march 19 thursday 5–6pm edt (utc–4) 
Deciding if a rightangled Artin group is freebyfree is NPcomplete
Speaker: Zoran Sunik (Hofstra University)
Zoom: link, meeting id: 385 634 430 (recording on YouTube, slides)
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Organizing institution: New York Group Theory Seminar
Abstract:
We show that deciding if a rightangled Artin group is freebyfree is an NPcomplete problem. The work is based on an earlier result by Susan Hermiller and the speaker stating that the rightangled Artin group $A\Gamma$ defined by the graph $\Gamma$ is freebyfree if and only if $\Gamma$ is 2breakable (a graph $\Gamma$ is 2breakable if there exists an independent set $D$ of vertices in $\Gamma$ such that every cycle in $\Gamma$ contains as least two vertices from $D$). We reduce the 3SAT Problem to the problem of deciding if a given graph is 2breakable (in fact, $k$breakable, for any fixed $k \ge 1$). Once it is shown that the problem is NPcomplete, it is not difficult to show that it stays NPcomplete even if we restrict it to rightangled Artin groups defined by planar graphs. Note that the more special problem of deciding if a rightangled Artin group is freebyinfinitecyclic has a very simple answer. Namely, it follows easily from known results that the following three statements are equivalent. (1) $A\Gamma$ is freebyinfinitecyclic. (2) $\Gamma$ is a forest. (3) $A\Gamma$ embeds in the right angled group defined by the path of length 3. (Joint work with David Carroll and Benjamin Francisco.)

march 26 thursday 12:30pm cdt (utc–5) 
From sofic groups to $MIP^*=RE$
Speaker: Lewis Bowen
Zoom: link, meeting id: 915 496 893 (recording on YouTube)
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Organizing institution: ut Austin
Abstract:
This talk will be a gentle introduction to sofic groups, hyperlinear groups, Connes embedding conjecture, Tsirelsonâ€™s problem and its recent disproof by JiNatarajanVidickWrightYuen. The story starts with symbolic dynamics over countable groups, then journeys to von Neumann algebras and ends in quantum information theory.

march 26 thursday 5–6pm edt (utc–4) 
Quasisymmetry group of the basilica Julia set
Speaker: Sergiy Merenkov (City College of cuny)
Zoom: link, meeting id: 479 396 647 (recording on YouTube)
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Organizing institution: New York Group Theory Seminar
Abstract:
I plan to discuss how Thompson’s group $T$ acts on the basilica Julia set $J$ (the Julia set of $f(z)=z^21$) by quasisymmetries, and show that the group generated by $T$ and a certain inversion $\iota$ (that interchanges the Fatou components that contain the critical cycle) is dense (in the uniform topology) in the group of all quasisymmetries of $J$, with uniform quasisymmetric distortion bounds. This is joint work with Misha Lyubich.

march 31 tuesday 16:30 cet (utc+2)

Weakly maximal subgroups of branch groups
Speaker: PaulHenry Leemann (ens Lyon)
Zoom: link, meeting id: 696 379 617
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Organizing institution: University of Geneva
Abstract:
The first Grigorchuk group and many other branch groups have the property that all their maximal subgroups are of finite index. The next step is to understand weakly maximal subgroups, i.e. maximal among subgroups of infinite index. One class of such subgroups are parabolic subgroups, but what about the others? We will give the full description in the case of the first Grigorchuk group and discuss the general case.

april 2 thursday 4pm bst (utc+1) 
Computing $k$th roots in braid groups
Speaker: Maria Cumplido (HeriotWatt)
Zoom: link, meeting id: 224 687 512
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Organizing institution: HeriotWatt (Edinburgh)
Abstract:
There are several computational problems in braid groups that have been proposed for their potential applications to cryptography. The interest of the subject has decreased, mainly due to the appearance of algorithms which solve the conjugacy problem extremely fast in the generic case. However, there are some other problems in braid groups whose genericcase complexity is still to be studied. This is the case of the $k$th root (extraction) problem. In this talk we will see that, generically, the $k$th root of a braid (that has a $k$th root) can be computed very fast. We will describe an algorithm to do so by using Garside theory tools.

april 2 thursday 12:30pm cdt (utc5) 
Characteristic measures of symbolic dynamical systems. Joint with Joshua Frisch
Speaker: Omer Tamuz
Zoom: link, meeting id: 777 584 5012 (new id: 662 800 845)
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Organizing institution: ut Austin
Abstract:
A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic. This talk will include a gentle introduction to this topic.

april 2 thursday 2–3pm edt (utc–4)

Model spaces for relatively hyperbolic pairs
Speaker: Burns Healy (University of WisconsinMilwaukee)
Zoom: link (video recording)
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Organizing institution: Ohio State University
Abstract:
Relatively hyperbolic pairs are groups with preferred peripheral subgroups and are meant to generalize the behavior of nonuniform lattices in rank one symmetric spaces of noncompact type. While in geometric actions hyperbolic spaces are welldefined up to quasiisometry, cuspuniform actions by relatively hyperbolic pairs require two choices to be made in order to determine a QIclass of hyperbolic space. We examine the symmetric space case for the motivation behind the choice of a preferred type of space and prove these model spaces exist and are uniquely determined. In doing this we examine different kinds of horospherical geometry, prove internal geometry conditions sufficient for uniform perfection of the boundary of a hyperbolic space when acted on cuspuniformly, note the connection between space quasiisometries and boundary quasisymmetries, and demonstrate existence of some classes of cuspuniform actions on nonmodel spaces.

april 2 thursday 4–5pm edt (utc–4) 
Buildings, C*algebras and new higherdimensional analogues of the Thompson groups
Speaker: Alina Vdovina (University of Newcastle)
Zoom: link, meeting id: 686 861 660 (recording on Youtube, slides)
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Organizing institution: New York Group Theory Seminar
Abstract:
We present explicit constructions of infinite families of CWcomplexes of arbitrary dimension with buildings as the universal covers. These complexes give rise to new families of C*algebras, classifiable by their Ktheory. The underlying building structure allows explicit computation of the Ktheory. We will also present new higherdimensional generalizations of the Thompson groups, which are usually difficult to distinguish, but the Ktheory of C*algebras gives new invariants to recognize nonisomophic groups.

april 7 tuesday 16:30 cet (utc+2) 
Jointspectrum, selfsimilar groups and Schreier graphs
Speaker: Rostislav Grigorchuk (Texas A&M)
Zoom: link
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Organizing institution: University of Geneva
Abstract:
We will explain how the idea of joint spectrum of a pencil of operators was used to study the spectral problem for graphs and groups. Selfsimilar groups will be defined and their role in mathematics will be outlined. A few results about joint spectra of operators associated with selfsimilar groups such as the “first” group of intermediate growth, the lamplighter group, and the Hanoi Towers groups on three pegs will be stated. Also it will be explained how renormalization is involved into the spectral problem

april 8 wednesday 4pm bst (utc+1) 
An analog to the curve complex for Artin groups: generalizing to the FCtype case
Speaker: Rose MorrisWright (Brandeis)
Zoom: link, meeting id: 826 667 917, password: 607189
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Organizing institution: HeriotWatt (Edinburgh)
Abstract:
Artin groups are a generalization of braid groups that provide a rich field of examples and counterexamples for many algebraic, and geometric properties. While many particular types of Artin groups, including finite type Artin groups, are well understood, generalizing these results requires a new set of geometric tools. One geometric structure recently constructed to study finite type Artin groups is the complex of parabolic subgroups. This simplicial complex, developed by Cumplido, GonzalezMeneses, Gebhardt and Weist, generalizes the curve complex for braid groups. I will explain how this complex is constructed and how their definition can be generalized to the FCtype case. I will also discuss some known and conjectured properties of this complex.

april 9 thursday 5–6pm edt (utc–4) 
Coarse computabilty and the Hausdorff distance between Turing degrees. (How even more geometric group theory invaded the theory of computability.)
Speaker: Paul Schupp (University of Illinois at UrbanaChampaign)
Zoom: link, meeting id: 542 955 793 (email Ilya Kapovich from a university email address for the password) (recording on YouTube, slides)
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Organizing institution: New York Group Theory Seminar
Abstract: Joint work with Carl Jockusch.
Coarse computabilty studies how well arbitrary sets can be approximated in terms of computable sets. Define two sets $A$ and $B$ of natural numbers to be coarsely similar, written $A \thicksim_c B$, if their symmetric difference $A \triangle B$ has density $0$ in the sense of classical asymptotic density from number theory. This relation is an equivalence relation, so we consider the space $\mathcal{S} = \mathcal{P}(\mathbb{N})/\thicksim_c $ of coarse similarity classes. There is a natural density metric defined on $\mathcal{S}$ by setting $\delta(A,C)$ to be the upper density of their symmetric difference.
The space $\mathcal{S}$ is very interesting. While neither separable nor compact, it is both complete and contractible. Indeed, $\mathcal{S}$ is a geodesic metric space so it is a hyperbolic space in the sense of Gromov with the property that there are uncountably many different geodesics be any two distinct points of $\mathcal{S}$.
Define the core, or lower cone, $\kappa(d)$, of a Turing degree $d$ to be the family $\{ [A] \}$ of all classes of sets such that $A \le_T d$. The closure $\overline{d}$ of the degree d is the closure of $\kappa(d)$ in $\mathcal{S}$. Define the distance $H(d, e)$ between two Turing degrees as the Hausdorff distance between their closures in $\mathcal{S}$. This distance has an equivalent definition solely in terms of computability theory. It turns out that the the Hausdorff distance between any two degrees is either $0$, $\frac12$ or $1$.

april 10 friday 2pm edt (utc4) 
Random walks on punctured convex real projective surfaces
Speaker: Harrison Bray (University of Michigan)
Zoom: link (password shared on mailing list)
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Organizing institution: Columbia University
Abstract:
I'll discuss the following result, joint with Giulio Tiozzo: Letting $\Gamma$ be the representation of a punctured hyperbolic surface group in $\mathrm{PSL}(3,\mathbb{R})$ acting discretely, properly discontinuously, and with finite covolume on a properly convex set in the projective plane, we have that hitting measure for a random walk on any $\Gamma$orbit with certain moment conditions is singular with respect to the classical PattersonSullivan measure. The approach extends and adapts the strategy of MaherTiozzo for punctured hyperbolic surfaces. We also prove an essential global shadow lemma for finite volume convex real projective manifolds.

april 16 thursday 3pm edt (utc4) 
Circumcenter extension maps for Hadamard manifolds
Speaker: Merlin IncertiMedici (University of Zurich)
Zoom: link (recording on YouTube)
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Organizing institution: Ohio State University
Abstract:
Given a CAT(1) space, we can associate to it a boundary at infinity and a cross ratio on said boundary. There is a series of results that tell us that, for sufficiently nice CAT(1) spaces, the boundary together with the cross ratio uniquely determines the interior space. The proof of these results can be understood in terms of the construction of a circumcenter extension map. It turns out that this relationship between boundary and interior space generalizes nicely to a large class of CAT(0) spaces. In this talk, we will survey some known results, explain the construction of the circumcenter extension and show that the boundary roughly determines the interior space for a large class of manifolds.

april 16 thursday 5–6pm edt (utc4) 
Spectra of Laplacians on Cayley and Schreier graphs
Speaker: Tatiana SmirnovaNagnibeda (University of Geneva)
Zoom: link, meeting id: 651 394 835 (email Ilya Kapovich from a university email address for the password) (recording on YouTube, slides)
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Organizing institution: New York Group Theory Seminar
Abstract:
We are interested in Laplacians on graphs associated with finitely generated groups: Cayley graphs and, more generally, Schreier graphs corresponding to some natural group actions. The spectrum of such an operator is a compact subset of the closed interval $[1,1]$, but not much more can be said about it in general. We will discuss various techniques that allow to construct examples with different types of spectra  connected, union of two intervals, totally disconnected  and with various types of spectral measure. The problem of spectral rigidity will also be addressed.

april 22 wednesday 15:00 bst (utc+1) 
Conjugator length
Speaker: Tim Riley (Cornell)
Zoom: link, meeting id: 969 8318 2430, password: 152893
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Organizing institution: HeriotWatt (Edinburgh)
Abstract:
The conjugator length function of a finitely generated group $G$ maps a natural number $n$ to the minimal $N$ such that if $u$ and $v$ are words representing conjugate elements of $G$ with the sum of their lengths at most $n$, then there is a word $w$ of length at most $N$ such that $uw=wv$ in $G$. I will explore why this function is important, will describe some recent results with Martin Bridson and Andrew Sale on how it can behave, and will draw attention to some of the many open questions.

april 23 thursday 5–6pm edt (utc–4) 
Torsion subgroups of groups with cubic Dehn function
Speaker: Frank Wagner (Vanderbilt University)
Zoom: link, meeting id: 452 756 4182 (email Ilya Kapovich from a university email address for the password) (recording on YouTube, slides)
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Organizing institution: New York Group Theory Seminar
Abstract:
The Dehn function of a finitely presented group, first introduced by Gromov, is a useful invariant that is closely related to the solvability of the groupâ€™s word problem. It is wellknown that a finitely presented group is word hyperbolic if and only if it has subquadratic (and thus linear) Dehn function. A result of Ghys and de la Harpe states that no word hyperbolic group can have a (finitely generated) infinite torsion subgroup. We show that the same does not hold for finitely presented groups with Dehn function as small as cubic. In particular, for every $m \geq 2$ and sufficiently large odd integer $n$, there exists an embedding of the free Burnside group $B(m,n)$ into a finitely presented group with cubic Dehn function.

april 24 friday 2:00pm edt (utc4) 
Some new CAT(0) freebycyclic groups
Speaker: Rylee Lyman (Tufts)
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Organizing institution: Columbia University
Abstract:
As with fundamental groups of 3manifolds fibering over the circle, freebycyclic groups form a varied and interesting class of groups whose geometry depends in large part on the corresponding monodromy, in this case an outer automorphism of the free group. For example, Hagen and Wise showed that wordhyperbolic freebycyclic groups act virtually cospecially on CAT(0) cube complexes, while Gersten found an example of a freebycyclic group that cannot be even a subgroup of a CAT(0) group. Gersten's group admits a cyclic hierarchy, an iterated splitting as a graph of groups with freebycyclic vertex groups and cyclic edge groups, terminating in $\mathbb{Z}\times\mathbb{Z}$. By contrast, we show that a large class of freebycyclic groups admitting an additional symmetry act geometrically on CAT(0) 2complexes. Up to taking powers this includes mapping tori of all polynomiallygrowing palindromic and symmetric automorphisms. A key tool in the proof is our construction of socalled CTs for free products.
