In the Fall 2026 semester the New York Group Theory Seminar will meet with most talks in-person and some occasional 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, September 18, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Jennifer Taback (Bowdoin College)
Title: An overview of medium-scale Ricci curvature for discrete groups
Abstract:
Bar-Natan, Duchin, and Kropholler introduced medium-scale Ricci curvature as a discrete curvature for Cayley graphs of finitely generated groups, computed at varying scales to capture different aspects of the geometry. In the first half of the talk I will motivate this definition and relate it to some standard properties studied in geometric group theory. I will then describe the unusual behavior of this curvature in Thompson's group F with respect to the standard finite generating set. Like the discrete Heisenberg group, F contains a positive density of elements of positive curvature, of negative curvature, and of zero curvature at any scale. Additionally, for each of the three possible signs, every isomorphism class of subgroups of F contains countably many representatives in which all nontrivial elements have curvature of that sign, at any scale. This is joint work with Sean Cleary.
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New York Group Theory Seminar: Friday, September 25, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Alina Vdovina (City College)
Title: Equations in Products of Free Groups and 3-Manifold Groups (joint with Olga Kharlampovich).
Abstract:
The fundamental groups of 3-manifolds attract lots of interest from mathematicians of different fields. As it was stated in a famous survey of Allen Hatcher "The classification of 3-manifolds", one would want to know exactly which groups occur as fundamental groups of these manifolds. We express the fundamental groups of all closed orientable 3-manifolds in terms of generators and relations in a uniform way, using algebraic descriptions of Dehn twists, discovered by Olga Kharlampovich and Alexei Miasnikov in their work on Tarski conjecture.
Our goal is to understand connections with existing results on 3-manifold groups.
One of the most interesting connections is
the Stallings-Jaco-Hempel reformulation of the Poincare conjecture. The Poincare conjecture was proved by Perelman in 2003.
Olshanskii in1989 constructed first non-trivial examples of splitting epimorphisms defined by Stallings and showed some of them were standard. We analyse a large class of such homomorphisms/presentations,including all Olshanskii's epimorphisms, and show that splitting epimorphisms are rare. In this case the corresponding balanced presentation of the trivial group can be reduced to the standard one by Andrews-Curtis transformations and the epimorphisms are standard.
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New York Group Theory Seminar: Friday, October 2, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Ilya Kapovich (Hunter College and CUNY Graduate Center)
Title: Small cancellation stability and isomorphism rigidity of generic finitely presented groups
Abstract:
For 0<\lambda<1, we say that a set R of nontrivial cyclically reduced words in F_m=F(a_1,..,a_m) is \lambda-stable if for every automorphism \Phi of F_m, the set \Phi(R), after cyclic reductions and symmetrization, satisfies the C'(\lambda) small cancellation condition. We prove that if q\ge 1 is any fixed integer, then there exists an exponentially generic set Q of q-tuples of cyclically reduced words in F_m such that every q-tuple W=(w_1,..,w_q) in this set is \lambda-stable. We combine this result with the prior results of Kapovich-Schupp on Nielsen uniqueness for generic finitely presented groups and the results of Kapovich-Schupp-Shpilrain on generic-case behavior of Whitehead's algorithm to prove that for any fixed m\ge 2, q\ge 1, generic m-generated finitely presented groups possess strong Isomorphism Rigidity. Namely, two such generic groups G=<a_1,..., a_m|w_1,..,w_q> and G'=<a_1,..,a_m|w_1',..,w_q'> are isomorphic as groups if and only if their Cayley graphs over A=\{a_1,..,a_m\} are isomorphic as labelled graphs, after possibly permuting A and inverting some generators from A. As an application, we prove that the number I_{m,q}(n) of isomorphism types of groups given by presentations <a_1,..,a_m|w_1,..,w_q>, where w_i are cyclically reduced of length n, is asymptotic to \frac{(2m-1)^{qn}}{2^{m+q}m!q!n^q}
The proof of generic \lambda-stability relies on the use of geodesic currents and on our deterministic sufficient criterion for a q-tuple W in F_m to be \lambda-stable in terms of the components of W being sufficiently projectively close to filling currents.
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New York Group Theory Seminar: Friday, October 9, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Yukun Du (University of Georgia)
Title: Two-Generator Discrete Subgroups of Tree Automorphism Groups
Abstract:
I will discuss the classification of discrete two-generator groups acting on locally finite trees. Under a small-geometry condition, the possible groups and quotient graphs are strongly constrained and can be classified explicitly. I will then explain how the picture becomes much richer beyond this regime, including higher-index amalgams and families with arbitrarily complicated quotient geometry.
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New York Group Theory Seminar: Friday, October 16, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Lucy Koch-Hyde (CUNY Graduate Center)
Title: Stallings core graphs and the growth of rank for subgroups of free groups
Abstract:
By analayzing the combinatorial properties of Stallings core graphs coresponding to subgroups of free groups we can establish bounds on their rank. These bounds directly answer a question posed by Dotsenko about the maximum rank of subgroups of free groups generated by words of limited length. However, they are also useful for studying the growth of basis-like subsets of the free group. In particular we can answer a problem from the 10th edition of the Kourovka notebook posed by Grigorchuk, which relates to the growth of infinite non-redundant relator sets. I will also discuss the implications for problems similar to Grigorchuk's.
Joint work with Éamonn Olive.
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New York Group Theory Seminar: Friday, October 23, 2026, 4:15pm, room 6417, CUNY Graduate Center
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New York Group Theory Seminar: Friday, October 30, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Maggie Shideler (Hunter College of CUNY)
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New York Group Theory Seminar: Friday, November 6, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Emma Dinowitz (CUNY Graduate Center)
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New York Group Theory Seminar: Friday, November 13, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Danielle West (Tel Aviv University)
Title: Cores of modules over free group algebras
Abstract:
Stallings core graphs are a powerful graphical representation of the finitely generated subgroups of a free group. They bring geometric insight to the study of free groups, make many properties and algorithmic tasks transparent, and are a ubiquitous tool in combinatorial and geometric group theory.
Free group algebras are strikingly analogous to free groups. Most notably, just as the Nielsen-Schreier theorem says that every subgroup of a free group is free, the Cohn-Lewin theorem says that every right (or left) ideal of a free group algebra is free. Yet free group algebras have had no counterpart to core graphs.
In this talk I will present one. We define the core of a module over a free group algebra, and show that it is unique whenever the module is algebraic (also known as bound). Many of the concepts of Stallings' theory, such as folding and pullbacks, generalize to these new objects, and this yields simple proofs and algorithms for many natural problems about free group algebras. For example, I will present an algorithm for testing primitivity in free modules which generalizes (Wilton's simplification of) Whitehead's classical algorithm for testing primitivity in free groups.
This is joint work with Doron Puder.
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New York Group Theory Seminar: Friday, November 20, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Iryna Kashuba (Southern University of Science and Technology Shenzhen)
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New York Group Theory Seminar: Friday, December 4, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: David Fisher (Rice University)
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New York Group Theory Seminar: Friday, December 11, 2026, 4:15pm, room 6417, CUNY Graduate Center
Speaker: Alon Dogon (Columbia University)
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