This summer school focuses on number theory and its practical applications in cryptography and coding theory. Broadly speaking, number theory investigates properties of integers, including primes and solutions of Diophantine equations. Despite being a very ancient branch of mathematics, number theory very much remains a dynamic branch of mathematics, with ongoing research uncovering impressive results every year, and with new puzzling questions regularly surfacing. In recent decades, number theory has come to play a pivotal role in numerous real-life problems : for instance, prime numbers and their properties lie at the heart of the algorithms used to secure online payments. With the rapid development of computing technologies, it is actually fair to say that number theory takes a rapidly growing importance in cryptography and coding theory.
Our summer school aims to bridge theory and practice by providing students both with introductions to several key areas of number theory, and with a hands-on understanding of some of their prominent applications in cryptography and coding theory. Our summer school offers four courses in fundamental number theory, focusing on important topics such as number fields, elliptic curves, lattices, and modular forms. While these courses delve into theoretical aspects, we've designed them to include concrete examples and hands-on exercises to help students grasp the practical applications of these concepts. Additionally, we provide a series of courses exploring how these mathematical notions are being applied in cryptography and coding theory. These courses emphasize real-world examples, self-programmed protocol implementations, and hands-on applications.
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Scientific program is available on the local website of the school:
http://www.rnta.eu/Yogyakarta2025/index.html
Official language of the school: english