Kristin Lauter (Microsoft Research, USA)

 
 
 
Supersingular Isogeny Graphs in Cryptography

Abstract: Supersingular Isogeny Graphs were proposed for use in Cryptography in 2006 by Charles-Goren-Lauter, and are currently being considered as candidates for standardization in several tracks of the 2017 NIST Post-Quantum Cryptography International Competition.  These are Ramanujan graphs whose nodes are supersingular elliptic curves and edges are isogenies between them.  This talk will introduce the hard problems and cryptographic applications in this space, and discuss a surprising connection to quantum arithmetic.

Adolfo Guillot (Instituto de Matemáticas-UNAM, Mexico)
Single-valued solutions of complex differential equations


Abstract: The success of the theory of elliptic functions in the nineteenth century motivated the quest for other special functions which were solutions of algebraic differential equations in the complex domain. On its turn, this led to the problem of understanding those differential equations that do not have multivalued solutions. We will talk about some instances of this problem for the autonomous differential equations given by holomorphic vector fields on complex manifolds, and particularly of some results in the case of surfaces.

Noga Alon (Tel Aviv University, Israel)

 
 
 
Structure, Randomness and Universality in Graph Theory

Abstract: What is the minimum possible number of vertices of a graph that contains every k-vertex graph as an induced subgraph ? What is the minimum possible number of edges in a graph that contains every k-vertex graph with maximum degree 3 as a subgraph ? These questions and related one were initiated by Rado in the 60s, and received a considerable amount of attention over the years, partly motivated by algorithmic applications. The study of the subject combines probabilistic arguments and explicit, structured constructions. I will survey the topic focusing on a recent asymptotic solution of the first question, where an asymptotic formula, improving earlier estimates by several researchers, is obtained by combining combinatorial and probabilistic arguments with group theoretic tools.

Sylvie Méléard (Ecole Polytechnique, France)

 
 
 
Stochastic dynamics for adaptation and evolution of microorganisms

Abstract: Understanding the adaptation and evolution of populations is a huge challenge, in particular for microorganisms since it plays a main role in the virulence evolution or in bacterial antibiotics resistances. We propose a general eco-evolutionary stochastic model of population dynamics with clonal reproduction and mutations, including competition  for resources and exchange of genes. We study some asymptotics of this general birth and death process depending on the respective demographic, ecological and exchange  time scales. We  show how the gene exchanges can drastically affect the evolutionary outcomes.


 

 
Stochastic dynamics for adaptation and evolution of microorganisms

Abstract: Understanding the adaptation and evolution of populations is a huge challenge, in particular for microorganisms since it plays a main role in the virulence evolution or in bacterial antibiotics resistances. We propose a general eco-evolutionary stochastic model of population dynamics with clonal reproduction and mutations, including competition  for resources and exchange of genes. We study some asymptotics of this general birth and death process depending on the respective demographic, ecological and exchange  time scales. We  show how the gene exchanges can drastically affect the evolutionary outcomes.

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