October 3, 2017

4:30pm - 6:00pm

Speaker: Yuval Peres , Microsoft Research

Location: Jadwin Hall 343

October 4, 2017

4:30pm - 5:45pm

Speaker: ,

October 11, 2017

4:30pm - 5:45pm

Speaker: ,

October 18, 2017

4:30pm - 5:45pm

Speaker: ,

November 13, 2017

4:30pm - 5:30pm

We shall briefly present in very elementary terms the 'games' of Steiner and Poncelet, amusing mathematical solitaires of the XIX Century, also related to elliptic billiards. We shall recall that the finiteness of the game is related to torsion in tori or elliptic curves. We shall illustrate how one can vary the data of the games, obtaining families of elliptic curves and sections on elliptic schemes, for which we seek torsion values. This is related to the so-called `Betti-map', which we shall describe.

Speaker: Umberto Zannier , Scuola Normale Superiore-Pisa

November 14, 2017

4:30pm - 5:30pm

We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear differential equations, Pell's equation in polynomials, Belyi maps, extremal polynomials, Integration in finite terms, Functional transcendence, Kodaira-Spencer map, ...) and state some theorems, both of existence type and finiteness type (obtained mainly in joint work with David Masser).

Speaker: Umberto Zannier , Scuola Normale Superiore-Pisa

November 16, 2017

4:30pm - 5:30pm

In this last lecture we shall further consider some of the mentioned contexts involving the Betti map. We shall also discuss in short some recent work with Yves André and Pietro Corvaja, where we obtain some general criteria ensuring that on appropriate assumptions the Betti map has a differential of maximal rank. The results extend what comes from Manin's theorem and for instance imply topological density of points in the base which yield torsion for the relevant section.

Speaker: Umberto Zannier , Scuola Normale Superiore-Pisa