Lattices and Geometry of numbers
- Lattices in Euclidean Space
- Minkowski's Convex Body Theorem, Minkowski's Theorem on Successive Minima.
Lecturer: Michel Waldschmidt (Paris 6)
(6 hours)
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Lattices and Number theory
- Ring of integers, Dirichlet Unit Theorem, Euclidean rings
- Arakelov divisors, ideal lattices, Arakelov class group, Buchmann's algorithm
Lecturers: Peter Stevenhagen (Leiden) - Tran Nguyen Thanh Ha (Aalto) (10 hours)
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Lattices and modular forms
- Theta functions, Modular forms for SL2(Z), Eisenstein series.
- Theta series, Unimodular even lattices.
Lecturers: René Schoof (Tor Vergata) - Valerio Talamanca (Roma Tre) (12 hours)
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Lattices in Lie algebras
- Lie groups and algebras, Root systems and Dynkin diagrams.
- Root lattices and Weight lattices.
Lecturer: Laura Geatti (Tor Vergata) (6 hours)
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Lattices and Mordell-Weil groups
- Elliptic curves, Mordell-Weil groups, Quadratic forms, Heights.
- Elliptic curves over function fields, Elkies constructions.
Lecturer: Francesco Pappalardi (Roma Tre) e Valerio Talamanca (Roma Tre) (10 hours)
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Lattices and Coding theory
- Linear codes, Hamming distance, Cyclic codes, Golay codes.
- Construction of the Leech lattice
Lecturer: Duong Hoang Dung (Kyushu)
(6 hours)
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Lattices and cryptography
- Lattice basis reduction, shortest vector problem, nearest vector problem, LLL-algorithm.
- Lattices based cryptography, Kissing number, sphere packings.
Lecturer Phong Nguyen, (INRIA) (10 hours)
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