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Conference Program

The conference will be held all day on Saturday, December 2, 2023. All events will be held in the Dolan School of Business (DSB), on the 1st floor. For directions, click on Directions above.

8:30 - 9:20am
Outside DSB 101 		Registration and Breakfast
Light breakfast (muffins and danishes) will be served.
9:20 - 9:30am
DSB 101 		Opening Remarks
9:30 - 10:15am
DSB 101 		Non-standard groups
Alexei Miasnikov (Stevens Institute of Technology)
In this talk I will introduce a notion of a non-standard version $G*$ of a given finitely generated (or countable) group \(G\), provided \(G\) satisfies some very mild conditions on its word problem. On the one hand these groups are kind of analogs of non-standard arithmetic or hyper reals, on the other hand they are non-standard points of the generalized algebraic schemes. I will touch on an unusual combinatorial/geometric group theory which comes together with these groups.
10:20 - 11:05am
DSB 101 		Simple groups, Turner groups and elementary equivalence
Anthony Gaglione (U.S. Naval Academy)
In this talk, we focus on some work that Dennis Spellman and I did with Ben Fine. We did alot of work with him so it is somewhat difficult to pick and choose one project over the other. We have decided, however, to talk about some of the questions left open in a paper we did jointly with Ben on Turner groups and first-order logic. This paper appeared in 2017 in the Communications in Algebra.
11:05 - 11:35am
Outside DSB 101 		Coffee & Tea Break
11:35 - 11:55am
DSB 101 		On Commutative Transitive and CSA Groups.
Dennis Spellman
In B. Fine, A.M. Gaglione, G. Rosenberger and D. Spellman, Commutative Transitivity (abb. CT) and the CSA property, "Infinite Group Theory From the Past to the Future," ed.'s: P. Baginski, B. Fine and A.M. Gaglione, World Sci., 2018, 95-117, a proof is given that a nonabelian CT group, \(G\), is not CSA iff it contains a nonabelian subgroup \(G_0\) which itself contains a nontrivial abelian subgroup, \(H\), which is normal in \(G_0\). In this talk, I give a new proof of that result.
12:00 - 12:50pm
DSB 101 		Hyperbolic groups, relatively hyperbolic groups, and the Cannon Conjecture.
Genevieve Walsh (Tufts University)
We describe several very interesting and rich classes of groups: hyperbolic groups and relatively hyperbolic groups. The fundamental group of a closed hyperbolic $3$-manifold is a good example of a hyperbolic group, and the fundamental group of a hyperbolic knot complement is a good example of a relatively hyperbolic group. We will explain some tools one can use with these groups, particularly their boundaries. We will explain several conjectures predicting when a hyperbolic group is a \(3\)-manifold group. If time permits, we will discuss partial results and relationships between these conjectures.
12:50 - 2:00pm
Dolan Event Hall - Side B 		Lunch
Assorted sandwiches and wraps.
2:00-2:20pm
DSB 101 		Session A: Algebraic Groups, Subgroups, and Invariants
Neha Hooda (Fairfield University)
Exceptional algebraic groups arise as groups of automorphisms of composition algebras. During the talk, I will discuss exceptional algebraic groups and the intricate relationship between their subgroups and invariants. Additionally, I will delve into the cohomology of these groups and how it influences their subgroup embeddings.
2:00 - 2:20pm
DSB 110 		Session B: Conformal dimension for certain Coxeter groups.
Emily Stark (Wesleyan University)
The boundary at infinity is an important tool to study the geometry of groups with aspects of negative curvature. The boundary of a group is a topological space that captures the directions to infinity in the group. For certain relatively hyperbolic groups this boundary further admits a canonical quasi-symmetric structure and has a well-defined conformal dimension. We study a family of Coxeter groups that fit in this framework, and we give bounds on the conformal dimension for these groups. Our results imply there are infinitely many quasi-isometry classes within this family. This is joint work with Elizabeth Field, Radhika Gupta, and Rylee Lyman.
2:30 - 2:50pm
DSB 101 		Session B: Encoding certain free group automorphisms and their associated geodesics in outer space.
Catherine Pfaff (Queens University)
Outer automorphisms of free groups are induced by homotopy equivalences of graphs. Stallings ('83) decomposed these homotopy equivalences into sequences of "folds" and Skora ('89) interpreted a Stallings fold decomposition as a sequence of folds performed continuously. Under the correct assumptions, this leads to geodesics in the deformation space of metrics on graphs, namely Culler-Vogtmann outer space. We create "train track automata" encoding a specific class of these geodesics. This is joint work with Damara Gagnier.
2:30 - 2:50pm
DSB 110 		Session A: Hypergeometric Sheaves and Finite General Linear Groups.
Tae Young Lee (Rutgers University)
Hypergeometric sheaves are certain continuous representations of the étale fundamental group of the multiplicative group which are, roughly speaking, "minimally wildly ramified". Katz, Rojas-Léon and Tiep have been studying which finite groups can be realized as the image of these representations. In this talk, I will briefly summarize their results, and discuss my results on the classification of irreducible hypergeometric sheaves which realize finite almost quasisimple groups which has PSL as its nonabelian factor.
2:50 - 3:30pm
Outside DSB 101 		Coffee & Tea Break
3:30 - 3:50pm
DSB 101 		Session A: Some Interesting Properties among the Baumslag Groups \(G(m,n)\).
Anthony Clement (Brooklyn College, CUNY)
The group \(G = \langle a, b | a = [ a, a^{b} ]\rangle\) re-expressed as \(G(1,2) = \langle a, b | b^{-1} a^{-1} bab^{-1} ab = a^2\rangle\) first appeared in G. Baumslag's 1969 paper ``A non-cyclic one-relator group all of whose finite quotients are cyclic" in which he showed that every finite quotient of \(G = \langle a, b | a = [ a, a^{b} ]\rangle\) is cyclic and as a result presented at the time yet another example of a one-relator group which was not residually finite. In this talk I will describe the structure and some interesting properties among the Baumslag groups \(\textit{G(m,n)}=\langle a,b; b^{-1}a^{-1} b a^m b^{-1} a b=a^n|m\neq 0, n\neq 0, m, n \in \mathbb{Z}\rangle\).
3:30 - 3:50pm
DSB 110 		Session B: The RAAG Recognition Problem for Bestvina--Brady Groups.
Yu Chan Chang (Wesleyan University)
Given a finite simplicial graph, the associated right-angled Artin group (RAAG) is generated by the vertex set of the graph, and two generators commute if they are connected by an edge. The RAAG Recognition Problem asks whether a given group is a RAAG. In joint work with Lorenzo Ruffoni, we consider this recognition problem for Bestvina–Brady groups (BBGs). In this talk, I will describe a graphical condition to certify when a BBG is a RAAG. In particular, we will see a complete solution to the RAAG Recognition Problem for the BBGs defined on 2-dimensional flag complexes.
4:00 - 4:20pm
DSB 101 		Session A: One-endedness of outer automorphism groups of free products.
Rylee Lyman (Rutgers University, Newark)
We classify the free products of finite groups and infinite cyclic groups whose outer automorphism groups are one ended. Surprisingly, this does not coincide with my conjectural classification: “when the virtual cohomological dimension is at least two”. As a consequence of our proof strategy, we show that all of these groups are semistable at each end.
4:00 - 4:20pm
DSB 110 		Session B: The 2-Complete Artin Complex.
Jill Mastrocola (Brandeis University)
Artin groups are a large and interesting class of groups with strong ties to Coxeter groups and mapping class groups. There are many long-standing open questions about Artin groups, and non-positively curved geometry has been a useful tool in many of the partial answers that we have. I will introduce the 2-complete Artin complex for locally reducible Artin groups and discuss a combinatorial version of non-positive curvature that it satisfies.
4:30 - 5:15pm
DSB 101 		Global-local conjectures in the representation theory of finite groups.
Pham Tiep (Rutgers University)
We will survey the history and progress on some of the main problems in the representation theory of finite groups. Then we will discuss the recent solution of one of them, the height zero conjecture of Richard Brauer, obtained in joint work with Malle, Navarro, and Schaeffer Fry, and building on previous work of many authors.
5:20 - 6:30pm
Dolan Event Hall - Side B 		Reception and Dinner
Italian and vegetarian buffet.