Coding theory and cryptography are important in everyday life, because they form some of the building blocks of e-commerce. Error-correction via coding theory protects information as it is stored or sent, and efficient error-correction may provide significant benefits and cost-savings for enterprise. Cryptographic systems are necessary to secure information in storage, transmission, and interaction, and provide both confidentiality and authenticity guarantees. While there has always been significant and fruitful interaction between algebraic geometry and both coding theory and cryptography, new directions in coding theory — such as locally decodable codes, codes for distributed storage systems, and network coding — suggest the possibility of new connections with algebraic geometry. This workshop will focus on questions such as: What new practical problems arising in applications lead to new questions or directions in algebraic geometry? How can new results in algebraic geometry advance the state of applications and practice in error-correction and cryptography?
Participants will spend one week working together in small groups on one of six projects related to the theme of the workshop. Instead of the more typical workshop structure where participants watch presentations of established results, participants will begin generating new results in collaboration with other participants. Participation is by invitation only.
(Center for Communications Research)
Kristin Lauter (Microsoft Research)
Judy Walker (University of Nebraska-Lincoln)