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Group theory seminar Jaikin-Zapirain/Marquis/Kharlampovich

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Group theory seminar Jaikin-Zapirain/Marquis/Kharlampovich

April 16 (Tuesday)

For this seminar we will have the pleasure of listening to three talks:
14.00 – 14.45 Andrei Jaikin-Zapirain (UAM), « Compressed subgroups in free groups are inert »
15.00 – 15.45 Timothée Marquis (UCL), « Amalgams of rational unipotent groups and residual nilpotence ».
16.15 – 17.00 Olga Kharlampovich (CUNY), « Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations ».

 Andrei Jaikin-Zapirain  « Compressed subgroups in free groups are inert ». 

 Let F be a free group. A finitely generated subgroup H is called compressed in F if it is not contained in a subgroup of F of smaller rank than H, and it is called inert in F if H ∩ U is compressed in U for any subgroup U of F. In my talk, I will show that compressed subgroups are also inert. The solves a conjecture of Dicks and Ventura from 1996.

Timothée Marquis , « Amalgams of rational unipotent groups and residual nilpotence ».

 Given a group property (P), a group G is called residually (P) if every nontrivial element of G has a nontrivial image in some quotient of G that satisfies (P). The study of residual properties of graphs of groups has a long and rich history, originating from Magnus’ theorem that free groups are residually torsionfree nilpotent. In this talk, I will start by reviewing a few key results of this history, before presenting an intriguing phenomenon concerning the residual nilpotence of certain amalgams of rational unipotent groups. Joint work with Pierre-Emmanuel Caprace. 

Olga Kharlampovich,   « Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations« .

 We answer the question asked by Louder, McReinolds and Patel and prove the following statement. Let L be a RAAG, H a cubically convex-cocompact subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental group of a hyperbolic 3-manifold. For any finitely generated subgroup H of a limit group L we prove the same results and, in addition, show that there exists a finite-index subgroup K containing H, such that K is a subgroup of a group obtained from H by a series of extensions of centralizers and free products with infinite cyclic group. If H is non-abelian, the K is fully residually H. A corollary is that a hyperbolic limit group satisfies the Geometric Hanna Neumann conjecture. These are joint results with K. Brown and A. Vdovina.

Organized by Andrei Alpeev, Laurent Bartholdi, Anna Erschler and Panagiotis Tselekidis 

Partially supported by ERC Advanced Grant 101097307 (P.I.:Laurent Bartholdi).

- Séminaire de théorie des groupes à l’ENS

Détails :

Orateur / Oratrice : Andrei Jaikin-Zapirain (UAM), Timothée Marquis (UCL), Olga Kharlampovich (CUNY)
Date : 16 avril 2024
Horaire : 14h00 - 17h00
Lieu : 14:00-17:00 Salle W