Thursday

Seminar February 2nd

Monday, February 2th, 13:00, CRM Small Room

Speaker: Francesco Matucci, CRM

Title: Structure Theorems for Subgroups of Homeomorphisms Groups.

Abstract: We give a classification of the solvable subgroups G of the group Homeo_+(S^1) of all orientation-preserving homeomorphisms of the unit circle. The key tool is proving that the rotation number map is a group homomorphism and it is done by relating the dynamics of G and its group structure. Applications include new proofs of known results as the Margulis' theorem on the existence of a G-invariant probability measure on S^1 and Burslem-Wilkinson theorem on the classification of solvable groups of analytic diffeomorphisms (this is joint work with C. Bleak and M. Kassabov).

Seminar January 26th

Monday, January 26th, 13:00, CRM Small Room

Speaker: Bob Gilman, Stevens Institute of Technology

Title: Group Theoretical Questions from Cryptography

Abstract:
The recent development of cryptosystems based on finitely presented groups has produced a number new questions in combinatorial group theory. We survey these questions and solve one of them.

Wednesday

Seminar December 22nd

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

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

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.

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.

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