Title: Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation
Speaker: Gilbert Hector (University Lyon 1) Title: Ends of graphs, finitely generated groups and group actions Date: September 23 (Fri), 16:30-17:30 Place: Ritsumeikan University Biwako-Kusatsu Campus West-Wing 7th floor 1st Labratory of Mathematics Abstract: We will present a simple and quick proof of the following genericity property for group actions first stated by Cantwell-Conlon:
Theorem. – Let G be a finitely generated group of homeomorphisms of a compact space K. If all orbits of G are dense, there exists a residual Baire set W of orbits such that i) all orbits in W have the same endset E(W), ii) E(W) is either a singleton, a pair of points or a Cantor set.
By the classical theorem of Hopf-Freudenthal the endset E(G) of G verifies property ii) as well; so we will also discuss the possible equality E(G) = E(W). We will recall all concepts needed for the talk.
Title : A co-dimension 3 sub-Riemannian structure on Gromoll-Meyer exotic sphere
Speaker : Kenro Furutani (Tokyo University of Science)
16:30-17:30, September 26, 2016
Room: Biwako-Kusatsu Campus (BKC), West Wing, 7th floor, 1st Laboratory of Mathematics
Abstract :
We construct a co-dimension 3 completely non-holonomic sub-bundle on the Gromoll-Meyer exotic 7 sphere based on its realization as a base space of Sp(2) principal bundle with the structure group Sp(1). The same method is valid for constructing a co-dimension 3 sub-bundle on the standard 7 sphere (and also on 4n+3 dimensional standard sphere). For the standard sphere cases a co-dimension 3 sub-bundle was constructed by making use of the Hopf bundle. Our method gives a simple proof for the standard case.