Information for
Quick links
Faculties
Mathematical Colloquium
Wintersemester 2026/27
Quantum Algorithms for Scientific Computing
This talk explores the mathematical principles behind quantum algorithms for scientific computing and their connections to classical numerical analysis. We discuss how familiar techniques, from preconditioning linear systems to Newton's method for nonlinear equations, can be adapted to quantum computation, with applications to partial differential equations. Complexity estimates reveal the conditions under which these approaches can offer computational advantages over classical methods. Numerical experiments, including computations on quantum hardware, complement the theoretical analysis.
Capabilities and Limits of Large Language Models
AI systems based on Large Language Models (LLMs) are showing stunning progress. What are the abilities and limits of these models? I will present an emerging theory, from my group and others, on the capabilities of the underlying neural network architecture — the Transformer. First, I will study which functions this architecture is able to generalizably learn from finite data. Then, I will show bounds on the number of tokens that a Transformer needs to produce to perform specific computations. While the focus is on mathematical results, I will illustrate them with empirical data from Transformers and real-world Large Language Models.