Organizing Committee
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.

Image for "Computational Challenges in the Theory of Lattices"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, April 23, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration121 South Main Street Providence RI 11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:00am EDTA Reverse Minkowski Theorem - Oded Regev, Courant Institute, New York University11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:45 - 11:30am EDTOn Approximating the Covering Radius and Finding Dense Lattice Subspaces - Daniel Dadush, CWI11th Floor Lecture Hall
11:40 - 12:40pm EDTLogarithmic Lattices - Leo Ducas, CWI11th Floor Lecture Hall
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:30pm EDTVariations and Applications of Voronoi’s Algorithm - Achill Schurmann, Universität Rostock11th Floor Lecture Hall
3:45 - 4:15pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:15 - 5:00pm EDTComputational Challenges in Perfect form theory - Mathieu Dutour Sikiric, Institut Rudjer Boskovic11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, April 24, 2018
TimeEventLocationMaterials
9:00 - 10:00am EDTOn algebraic variants of the LWE problem - Damien Stehlé, ENS de Lyon11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTHardness and advantages of Module-SIS and LWE - Adeline Roux-Langlois, Univ Rennes, CNRS, IRISA11th Floor Lecture Hall
11:30 - 12:15pm EDTAutomorphisms of even unimodular lattices - Eva Bayer, EPFL11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTLattice methods for algebraic modular forms on orthogonal groups - John Voight, Dartmouth College11th Floor Lecture Hall
3:30 - 5:00pm EDTPoster Session 11th Floor Collaborative Space 
Wednesday, April 25, 2018
TimeEventLocationMaterials
9:00 - 10:00am EDTApplications of harmonic analysis to packing and covering problems - Stephen Miller, Rutgers University11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:45 - 11:30am EDTSphere packing, lattice packing, and related problems - Abhinav Kumar, Stony Brook University11th Floor Lecture Hall
11:40 - 12:25pm EDTLattice packings of superballs - Maria Dostert, ICERM - EPFL11th Floor Lecture Hall
12:30 - 12:40pm EDTWorkshop Group Photo11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTTesting isomorphism of lattices over CM-orders - Alice Silverberg, University of California, Irvine11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTOrders and their discriminants - Hendrik Lenstra, Universiteit Leiden11th Floor Lecture Hall
Thursday, April 26, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTFully Homomorphic Encryption - Simple Construction and Open Problems - Daniele Micciancio, UCSD11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTThe hidden number problem revisited - Nadia Heninger, University of Pennsylvania11th Floor Lecture Hall
11:30 - 12:15pm EDT On the Probability of Primitive Sets and Generators in Lattices - Phong Nguyen, Inria and CNRS, JFLI, University of Tokyo11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTLattices generated by equiangular tight frames - Lenny Fukshansky, Claremont McKenna College11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
4:00 - 4:45pm EDTOn the Density of Sets Avoiding Parallelohedron Distance 1 - Philippe Moustrou, ICERM11th Floor Lecture Hall
Friday, April 27, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTSignatures from finite field isomorphisms - Jeffrey Hoffstein, Brown University11th Floor Lecture Hall 
10:00 - 10:30am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15am EDTSpinor regular ternary quadratic lattices - Anna Haensch, Duquesne Univeristy and Max Planck Institute for Mathematics11th Floor Lecture Hall
11:30 - 2:00pm EDTBreak for Lunch / Free Time  
2:00 - 3:30pm EDTOpen Problem Sessions - Ed Saff, Vanderbilt University11th Floor Lecture Hall
3:30 - 5:00pm EDTSemester Program Closing Reception 11th Floor Collaborative Space 

Associated Semester Workshops

Optimal and Random Point Configurations
Image for "Optimal and Random Point Configurations"

Lecture Videos

Spinor regular ternary quadratic lattices

Anna Haensch
Duquesne Univeristy and Max Planck Institute for Mathematics
April 27, 2018

The hidden number problem revisited

Nadia Heninger
University of Pennsylvania
April 26, 2018

A Reverse Minkowski Theorem

Oded Regev
Courant Institute, New York University
April 23, 2018