Tuesday February 2nd, 15:00, CRM Small Room
Speaker: Natalia Castellana (UAB)
Title: Maps between p-local finite groups
Thursday
Seminar January 12th
We will have a double session this week.
Tuesday January 12th, 15:00, CRM Small Room
Speaker: Francesco Matucci (University of Virginia)
Title: Bounding the residual finiteness of free groups.
Abstract: We find a lower bound to the size of finite groups detecting a given word in the free group. More precisely, by using results on the length of shortest identities in finite simple groups we construct a word w of length n in non-abelian free groups with the property that w is the identity on all finite quotients of size ~ n^{2/3} or less. This improves on a previous result of Bou-Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups. This is joint work with Martin Kassabov.
Second talk, 16:00
Speaker: Sean Cleary (The City College of New York and the CUNY Graduate Center)
Title: Weak almost convexity and tame combing conditions
Abstract: Cannon introduced the notion of almost convexity for a Cayley graph of a group, developing effective algorithms for understanding the geometry of the Cayley graph. Though wide classes of groups are almost convex, there are a number of weaker notions of almost convexity satisfied by yet more groups. Mihalik and Tschantz introduced the notion of tame 1-combings for Cayley complexes, and there are connections between the very strongest notions of tame combings and the strongest notions of almost convexity. We answer questions about possible further connections between these two notions by showing that there are groups which satisfy some of the strongest tame combing conditions which do not satisfy even the weakest non-trivial almost convexity conditions. Examples include some Baumslag-Solitar groups and Thompson's group F. This is joint work with Susan Hermiller, Melanie Stein and Jennifer Taback.
Tuesday January 12th, 15:00, CRM Small Room
Speaker: Francesco Matucci (University of Virginia)
Title: Bounding the residual finiteness of free groups.
Abstract: We find a lower bound to the size of finite groups detecting a given word in the free group. More precisely, by using results on the length of shortest identities in finite simple groups we construct a word w of length n in non-abelian free groups with the property that w is the identity on all finite quotients of size ~ n^{2/3} or less. This improves on a previous result of Bou-Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups. This is joint work with Martin Kassabov.
Second talk, 16:00
Speaker: Sean Cleary (The City College of New York and the CUNY Graduate Center)
Title: Weak almost convexity and tame combing conditions
Abstract: Cannon introduced the notion of almost convexity for a Cayley graph of a group, developing effective algorithms for understanding the geometry of the Cayley graph. Though wide classes of groups are almost convex, there are a number of weaker notions of almost convexity satisfied by yet more groups. Mihalik and Tschantz introduced the notion of tame 1-combings for Cayley complexes, and there are connections between the very strongest notions of tame combings and the strongest notions of almost convexity. We answer questions about possible further connections between these two notions by showing that there are groups which satisfy some of the strongest tame combing conditions which do not satisfy even the weakest non-trivial almost convexity conditions. Examples include some Baumslag-Solitar groups and Thompson's group F. This is joint work with Susan Hermiller, Melanie Stein and Jennifer Taback.
Seminar December 15th
Tuesday December 15th, 15:00, CRM Small Room
Speaker: Enric Ventura (UPC)
Title: Subgroups of F_n generated by conjugates of powers of letters
Speaker: Enric Ventura (UPC)
Title: Subgroups of F_n generated by conjugates of powers of letters
Seminar November 24th
Tuesday November 24th, 15:00, CRM Small Room
Speaker: Claas Röver (NUI Galway)
Title: Free Automata Groups
Speaker: Claas Röver (NUI Galway)
Title: Free Automata Groups
Seminar November 17th
Tuesday November 17th, 15:00, CRM Small Room
Speaker: Yago Antolin (UAB)
Title: Geodesics in virtually free groups
Abstract: I will survey the following result of Gilman, Hermiller, Holt and Rees. A finitely generable group G is virtually free if and only if there exists a generating set X of G and a finite set of words S such that a word in X is geodesic if and only if it do not contain, as a subword, any element of S.
Speaker: Yago Antolin (UAB)
Title: Geodesics in virtually free groups
Abstract: I will survey the following result of Gilman, Hermiller, Holt and Rees. A finitely generable group G is virtually free if and only if there exists a generating set X of G and a finite set of words S such that a word in X is geodesic if and only if it do not contain, as a subword, any element of S.
Seminar November 10th
Tuesday, November 10th, 15:30, CRM Small Room
Speaker: Xaro Soler Escriva (Universitat d’Alacant)
Title: Languages recognized by finite supersoluble groups
Abstract: There exists a natural relationship between the classical theory of finite groups and the theory of formal languages. Given a finite alphabet A, one can easily associate to each regular language L of the free monoid A* an algebraic structure: its syntactic monoid. A regular language is a group language if its syntactic monoid is a group. Conversely, given a finite group G and a finite alphabet A, there exists a language of A* whose syntactic monoid is G (this is not true in
general if G is just a monoid).
After recalling the main ideas of the algebraic theory of regular languages, we will see some examples of languages recognized by finite groups. Then we will state Eilenberg’s theorem for varieties and the specific known results for abelian groups, nilpotent groups,
supersoluble groups, and soluble groups.
Speaker: Xaro Soler Escriva (Universitat d’Alacant)
Title: Languages recognized by finite supersoluble groups
Abstract: There exists a natural relationship between the classical theory of finite groups and the theory of formal languages. Given a finite alphabet A, one can easily associate to each regular language L of the free monoid A* an algebraic structure: its syntactic monoid. A regular language is a group language if its syntactic monoid is a group. Conversely, given a finite group G and a finite alphabet A, there exists a language of A* whose syntactic monoid is G (this is not true in
general if G is just a monoid).
After recalling the main ideas of the algebraic theory of regular languages, we will see some examples of languages recognized by finite groups. Then we will state Eilenberg’s theorem for varieties and the specific known results for abelian groups, nilpotent groups,
supersoluble groups, and soluble groups.
Tuesday
Seminar October 20th
Tuesday, October 20th, 15:30, CRM Small Room
Speaker: Olivier Siegenthaler (ETH Zurich)
Title: The Twisted Twin of the Grigorchuk Group
Speaker: Olivier Siegenthaler (ETH Zurich)
Title: The Twisted Twin of the Grigorchuk Group
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