Reminder: Luca Rizzi's seminars at SISSA

[Emanuele Tuillier Illingworth]

> SEMINAR ANNOUNCEMENT
> ---------------------------------------------
>
> *
> **Tuesday 27.10.2015, 14:00  Luca Rizzi, Ecole Polytechnique, Paris 
> (SISSA, room 133)*
>
> Title: A sub-Riemannian Santaló formula with applications to 
> isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic 
> operators
>
> Abstract: We prove a sub-Riemannian version of the classical Santaló 
> formula: a result in integral geometry that describes the intrinsic 
> Liouville measure on the unit cotangent bundle in terms of the 
> geodesic flow.
>
> As an application, we derive (p-)Hardy-type and isoperimetric-type 
> inequalities for a compact domain with Lipschitz boundary and 
> negligible characteristic set. Moreover, we prove a universal (i.e. 
> curvature independent) lower bound for the first Dirichlet eigenvalue 
> of the intrinsic sub-Laplacian, All our results are sharp for the 
> sub-Riemannian structures on the hemispheres of the complex and 
> quaternionic Hopf fibrations.
>
> If time allows, we discuss an interesting bound on the first Dirichlet 
> eigenvalue on fundamental domain of the Heisenberg nilmanifold (the 
> quotient of the 3D Heisenberg group by a cocompact lattice).
>
> *
> **Wednesday 28.10.2015, 16:00  Luca Rizzi, Ecole Polytechnique, Paris 
> (SISSA, room 133)*
>
> Title: Intrinsic random walks in Riemannian and sub-Riemannian 
> geometry via volume sampling
>
> Abstract: We relate some basic constructions of stochastic analysis to 
> differential geometry, via random walk approximations. The motivation 
> is largely to explore how one can pass from geodesics to diffusion 
> (and hence their infinitesimal generators) on sub-Riemannian 
> manifolds, which is interesting in light of the fact that geodesics 
> are relatively well understood, while there is no completely canonical 
> notion of sub-Laplacian on a general sub-Riemannian manifold. However, 
> even in the Riemannian case, this random walk approach illuminates the 
> geometric significance of Ito and Stratonovich stochastic differential 
> equations.
>
>
>