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Organizing Committee

Christine Bachoc
Université de Bordeaux

Henry Cohn
Microsoft Research New England

Renaud Coulangeon
Université de Bordeaux

Christopher Peikert
University of Michigan, Ann Arbor

Abstract

This workshop will focus on the computational aspects of the theory of Euclidean lattices and on their applications to other areas in mathematics and computer science. It will put emphasis on computational challenges on lattice problems that have recently arisen from unexpected connections to other domains such as algebraic topology, automorphic forms, or cryptography.

A major goal of this workshop is to bring together researchers from different areas, working with Euclidean lattices, and to facilitate their interactions.

Topics will include the reduction theory of lattices and its applications, Voronoi algorithms and their use to compute the cohomology of arithmetic groups, the classification of lattice genera and the computation of spaces of modular forms, the algorithmic aspects of lattice based cryptography, in particular the relationship between the security of cryptographic primitives and the hardness of lattice problems.

Computational Challenges in the Theory of Lattices

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Lecture Videos

A Reverse Minkowski Theorem

Oded Regev

New York University, Courant Institut

April 23, 2018 • 12:00 AM

Computational Challenges in the Theory of Lattices

Apr 23 - 27, 2018

Organizing Committee

Abstract

Lecture Videos

A Reverse Minkowski Theorem

On Approximating the Covering Radius and Finding Dense Lattice Subspaces

Logarithmic Lattices

Variations and Applications of Voronoi's Algorithm

Computational Challenges in Perfect form theory

Hardness and advantages of Module-SIS and LWE

Automorphisms of even unimodular lattices

Lattice methods for algebraic modular forms on orthogonal groups

Applications of harmonic analysis to packing and covering problems

Lattice packings of superballs

Orders and their discriminants

The hidden number problem revisited

On algebraic variants of the LWE problem

Lattices generated by equiangular tight frames

On the Density of Sets Avoiding Parallelohedron Distance 1

Signatures from finite field isomorphisms

Spinor regular ternary quadratic lattices

Fully Homomorphic Encryption - Simple Construction and Open Problems

Associated Semester Workshops

Point Configurations in Geometry, Physics and Computer Science

Optimal and Random Point Configurations

Fast Algorithms for Generating Static and Dynamically Changing Point...

Computation and Optimization of Energy, Packing, and Covering

Computational Challenges in the Theory of Lattices

Apr 23 - 27, 2018

Organizing Committee

Abstract

Confirmed Speakers & Participants

Lecture Videos

A Reverse Minkowski Theorem

On Approximating the Covering Radius and Finding Dense Lattice Subspaces

Logarithmic Lattices

Variations and Applications of Voronoi's Algorithm

Computational Challenges in Perfect form theory

Hardness and advantages of Module-SIS and LWE

Automorphisms of even unimodular lattices

Lattice methods for algebraic modular forms on orthogonal groups

Applications of harmonic analysis to packing and covering problems

Lattice packings of superballs

Orders and their discriminants

The hidden number problem revisited

On algebraic variants of the LWE problem

Lattices generated by equiangular tight frames

On the Density of Sets Avoiding Parallelohedron Distance 1

Signatures from finite field isomorphisms

Spinor regular ternary quadratic lattices

Fully Homomorphic Encryption - Simple Construction and Open Problems

Associated Semester Workshops

Point Configurations in Geometry, Physics and Computer Science

Optimal and Random Point Configurations

Fast Algorithms for Generating Static and Dynamically Changing Point...

Computation and Optimization of Energy, Packing, and Covering

Confirmed Speakers & Participants