Titles and abstracts​

 

Friday, March 20th (room TBA)

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• 15:00 - 15:50 Macarena Arenas (University of Cambridge)

Cubical quotients of cubical non-products

Burger and Mozes constructed examples of simple groups acting geometrically on a CAT(0) complex which is a product of trees. We show that, in a sense, this is the only possibility. Namely that every group acting geometrically on a CAT(0) cube complex which is not a product admits a nontrivial quotient which also acts geometrically on a CAT(0) cube complex. The proof utilises cubical small-cancelation theory, which I will survey during the talk. This is joint work with Kasia Jankiewicz and Dani Wise.

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• 16:00 - 16:50 Asif Shaikh (R. A. Podar College of Commerce and Economics)

Cogrowth and Whitehead Moves in Free Groups

I will begin with the subgroup version of the classical Whitehead minimization problem. I then reinterpret this problem from the perspective of cogrowth and formulate a new question, which I call the Whitehead maximal cogrowth problem. Using a refinement of Whitehead’s algorithm given by Ascari, I explain how cogrowth behaves monotonically under certain Whitehead moves, leading to a strict cogrowth inequality. If time permits, I will discuss partial progress toward a solution of the maximal cogrowth problem.​​​​

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• 17:00 - 17:50 Luis Paris (Université de Bourgogne)

Trickle Groups​

We present a new family of groups, called trickle groups, which generalize the right angled Artin and Coxeter groups, as well as the Cactus groups. These are defined by relations of the form xy = yz and x^μ = 1, which depend on some combinatorial data called trickle graph. The aim of the talk is to provide the definition of a trickle group, to show several important examples, such as the Thomson group F, and to give some combinatorial results, such as a solution to the word problem.​

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Saturday, March 21th (room TBA)

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• 10:00 - 10:50 Nicolás Matte Bon (Université Claude Bernard Lyon 1)

TBA

TBA

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• 11:00 - 11:50 Oorna Mitra (Indian Institute of Science Education and Research)

On certain algebraic and algorithmic questions about solvable Baumslag-Solitar groups

In the first part of the talk, I will introduce certain algorithmic problems in group theory—namely, the Twisted Conjugacy Problem (TCP) and Orbit Decidability (OD)—which are closely related to the classical Conjugacy Problem (CP). I will then present some recent results addressing the CP in specific extensions of solvable Baumslag–Solitar (BS) groups, based on joint work with Mallika Roy and Enric Ventura. In the second part, I will discuss some new algebraic and algorithmic results concerning fixed point subgroups of solvable BS groups. This part is based on joint work with Ramya Nair.​

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• 12:00 - 12:50 Corentin Bodart (University of Oxford)

Subgroup membership and formal languages

The intersection of Geometric Group Theory and Formal Language Theory has been fruitful in the last 50 years. I'll start by recalling some of the key results in the area, such as the Muller-Schupp theorem on groups with context-free Word Problem and Lehnert's conjecture on groups with co-context-free Word Problem. In joint work with André Carvalho and Carl-Fredrik Nyberg-Brodda, we have been looking at similar languages related to another decision problem in groups: Subgroup Membership. I'll explain the toolbox we have been developing, apply it to examples and non-examples, and highlight some open problems along the way.