Nineteenth Barcelona Weekend in Group Theory
March 20th and 21th, 2026
The Nineteenth Barcelona Weekend in Group Theory will take place on March 20-21, starting on Friday afternoon and ending before the conference lunch on Saturday, at the Escola Politècnica Superior d'Enginyeria de Manresa, Universitat Politècnica de Catalunya.
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Confirmed speakers are Macarena Arenas (University of Cambridge), Corentin Bodart (University of Oxford), Nicolás Matte Bon* (Université Claude Bernard Lyon 1), Oorna Mitra (Indian Institute of Science Education and Research), Luis Paris (Université de Bourgogne), and Asif Shaikh (R. A. Podar College of Commerce and Economics).
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*To be confirmed.
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Attendance is free, but if you are interested in joining, please register using the form provided below.
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Titles and abstracts​
Friday, March 20th (room TBA)
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15:00 - 15:50 Macarena Arenas (University of Cambridge)
TBA
TBA​​​
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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 Nicolás Matte Bon (Université Claude Bernard Lyon 1)
TBA​
TBA​
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Saturday, March 21th (room TBA)
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10:00 - 10:50 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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11:00 - 11:50 Oorna Mitra (Indian Institute of Science Education and Research)
TBA
TBA​
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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.