were recently introduced in 2012 as a mathematical curiosity, our example comes from studying the fundamental equations of fluid mechanics and shock singularities which arise therein. No prior knowledge of Lorentzian geometry or fluid mechanics will be assumed for this talk.

Anastasios Fragkos – Georgia Tech

For $c\in(1,2)$ we consider the following operators
\[\mathcal{C}_{c}f(x) \coloneqq \sup_{\lambda \in [-1/2,1/2)}\bigg| \sum_{n \neq 0}f(x-n) \frac{e^{2\pi i\lambda \lfloor |n|^{c} \rfloor}}{n}\bigg|\text{,}\quad        \mathcal{C}^{\mathsf{sgn}}_{c}f(x) \coloneqq \sup_{\lambda \in [-1/2,1/2)}\bigg| \sum_{n \neq 0}f(x-n) \frac{e^{2\pi i\lambda \mathsf{sign(n)} \lfloor |n|^{c} \rfloor}}{n}\bigg| \text{,}\]
and prove that both extend boundedly on $\ell^p(\mathbb{Z})$, $p\in(1,\infty)$. The second main result is establishing almost everywhere pointwise convergence for the following ergodic averages
\[A_Nf(x)\coloneqq\frac{1}{N}\sum_{n=1}^Nf(T^nS^{\lfloor n^c\rfloor}x)\text{,}\]
where $T,S\colon X\to X$ are commuting measure-preserving transformations on a $\sigma$-finite measure space $(X,\mu)$, and $f\in L_{\mu}^p(X)$, $p\in(1,\infty)$. The point of departure for both proofs is the study of exponential sums with phases $\xi_2 \lfloor |n^c|\rfloor+ \xi_1n$ through the use of a simple variant of the circle method.

Madeline Brandt – Vanderbilt

Abstract- TBA

Oishee Banerjee – Florida State University

Abstract- TBA

Host – Dan Margalit

Steve Trettel, University of San Francisco

What do 3-manifolds Look Like?

Thurston’s Geometrization Theorem, later proved by Perelman, describes 3-manifolds in terms of geometric building blocks. Each manifold decomposes into pieces modeled on one of just eight homogeneous 3-dimensional spaces, known as the Thurston geometries.

In this talk, we explore the question: ‘What does a 3-manifold look like?’ through the lens of geometrization. After discussing how one might compute the “inside view” one would see in such spaces, we will use software written in collaboration with Remi Coulon, Sabetta Matsumoto, and Henry Segerman to explore some manifolds built from the Thurston geometries. Finally, we will see how these geometric pieces can be fit together to form a picture of general 3-manifolds.

Caglar Uyanik- University of Wisconsin, Madison

Abstract- TBA

Ronnie Pavlov, University of Denver

Title and abstract tba

John Ratcliffe – Emeriti- Vanderbilt

In this talk, we will show how to compute the G-index of a spin closed hyperbolic 4-manifold M for a group G of symmetries of a spin structure on M. As an example, we will compute the G-index for the group G of symmetries of the fully symmetric spin structure on the Davis closed hyperbolic 4-manifold M. Our talk will involve finite groups, infinite discrete groups, and Lie groups.  The talk is based on joint work with Steven Tschantz.

Robbie Lyman – Rutgers

In geometric group theory, we love groups and graphs. Every (abstract) group has (many) Cayley graphs, each one associated with a choice of a generating set. Recently I’ve been curious about topological groups, inspired by the budding theory around and community of people inspired by mapping class groups of infinite-type surfaces and by Christian Rosendal’s breakthrough work on geometries for topological groups. I’m hoping to share out some of what I’ve learned about topological groups acting on graphs. Much of this comes from recent joint work with Beth Branman, George Domat and Hannah Hoganson.

Host: Talia Fernos

Mark de Cataldo, Stony Brook University

Title and abstract tba