In the Spring 2024 semester the New York Group Theory Seminar will meet in a hybrid format, with most talks in-person and some talks online.

The in-person talks will be on Fridays at 4:15pm eastern time, room 6417. The online Zoom talks will be on Fridays at 4:00pm U.S. eastern time.

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New York Group Theory Seminar: Friday, February 9, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:  Rylee Lyman  (Rutgers University - Newark)

Title:  When is (the spine of) the Outer Space of a free product CAT(0)?

Abstract: 

CAT(0) geometry, a comparison geometry introduced by Gromov, is a beautiful "fine-scale" geometry providing a common generalization of the geometries of Euclidean and hyperbolic spaces, on the one hand, and certain nonmanifold spaces, like trees, on the other. Bridson in his thesis showed that the spine of Culler and Vogtmann's Outer Space for the free group never supports a "nice" CAT(0) metric when the rank of the free group in question is at least three.  Guirardel and Levitt generalized Culler and Vogtmann's construction of an Outer Space to the case of free products of groups. In this talk we will completely settle the question of when these Outer Spaces admit "nice" CAT(0) metrics. Like Bridson, our results are mostly negative, with one surprising family of positive results.

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New York Group Theory Seminar: Friday, February 23, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:  Martin Bridson  (University of Oxford)

Title:  Acyclic embeddings of groups,  profinite rigidity, and finiteness properties

Abstract: 

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. Related to this, one wants to know which properties of groups are profinite invariants, i.e. if G has a property P and H has the same finite quotients as G, does H have property P? I shall sketch the proof of an embedding theorem for groups that can be used to construct Grothendieck pairs showing that many properties are not profinite invariants of finitely generated, residually finite groups -- for example, containing Z^3, or being  virtually free-by-free. I shall also describe results showing that there is a sharp difference between finitely generated and finitely presented groups in this context.

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New York Group Theory Seminar: Friday,  March 1, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:  Olga Kharlampovich  (Hunter College)

Title:  Quantifying separability in RAAGs via representations

Abstract: 

We answer the question asked by Louder, McReinolds and

Patel  and prove the following statement. Let L be a RAAG, H a

cubically convex-cocompact subgroup of L, then there is a finite

dimensional representation of L that separates the subgroup H

in the induced Zariski topology. As a corollary, we establish a

polynomial upper bound on the size of the quotients used to separate H

in L.

This implies the same statement for a virtually special group L and, in

particular, a fundamental group of a hyperbolic 3-manifold.

We use techniques similar to the ones used

in  the paper by K. Brown and O. Kharlampovich, quantifying

separability for limit groups.

This is a joint work with Alina Vdovina.

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New York Group Theory Seminar: Friday,  March 8, 2024,  4:00pm U.S. eastern time,  online Zoom talk

Zoom link: If you did not receive the meeting Zoom info from an NYGT mailing list message, please e-mail Ilya Kapovich at ik535@hunter.cuny.edu to a request for a Zoom link.

Speaker:  Laura Ciobanu (Heriot-Watt University)

Title:  Group equations, constraints and decidability

Abstract: 

In this talk I will discuss group equations with non-rational constraints, a topic inspired by the long line of work on word equations with length constraints. Deciding algorithmically whether a word equation has solutions satisfying linear length constraints is a major open question, with deep theoretical and practical implications. I will introduce equations in groups and several kinds of constraints, and show that equations with length, abelian or context-free constraints are decidable in virtually abelian groups (joint with Alex Evetts and Alex Levine). This contrasts the fact that solving equations with abelian constraints is undecidable for non-abelian right-angled Artin groups and hyperbolic groups with ‘large’ abelianisation (joint work with Albert Garreta).

A link to the YouTube video recording of the talk is available here.

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New York Group Theory Seminar: Friday,  March 22, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:   Cargi Sert (University of Zurich)

Title:  Counting limit theorems for representations of Gromov-hyperbolic groups

Abstract: 

Let \Gamma be a Gromov-hyperbolic group and S a finite symmetric generating set.

The choice of S determines a metric on \Gamma (namely the graph metric on the associated

Cayley graph). Given a representation  \Gamma \to GLd(R), we are interested

in obtaining statistical information on the deterministic sequence of spherical

averages (with respect to S-metric) for various numerical quantities (such as Eu-

clidean norm) associated to elements of \Gamma via the representation. We will discuss

a general law of large numbers and more re fined limit theorems such as central

limit theorem and large deviations. The connections with the results of Lubotzky-Mozes-Raghunathan

and Kaimanovich-Kapovich-Schupp will also be discussed.

Joint work with Stephen Cantrell.

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New York Group Theory Seminar: Friday,  April 12, 2024: the talk is rescheduled to Friday, May, 10, 2024

Speaker:  Lisa Carbone  (Rutgers University)

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New York Group Theory Seminar: Friday,  April 19, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:   Tamunonye Cheetham-West (Yale University)

Title:  Finite quotients and Property FA

Abstract: 

Some groups have actions on trees that have no global fixed point while other groups always have a global fixed point whenever they act on a tree. The latter are said to have Property FA. I will discuss examples of group pairs where both groups in each pair have all the same finite quotients, but one group has Property FA and the other group doesn't. This is joint work with Alex Lubotzky, Alan Reid, and Ryan Spitler.

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New York Group Theory Seminar: Friday,  May 3, 2024,  4:00pm U.S. eastern time,  online Zoom talk

Zoom link: If you did not receive the meeting Zoom info from an NYGT mailing list message, please e-mail Ilya Kapovich at ik535@hunter.cuny.edu to a request for a Zoom link.

Speaker:  Susan Hermiller (University of Nebraska - Lincoln)

Title:  Subgroups of the group of dyadic piecewise linear homeomorphisms of the real line

Abstract: 

The group of dyadic orientation-preserving piecewise linear (PL) homeomorphisms of the unit interval is called Thompson's group F, and the question of which groups are - or cannot be - subgroups of F has yielded many interesting results. In this talk I'll discuss the question of what groups can or cannot be subgroups of Aut(F) (the automorphism group of F), and more particularly subgroups of an index 2 subgroup of Aut(F) that is isomorphic to a group of dyadic PL homeomorphisms of the real line. This is joint work (in progress) with Conchita Martinez-Perez.

A link to a Youtube video recording of the talk is available here.

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New York Group Theory Seminar: Friday,  May 10, 2024,  4:15pm, room 6417, CUNY Graduate Center

Speaker:  Lisa Carbone  (Rutgers University)

Title:  The primary Lie group for the Monster Lie algebra

Abstract: 

The Monster Lie algebra m is a Borcherds algebra which admits an action of the Monster finite simple group M. This infinite dimensional Lie algebra was an important structure in Borcherds' proof of part of the Conway-Norton Monstrous Moonshine conjecture. We discuss the construction of a Lie group analog G(m) associated to m. The group G(m)  has a subgroup GL_2(-1) corresponding to the unique real simple root (1,-1) and an infinite family of subgroups GL_2(n,u,v) corresponding to imaginary simple roots (1,n) and suitable pairs of primary vectors u,v in V^\natural, the Moonshine module of Frenkel, Lepowsky and Meurman. The Monster finite simple group M acts on this set of subgroups. The group G(m) also has a subgroup U^+ analogous to a unipotent group, which acts on a completion of m. The group M  acts on U^+ and the map from the completion to U^+ is M-equivariant.

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