CIMPA-ICTP Mathematics Research School on Lattices and Application to Cryptography and Coding Theory | (smr 2894)
Starts 1 Aug 2016
Ends 12 Aug 2016
Etc/GMT+7
Ho Chi Minh City - Viet Nam
The Abdus Salam International Centre for Theoretical Physics (ICTP) and the Centre International de Mathématiques Pures et Appliquées (International Center for Pure and Applied Mathematics - CIMPA) are jointly organizing a research School on "Lattices and applications to cryptography and coding theory", to be held at Saigon University, Vietnam from 1 to 12 August 2016.
PURPOSE OF THE ACTIVITY
Lattices play a central role in number theory and its applications. The aim of this school is to introduce participants to the ubiquity of lattices in number theory, algebra, arithmetic algebraic geometry, cryptography and coding theory. The theory of lattices will be developed from its very beginning and the basic notions required for the applications in number theory, algebra and arithmetic algebraic geometry will be provided. Appearances of lattices that we intend to cover include: the natural lattices structures of Mordell-Weil groups and unit groups, lie algebra root lattices, the lattice basis reduction algorithm "LLL", which has many applications to many areas of mathematics and finally the construction of the famous Leech lattice. On the applied side we plan to cover constructions of good error-correcting codes and of good sphere packings via dense lattices.
TOPICS to be covered by the activity include:
- Lattices and Number theory (Ring of integers, Dirichlet Unit Theorem, Minkowski Theorem, Euclidean rings; Arakelov divisors, ideal lattices, Arakelov class group, Buchmann's algorithm)
- Lattices in Lie algebras (Lie groups and algebras, Root systems and Dynkin diagrams; Root lattices and Weight lattices)
- Lattices and cryptography (Lattice basis reduction, shortest vector problem, nearest vector problem, LLL-algorithm; Lattices based cryptography, Kissing number, sphere packings)
- Lattices and Coding theory (Linear codes, Hamming distance, Cyclic codes, Golay codes; Construction of the Leech lattice)
- Lattices and modular forms (Theta functions, Modular forms for SL2(Z), Eisenstein series; Theta series, Unimodular even lattices)
- Lattices and Mordell-Weil groups (Elliptic curves, Mordell-Weil groups, Quadratic forms, Heights; Elliptic curves over function fields, Elkies constructions)
Scientific Committee:
Laura Geatti (Università di Roma Tor Vergata)
Phong Nguyen (Institut national de recherche en informatique et en automatique) René Schoof (Università di Roma Tor Vergata)
Anton Mellit (SISSA-ICTP)
Peter Stevenhagen (Leiden Universiteit)
Valerio Talamanca (Università Roma Tre)
REGISTRATION PROCEDURE: Only applicants who are NOTfrom Vietnam should submit their request for participation through the following online application system
Applicants from Vietnam should instead contact the local organizing committe by e-mail (cimpa2016@gmail.com)