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
Seminar October 13th
Tuesday, October 13th, 15:30, CRM Small Room
Speaker: Enric Ventura (UPC)
Title: Computing fixed closures in free groups
Abstract: Let F be a finitely generated free group. We present an algorithm such that, given a subgroup H in F, decides whether H is the fixed subgroup of some family of automorphisms, or family of endomorphisms of F and, in the affirmative case, finds such a family. The algorithm combines both combinatorial and geometric methods.
Speaker: Enric Ventura (UPC)
Title: Computing fixed closures in free groups
Abstract: Let F be a finitely generated free group. We present an algorithm such that, given a subgroup H in F, decides whether H is the fixed subgroup of some family of automorphisms, or family of endomorphisms of F and, in the affirmative case, finds such a family. The algorithm combines both combinatorial and geometric methods.
Seminar September 22nd
Welcome to the Barcelona Group Theory Seminar for the year 2009-10. Official meeting time this semester is Tuesdays at 15:30.
Tuesday, September 22nd, 15:30, CRM Small Room
Speaker: Warren Dicks (UAB)
Title: On Leighton's graph covering theorem
Tuesday, September 22nd, 15:30, CRM Small Room
Speaker: Warren Dicks (UAB)
Title: On Leighton's graph covering theorem
Wednesday
Seminar June 29th
Monday, June 29th, 13:00, CRM Small Room
Speaker: Martin Kassabov, Cornell University
Title: Subspace arrangements and property T
Abstract: I will mainly talk about (my viewpoint at) a method for proving property T started by Dymara and Januszkiewicz. Their original motivation came from groups action on dimensional building, but the refined idea does not used anything more angles between subspaces in an finite dimensional Euclidean space. Parts of the talk are based on a work of M. Ershov and A. Jaikin.
Speaker: Martin Kassabov, Cornell University
Title: Subspace arrangements and property T
Abstract: I will mainly talk about (my viewpoint at) a method for proving property T started by Dymara and Januszkiewicz. Their original motivation came from groups action on dimensional building, but the refined idea does not used anything more angles between subspaces in an finite dimensional Euclidean space. Parts of the talk are based on a work of M. Ershov and A. Jaikin.
Friday
Seminar June 3rd
We will have a double session of the seminar at the same time as the Hyperbolic Groups course:
Wednesday June 3rd, Room 005, FME, Campus Sud UPC
First Talk, 11:00
Speaker: José Manuel Higes López, Universidad Complutense de Madrid
Title: The coarse classification of countable abelian groups
Abstract: We will show the classification of countable abelian groups up to coarse equivalence. As an application we will use this result to detect which groups are coarsely equivalent to countable abelian groups. Joint with T. Banakh, I. Zarichnyi.
Second talk, 12:00
Speaker: Lars Louder, University of Michigan
Title: Graphs of subgroups of free groups
Abstract: We will develop, using Stallings' folding, graphs of groups, and a process called "blowing up," a simple topological model for representing graphs of subgroups of free groups. Applications to be discussed include simple proofs of some old results of combinatorial group theory. Generalizations of the technique and of these seemingly simple ideas to limit groups are important in the dimension theory for algebraic varieties defined over the free group.
Wednesday June 3rd, Room 005, FME, Campus Sud UPC
First Talk, 11:00
Speaker: José Manuel Higes López, Universidad Complutense de Madrid
Title: The coarse classification of countable abelian groups
Abstract: We will show the classification of countable abelian groups up to coarse equivalence. As an application we will use this result to detect which groups are coarsely equivalent to countable abelian groups. Joint with T. Banakh, I. Zarichnyi.
Second talk, 12:00
Speaker: Lars Louder, University of Michigan
Title: Graphs of subgroups of free groups
Abstract: We will develop, using Stallings' folding, graphs of groups, and a process called "blowing up," a simple topological model for representing graphs of subgroups of free groups. Applications to be discussed include simple proofs of some old results of combinatorial group theory. Generalizations of the technique and of these seemingly simple ideas to limit groups are important in the dimension theory for algebraic varieties defined over the free group.
Course on Hyperbolic Groups, June 2nd to 4th
As an event for the graduate class "Seminar on Group Theory", there will be a three-day minicourse.
Tuesday June 2nd to Thursday June 4th, 15.00 to 18:00, Room 005, FME, UPC Campus Sud
Speaker: Oleg Bogopolski, Universität Düsseldorf
Title: Hyperbolic groups
Tuesday June 2nd to Thursday June 4th, 15.00 to 18:00, Room 005, FME, UPC Campus Sud
Speaker: Oleg Bogopolski, Universität Düsseldorf
Title: Hyperbolic groups
Thursday
Seminar May 25th
Monday, May 25th, 13:00, CRM Small Room
Speaker: Lluís Bacardit (UAB)
Title: A generalization of theorem of Birman and Hilden
Abstract: A Theorem of Birman and Hilden says that the standard representation of the braid group by automorphisms of a free group $F_n$ remains faithful after passing to a free product of cyclic groups $C_k^{*n}$. If we take a finite index subgroup of $C_k^{*n}$ invariant by the action of the braid group, the action also is faithful. These two facts allow us to embed braid group in mapping class group of genus greater than 0. We will give a generalization of the Birman Hilden theorem to orientable surface with one boundary component and show some inclusion of mapping class groups in mapping class groups of greater genus.
Speaker: Lluís Bacardit (UAB)
Title: A generalization of theorem of Birman and Hilden
Abstract: A Theorem of Birman and Hilden says that the standard representation of the braid group by automorphisms of a free group $F_n$ remains faithful after passing to a free product of cyclic groups $C_k^{*n}$. If we take a finite index subgroup of $C_k^{*n}$ invariant by the action of the braid group, the action also is faithful. These two facts allow us to embed braid group in mapping class group of genus greater than 0. We will give a generalization of the Birman Hilden theorem to orientable surface with one boundary component and show some inclusion of mapping class groups in mapping class groups of greater genus.
Tuesday
Seminar May 18th
Monday, May 18th, 13:00, CRM Small Room
Speaker: Yago Antolín (UAB)
Title: Grupos de dimensión asintótica 1.
Abstract: Veremos ejemplos de grupos de dimensión asintótica 0,1 y 2. Caracterizaremos algebraicamente los grupos finitamente presentados de dimensión asintótica menor o igual que 1. El juego del Hex.
Speaker: Yago Antolín (UAB)
Title: Grupos de dimensión asintótica 1.
Abstract: Veremos ejemplos de grupos de dimensión asintótica 0,1 y 2. Caracterizaremos algebraicamente los grupos finitamente presentados de dimensión asintótica menor o igual que 1. El juego del Hex.
Seminar May 11th
Monday, May 11th, 13:00, CRM Small Room
Speaker: Arye Juhasz (Technion, Israel Institute of Technology)
Title: Solution of the Membership Problem for Magnus subsemigroups in certain one-relator groups.
Abstract: Let G be a one-relator group given by a finite presentation. A subgroup of G generated by a proper subset of X is called a Magnus subgroup of G, after W.Magnus, who introduced them to classical Combinatorial Group Theory. They are important building blocks of the theory of one-relator groups. Two of their main properties are that they are free and they have solvable Membership Problem. (The Membership Problem ask for an algorithm to decide whether a given element of the group belongs to a given subgroup).
Quite recently it became clear that the Word Problem for some one-relator algebraic structures which are more complicated than groups can be reduced to the Membership Problem for certain subsemigroups of one-relator groups.
Unfortunately, the existing algebraic and geometrical methods applied to subgroups do not work for subsemigroups. In this talk, using combinatorial methods, we consider the Membership Problem and the Freeness Problem for Magnus subsemigroups of one-relator groups with a small-cancellation condition. (These are subsemigroups of G generated by proper subsets of X union X-1). The main ingredients are van Kampen diagrams and word combinatorics.
Speaker: Arye Juhasz (Technion, Israel Institute of Technology)
Title: Solution of the Membership Problem for Magnus subsemigroups in certain one-relator groups.
Abstract: Let G be a one-relator group given by a finite presentation
Quite recently it became clear that the Word Problem for some one-relator algebraic structures which are more complicated than groups can be reduced to the Membership Problem for certain subsemigroups of one-relator groups.
Unfortunately, the existing algebraic and geometrical methods applied to subgroups do not work for subsemigroups. In this talk, using combinatorial methods, we consider the Membership Problem and the Freeness Problem for Magnus subsemigroups of one-relator groups with a small-cancellation condition. (These are subsemigroups of G generated by proper subsets of X union X-1). The main ingredients are van Kampen diagrams and word combinatorics.
Fourth Barcelona Weekend in Group Theory, April 24th and 25th
The program of the Fourth Barcelona Weekend in Group Theory is:
Friday April 24th, Auditori Centre de Recerca Matemàtica
- 15:00 Gilbert Levitt (Université de Caen, France)
From Baumslag-Solitar groups to companion matrices. - 16:15 Claas Röver (National University of Ireland, Galway)
Groups with Context-Free Conjugacy Problem.
- 17:30 Armando Martino (University of Southampton, England)
Isometries of Outer Space.
Saturday April 25th, FME Aula 102, Edifici U, UPC Campus Sud
- 10:00 Oleg Bogopolski (Universität Düsseldorf, Germany)
On the fundamental and the first singular homology groups of the Hawaiian Earrings and of Griffiths' space.
- 11:15 Adolfo Ballester Bolinches (Universitat de València, Spain)
On abnormal maximal subgroups of finite groups. - 12:30 Goulnara Arzhantseva (Université of Genéve, Switzerland)
Geometric small cancellation conditions with applications.
Friday
Seminar March 30th
Monday, March 30th, 13:00, CRM Small Room
Speaker: Elena Pribavkina (Ural State University, Ekaterinburg)
Title: A dynamical approach to Thompson's group V
Abstract: A word w over a finite alphabet A is called n-collapsing if for an arbitrary deterministic finite automaton the inequality |\delta(Q,w)|\le |Q| − n holds provided that |\delta(Q,u)|\le |Q| − n for some word u (depending on the automaton). In case n=2 there is a gruop-theoretic characterization of 2-collapsing words. To every word w is associated a finite family of finitely generated subgroups in finitely generated free groups. Then the word is 2-collapsing iff each of these subgroups has index at most 2 in the corresponding free group. There is also a similar characterization for the closely related class of so-called 2-synchronizing words.
Such a characterization allows to establish some new properties of the language of 2-collapsing words, for instance, to show that this language over a binary alphabet is not context free, and to find a new lower bound on the length of 2-collapsing words. In the talk will also be discussed some open problems concerning collapsing words for which such a group-theoretic approach might be useful.
Speaker: Elena Pribavkina (Ural State University, Ekaterinburg)
Title: A dynamical approach to Thompson's group V
Abstract: A word w over a finite alphabet A is called n-collapsing if for an arbitrary deterministic finite automaton
Such a characterization allows to establish some new properties of the language of 2-collapsing words, for instance, to show that this language over a binary alphabet is not context free, and to find a new lower bound on the length of 2-collapsing words. In the talk will also be discussed some open problems concerning collapsing words for which such a group-theoretic approach might be useful.
Seminar March 16th
Monday, March 16th, 13:00, CRM Small Room
Speaker: Eugenia Sapir, ENS-Lyon
Title: A dynamical approach to Thompson's group V
Abstract: We describe the structure of centralizers of elements in Thompson's group V. In this group, centralizers are determined by the dynamics of the elements. Each element divides the Cantor set into regions where it acts as the identity, as a permutation of intervals, or as a network between attractors and repellers. We work with two equivalent element representations. The first one is the classical tree pair approach which allows us to use the revealing pair technique introduced by Matt Brin, to easily identify the three types of regions. The second one involves representing elements as diagrams of strands to understand conjugacy classes. (This is joint work with C.Bleak, A.Gordon, G.Graham, J.Hughes, F.Matucci and H.Newfield-Plunkett)
Speaker: Eugenia Sapir, ENS-Lyon
Title: A dynamical approach to Thompson's group V
Abstract: We describe the structure of centralizers of elements in Thompson's group V. In this group, centralizers are determined by the dynamics of the elements. Each element divides the Cantor set into regions where it acts as the identity, as a permutation of intervals, or as a network between attractors and repellers. We work with two equivalent element representations. The first one is the classical tree pair approach which allows us to use the revealing pair technique introduced by Matt Brin, to easily identify the three types of regions. The second one involves representing elements as diagrams of strands to understand conjugacy classes. (This is joint work with C.Bleak, A.Gordon, G.Graham, J.Hughes, F.Matucci and H.Newfield-Plunkett)
Thursday
Seminar February 23rd
Monday, February 23rd, 13:00, CRM Small Room
Speaker: Borja de Balle Pigem, UPC
Title: Extensions de l'algorisme clàssic de Whitehead.
Speaker: Borja de Balle Pigem, UPC
Title: Extensions de l'algorisme clàssic de Whitehead.
Saturday
Seminar February 16th
Monday, February 16th, 13:00, CRM Small Room
Speaker: Xaro Soler Escrivà, Universitat d'Alacant
Title: Algunes qüestions de permutabilitat en grups finits.
Speaker: Xaro Soler Escrivà, Universitat d'Alacant
Title: Algunes qüestions de permutabilitat en grups finits.
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