Schedule

11:00 — 12:00 Francisco Torralbo (UGR)

Title: Topology of compact minimum submanifolds

Abstract: In this talk we will begin by exploring when a Riemannian manifold has compact minimal submanifolds. In the simplest affirmative cases, we will study which topological types are admissible. In particular, we will prove that any compact surface with even Euler characteristic can be minimally embedded in $$\mathbb{S}^2\times \mathbb{S}^1(r)$$ for any r > 0. If time permits, we will present how to build such embeddings.

12:30 — 13:30 Antonio Díaz Ramos (UMA)

Title: Quillen's conjecture for unitary groups

Abstract: Quillen's conjecture about the complex of p-subgroups was introduced in the 1970s and, thanks to the work of Aschbacher and Smith in the 1990s and the more recent work of Smith and Piterman, it is reduced to the case of unit groups if the prime p is odd. In this talk we will explain a geometric method that applies to soluble and p-soluble groups, several families of simple finite groups, and also to unit groups. As a consequence we will obtain that the conjecture is true for all odd primes.