Thu, 12 May 2016
16:00
L6

Joint Number Theory/Logic Seminar: Two models for the hyperbolic plane and existence of the Poincare metric on compact Riemann surfaces

Norbert A'Campo
(Basel)
Abstract
An implicite definition for the hyperbolic plane $H=H_I$ is in:
${\rm Spec}(\mathbb{R}[X]) = H_I \setunion  \mathbb{R}$.
All geometric hyperbolic features will follow from this definition in an elementary way.
 
A second definition is 
$H=H_J=\{J \in {\rm End}(R^2) \mid J^2=-Id, dx \wedge dy(u,Ju) \geq 0 \}$.
Working with $H=H_J$ allows to prove rather directly main theorems about Riemann surfaces.
Thu, 09 Jun 2011

16:00 - 17:00
L3

TBA

David Masser
(Basel)
Thu, 27 Nov 2008

16:00 - 17:00
L3

Linear equations over multiplicative groups in positive characteristic, sums of recurrences, and ergodic mixing

David Masser
(Basel)
Abstract
Solving completely $x+y-z=1$ in unknowns taken from the group generated by a variable $t$ with $1-t$ over a finite field is not so easy as might be expected. We present a generalization to arbitrary linear varieties and finitely generated groups (keywords effective Mordell-Lang). We also mention applications to (a) solving equations like $u_n+v_m+w_l+f_k=0$ in $n,m,l,k$ for given recurrences $u,v,w,f$; and to (b) finding the smallest order of non-mixing of a given algebraic ${\bf Z}^s$-action. This is joint work with Harm Derksen.

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