30/10, IMPA. Sala 228
10:3011:30 
Charles Favre (École Polytechnique, Centre de Mathématiques Laurent Schwartz),
NonArchimedean links of normal surface singularities.
Resumo. (j.w. with Lorenzo Fantini and Matteo Ruggiero) One can associate to any complex normal surface singularity a nonArchimedean analog of its classical link. This nonArchimedean link carries a natural analytic structure that is locally modelled on Berkovich analytic spaces over C((t)). We shall explain how to obtain a characterization of sandwich singularities in term of selfsimilar properties of this link.
 12:0013:00 
Ben Smith (École Polytechnique, INRIA),
Applications of arithmetic geometry in contemporary cryptology.
Resumo. Elliptic curves and lowdimensional Jacobian varieties over finite fields are an important tool in contemporary publickey cryptography.
Formallythat is, from the point of view of cryptographic protocolsthey can often be used as a dropin replacement for the multiplicative group of a finite field, where they offer higher levels of security with much more compact keys. But this purely formal point of view ignores the rich arithmetic structure of elliptic curves, Jacobians, and their Kummer varieties, which we can exploit to create practical improvements (and even some cryptographic attacks) that have no analogues in conventional finite fieldbased cryptosystems.
In this talk, we will survey some explicit applications of the arithmetic of lowdimensional abelian varieties in cryptography. These techniques include
* the construction of models with more efficient group laws and scalar multiplication operations,
* using isogenies and endomorphisms to accelerate encryption and decryption algorithms,
* using endomorphism ring structures to accelerate point counting (ie, zeta function computation) for elliptic and genus 2 curves, and
* using isogenies to attack discrete logarithm problems.

