While landmark achievements by Perelman, Agol, and others have recently resolved major questions in dimension 3, the field of low-dimensional topology remains vibrant. Significant challenges persist—such as the L-space conjectureand the smooth Poincaré conjecture in dimension 4—alongside emerging questions at the intersection of various mathematical disciplines.

This is a thematic trimester programme with short courses, seminars and workshops on mathematical developments in Advances in Quantum Cryptography (QCRYPTO).

Timeline for the trimester:

September 13 to 17 - Introductory school at IHP, Paris, amphitheater Hermite

October 11 to 15 - Workshop 1 at IHP, Paris: Advances in Quantum Cryptography: Information-theoretic Foundations

Khazhgali Kozhasov

Patrick Tchepmo Djomegni

Ilpo Laine 

Summary: 

1. Basic notions of tropical analysis and tropical functions
2. Nevanlinna functions for tropical functions 
3. Tropical entire functions
4. First main theorem in tropical analysis
5. Tropical variants of some complex analysis results 
6. Tropical analysis in a finite interval 
7. Non-linear tropical functions 
8. Clunie, Valiron etc. in the tropical setting

Christophe Ritzenthaler

Summary: motivation sur l’exemple des courbes planes ; introduction des bases de géométrie algébriques (variétés, dimension, singularité, variété projective,…), problématique des courbes maximales sur les corps finis; présentation de 3 projets de recherches. 

Meysam Miralaei

Idrissa Kaboré

Fabio Gironella

Xavier Massaneda