Date and place: October 17, 2014. 12:00. CRM, small lecture room.
Speaker : Assaf Libman (University of Aberdeen)
Title: On homotopy groups of the spaces of self equivalences of equivariant spheres.
Abstract: It is a classical result that the nth homotopy group of the space of self equivalences of the spheres $S^k$ where k=1,2,3,... stabilizes (on the nth stable homotopy group of the spheres). Note that $S^k$ is the $k$fold join of $S^1$. An equivariant version of this question is: Suppose a finite group $G$ acts on a sphere $S^d$. What can one say about the nth homotopy groups of the space of equivariant self equivalences of the kfold joint of $S^r$ where $r=1,2,3,...$. The case when $S^r$ is a linear sphere will be studied.
Date and place: October 10, 2014. 12:00. CRM, small lecture room.
Speaker : Nguyen The Cuong
Title: On the algebraic EHP sequence
Abstract: One of the most basic problems in homological algebra is to construct explicit injective (projective) resolutions of modules. We are interested in finding such construction for the reduced cohomology $\tilde{H}^*(S^n; \mathbb F_2)$ of the spheres $S^n$ in the category of unstable modules U. The pseudohyper resolution is developed as an attempt to deal with this problem. The question is at present far from being solved but we manage somehow to archive some interesting properties of minimal injective resolutions of $\tilde{H}^*(S^n; \mathbb F_2)$ in U. These results provide a new point of view for the problem of computing the E2 page of the unstable Adams spectral sequence converging to homotopy groups of spheres. One of the first applications of these computations, which is also the main goal of this talk, is an elementary reconstruction of the algebraic EHP sequence and an approximation to the sphere of origin question.
