Abstract: We obtain a new obstruction to symplectic embeddings derived using the Symplectic Field Theory.

Abstract: Although we might not be aware of it, Number Theory has entered our daily lives: encrypted Internet connections (e.g., for online banking) are based on algorithms involving giant prime numbers with several hundred or more digits.

In this talk, I will explain how RSA, the most prominent of these public key encryption schemes, works. Then I will address the important question of how one can actually find the large primes needed for these applications. The primality tests used in practice turn out to be probabilistic, which means that they may sometimes give a wrong answer. Hopefully, I will convince you that this is no reason to be worried about the money in your account.