Upcoming Seminars & Events

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October 3, 2017
4:30pm - 6:00pm
TBA - Yuval Peres
Speaker: Yuval Peres , Microsoft Research
Location:
Jadwin Hall 343
October 4, 2017
4:30pm - 5:45pm
New Faculty Talks, I
Speaker: ,
Location:
TBD
October 11, 2017
4:30pm - 5:45pm
New Faculty Talks, II
Speaker: ,
Location:
TBD
October 18, 2017
4:30pm - 5:45pm
New Faculty Talks, III
Speaker: ,
Location:
TBD
November 13, 2017
4:30pm - 5:30pm
Lecture 1: The games of Steiner and Poncelet and algebraic group schemes

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
Location:
TBD
November 14, 2017
4:30pm - 5:30pm
Lecture 2: Torsion values for sections in abelian schemes and the Betti map

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
Location:
TBD
November 16, 2017
4:30pm - 5:30pm
Lecture 3: Ambients for the Betti map and the question of its rank

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
Location:
TBD