Department Kolloquium Januar 2026

Applying Algebra to the Real World: From Reliable Communication to Post-Quantum Security

Violetta Weger (TUM)

Abstract:

In our modern digital world, nearly everything we do (from sending messages, sharing photos, storing documents, to retrieving information) happens electronically. For all of this to work smoothly, two things must happen behind the scenes: our messages must travel through noisy networks without being distorted, and they must stay private along the way. The first challenge is the realm of coding theory, which protects information from errors which might be added in noisy channels. The second challenge is handled by cryptography, which keeps our data secret from eavesdroppers.

Although these problems feel timeless today, the mathematics behind their solutions is surprisingly young. Starting only in the 1950s and 1970s, researchers discovered that elegant algebraic structures could be used to correct errors and secure communication. As technology evolves, the challenges and questions in both fields evolve with it - especially in cryptography, where the possibility of future quantum computers forces us to rethink long-trusted systems.

In this lecture, I will give an accessible introduction to coding theory and cryptography, highlight how abstract algebra shapes both areas, and explore their intersection in code-based cryptography, which are cryptographic systems designed to remain secure even in a world with quantum computers.

Quantum Geometry

Murad Alim (TUM)

Abstract:

Quantum theory has not only reshaped our understanding of the physical world; it has also become a powerful source of ideas for modern mathematics. In this talk, I will introduce aspects of the emerging field of quantum geometry, where insights from quantum field theory and string theory interact with symplectic, complex, and algebraic geometry. I will explain how dualities in physical theories often reveal that seemingly different mathematical structures share common underlying principles, leading to deep new results and unexpected bridges between diverse areas. A central example is mirror symmetry, a duality relating symplectic and complex geometry with far-reaching consequences for enumerative geometry, representation theory and number theory.