We will have a double session this week:
Monday December 22nd, 13:00, CRM Small Room
Speaker: Ilya Kazatchkov, McGill University
Title: Equivalence of right-angled Coxeter groups and graph products of finite abelian groups
Second talk, 13:30
Speaker: Montse Casals, McGill University
Title: On systems of equations over partially commutative groups
Wednesday
Seminar December 1st
Monday December 1st, 13:00, CRM Small Room
Speaker: Enric Ventura, UPC
Title: Unsolvability of the conjugacy and the isomorphism problems for Z^n-by-free groups
Speaker: Enric Ventura, UPC
Title: Unsolvability of the conjugacy and the isomorphism problems for Z^n-by-free groups
Thursday
Seminar November 3rd
Monday November 3rd, 13:00, CRM Small Room
Speaker: Lluís Bacardit, UAB
Title: Generadors of Punctured Mapping Class Groups
Abstract: És un resultat clàssic que el mapping-class group d'una superficie orientable sense vora és isomorf a un subgrup de Out(F), on F és un grup lliure. Si la superficie té vora, llavors el mapping-class group de la superficie és isomorf a un subgrup de Aut(F). Utilitzant aquest resultat clàssic, J. McCool va ser el primer en demostrar que el mapping-class group d'una superficie orientable es finitament presentat. Posteriorment, McCool va donar generadors explicits del mapping-class group de superficies orientable amb una vora i sense punts. L'argument de McCool és purament algebraic i utilitza la teoria de Whitehead sobre automorfismes de grups lliures. Nosaltres generalitzem el resultat de McCool a superficies orientable amb punts. A més, la nostra demostració no utilitza resultats de Whitehead.
Speaker: Lluís Bacardit, UAB
Title: Generadors of Punctured Mapping Class Groups
Abstract: És un resultat clàssic que el mapping-class group d'una superficie orientable sense vora és isomorf a un subgrup de Out(F), on F és un grup lliure. Si la superficie té vora, llavors el mapping-class group de la superficie és isomorf a un subgrup de Aut(F). Utilitzant aquest resultat clàssic, J. McCool va ser el primer en demostrar que el mapping-class group d'una superficie orientable es finitament presentat. Posteriorment, McCool va donar generadors explicits del mapping-class group de superficies orientable amb una vora i sense punts. L'argument de McCool és purament algebraic i utilitza la teoria de Whitehead sobre automorfismes de grups lliures. Nosaltres generalitzem el resultat de McCool a superficies orientable amb punts. A més, la nostra demostració no utilitza resultats de Whitehead.
Wednesday
Seminar October 27th
Monday, October 27th, 13:00, CRM Small Room
Speaker: Ferran Cedó, UAB
Title: Grups involutius de Yang-Baxter
Abstract: Sigui $X$ un conjunt finit. Una aplicació $r\colon X\times X\rightarrow X\times X$ tal que $r^2=id$ es diu que és una solució involutiva conjuntista de l'equació de Yang-Baxter si compleix que $$r_{12}r_{23}r_{12}= r_{23}r_{12}r_{23},$$ on $r_{12}$ i $r_{23}$ són aplicacions de $X^3$ en ell mateix definides per $r_{12}(x,y,z)=(f_x(y),g_y(x),z)$ i $r_{23}(x,y,z)=(x,f_y(z),g_z(y))$, i $r(x,y)=(f_x(y),g_y(x))$. Observem que en aquest cas les aplicacions $f_x$ i $g_y$ són permutacions del conjunt $X$. Es diu que un grup finit $G$ és un grup involutiu de Yang-Baxter (que escriurem grup IYB) si és isomorf al subgrup $\langle f_x\mid x\in X\rangle$ de $Sym_X$ per a alguna solució involutiva conjuntista $r$ de l'equació de Yang-Baxter. El 1999, Etingof, Schedler i Soloviev van demostrar que tot group IYB és resoluble. Nosaltres conjecturem que tot grup finit resoluble és IYB. En aquesta xerrada parlaré dels resultats parcials que hem obtingut i que suporten aquesta conjectura.
Speaker: Ferran Cedó, UAB
Title: Grups involutius de Yang-Baxter
Abstract: Sigui $X$ un conjunt finit. Una aplicació $r\colon X\times X\rightarrow X\times X$ tal que $r^2=id$ es diu que és una solució involutiva conjuntista de l'equació de Yang-Baxter si compleix que $$r_{12}r_{23}r_{12}= r_{23}r_{12}r_{23},$$ on $r_{12}$ i $r_{23}$ són aplicacions de $X^3$ en ell mateix definides per $r_{12}(x,y,z)=(f_x(y),g_y(x),z)$ i $r_{23}(x,y,z)=(x,f_y(z),g_z(y))$, i $r(x,y)=(f_x(y),g_y(x))$. Observem que en aquest cas les aplicacions $f_x$ i $g_y$ són permutacions del conjunt $X$. Es diu que un grup finit $G$ és un grup involutiu de Yang-Baxter (que escriurem grup IYB) si és isomorf al subgrup $\langle f_x\mid x\in X\rangle$ de $Sym_X$ per a alguna solució involutiva conjuntista $r$ de l'equació de Yang-Baxter. El 1999, Etingof, Schedler i Soloviev van demostrar que tot group IYB és resoluble. Nosaltres conjecturem que tot grup finit resoluble és IYB. En aquesta xerrada parlaré dels resultats parcials que hem obtingut i que suporten aquesta conjectura.
Thursday
Seminar October 13th
Monday October 13th, 13:00, CRM Small Room
Speaker: Enric Ventura, UPC
Title: Orbit undecidability and a recursive presentation for Mihailova's group
Speaker: Enric Ventura, UPC
Title: Orbit undecidability and a recursive presentation for Mihailova's group
Monday
Seminar October 6th
We will have a double session this week.
Monday October 6th, 12:30, CRM Small room
Speaker: Sean Cleary, The City College of New York
Title: Rotation distances and generating sets for Thompson's group F
Abstract: Rotation distances measure differences in tree shape between binary trees, by counting a minimum number of rotations needed to transform a first given tree into another. These correspond to word metrics for Thompson's group F with respect to different generating sets, depending upon where rotations are allowed. These connections give useful results in both directions.
Second talk, 13:30
Speaker: Laura Ciobanu, Université de Fribourg
Title: Properties of generic subgroups of free and hyperbolic groups
Monday October 6th, 12:30, CRM Small room
Speaker: Sean Cleary, The City College of New York
Title: Rotation distances and generating sets for Thompson's group F
Abstract: Rotation distances measure differences in tree shape between binary trees, by counting a minimum number of rotations needed to transform a first given tree into another. These correspond to word metrics for Thompson's group F with respect to different generating sets, depending upon where rotations are allowed. These connections give useful results in both directions.
Second talk, 13:30
Speaker: Laura Ciobanu, Université de Fribourg
Title: Properties of generic subgroups of free and hyperbolic groups
Abstract: Let F be a finitely generated free group, and K be a finitely generated, infinite index subgroup of F. We show that generically many finitely generated subgroups H have trivial intersection with all conjugates of K, thus proving a stronger, generic form of the Hanna Neumann Conjecture. As an application, we show that the equalizer of two free group homomorphisms is generically trivial, which implies that the Post Correspondence Problem is generically solvable in free groups. Then let G be a word hyperbolic group. We show that generically, finitely generated subgroups of G are free and quasiconvex. This is joint work with Armando Martino and Enric Ventura.
Wednesday
Seminar September 29th
Monday September 29th, 13:00, CRM Small room
Speaker: Francesco Matucci, CRM
Title: Centralizers in R. Thompson's groups
Abstract: R. Thompson's groups F, T and V are countable groups whose elements can be represented as homeomorphisms of a real interval, of the circle, and of the Cantor set, respectively. Elements of the groups can be represented both from a dynamical point of view and from a combinatorial one, using suitable types of diagrams. We give a classification of centralizers of elements in these groups.
We achieve this by using techniques derived from the available solutions of the conjugacy problem. Using the piecewise-linear perspective one can derive centralizers in F by observing the bumps of a map. This description can be "lifted" to centralizers in T, up to finite index. The case of V is treated using the point of view of tree diagrams and choosing a suitable representative that describes the action on the underlying Cantor set by looking at the diagram. We give combinatorial and topological applications of this description.
Speaker: Francesco Matucci, CRM
Title: Centralizers in R. Thompson's groups
Abstract: R. Thompson's groups F, T and V are countable groups whose elements can be represented as homeomorphisms of a real interval, of the circle, and of the Cantor set, respectively. Elements of the groups can be represented both from a dynamical point of view and from a combinatorial one, using suitable types of diagrams. We give a classification of centralizers of elements in these groups.
We achieve this by using techniques derived from the available solutions of the conjugacy problem. Using the piecewise-linear perspective one can derive centralizers in F by observing the bumps of a map. This description can be "lifted" to centralizers in T, up to finite index. The case of V is treated using the point of view of tree diagrams and choosing a suitable representative that describes the action on the underlying Cantor set by looking at the diagram. We give combinatorial and topological applications of this description.
Seminar September 22nd
The first meeting of the Seminar in the year 2008/09.
Monday September 22nd, 13:00, CRM Small room
Speaker: Jonathan Hillman, University of Sydney
Title: Indecomposable PD3 Complexes
Abstract: $PD$-complexes model the homotopy theory of manifolds. In dimension 3, the unique factorization theorem holds in the sense that a $PD3$-complex is a connected sum if and only if its fundamental group is a free product, and the indecomposables are either aspherical or have virtually free fundamental group [Tura'ev, Crisp]. However in contrast to the 3-manifold case the group of an indecomposable may have infinitely many ends (i.e., not be virtually abelian). We shall sketch the construction of one such example, and outline some recent work using only elementary group theory that imposes strong restrictions on any other such examples.
Monday September 22nd, 13:00, CRM Small room
Speaker: Jonathan Hillman, University of Sydney
Title: Indecomposable PD3 Complexes
Abstract: $PD$-complexes model the homotopy theory of manifolds. In dimension 3, the unique factorization theorem holds in the sense that a $PD3$-complex is a connected sum if and only if its fundamental group is a free product, and the indecomposables are either aspherical or have virtually free fundamental group [Tura'ev, Crisp]. However in contrast to the 3-manifold case the group of an indecomposable may have infinitely many ends (i.e., not be virtually abelian). We shall sketch the construction of one such example, and outline some recent work using only elementary group theory that imposes strong restrictions on any other such examples.
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