## Department Colloquium - Alessandro Portaluri (University of Turin)

### Friday, March 1st, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Alessandro Portaluri (University of Turin)

**Title:** Existence and stability results in Celestial Mechanics

**Abstract: ** Is the solar system stable? This is maybe one of the oldest open question in dynamical systems. It is still a lively and very active research field starting from Newton, Lagrange, Maxwell, Poincare and Birkhoff (only to mention a few of them) who proved several astonishing results in this direction.

A lot of useful techniques to tackle this problem, were developed during the last decades: KAM theory, symplectic and contact methods, interval arithmetic, etc. One more (variationally oriented) piece we add to this arsenal: the index theory!

In this talk we introduce some new ideas behind many recent results on this topic and we discuss some new perspectives and challenges on singular (weak force) Lagrangian problems. We show the existence of equivariant periodic orbits and we investigate some (in)stability results for a plethora of periodic motions via symplectic techniques.

**Prof. Portaluri (University of Turin)** obtained his PhD in 2004 from the University of Turin, then worked at the University of Milano-Bicocca and the University of Salento before going back to Turin in 2012. He is currently on sabbatical at Queen's. His research interests include index theory for ordinary and partial differential operators via Maslov index and spectral flow techniques, and linear stability analysis in singular Lagrangian systems.