Vorträge in der Woche 10.02.2025 bis 16.02.2025

Dienstag, 11.02.2025: Degenerations and irreducibility problems in dynamics

Rohini Ramadas (Warwick)

This talk is about an application of combinatorial algebraic geometry to complex/arithmetic dynamics. The n-th Gleason polynomial G_n is a polynomial in one variable with Z-coefficients, whose roots correspond to degree-2 self-maps of C with an n-periodic ramification point. Per_n is an affine algebraic curve, defined over Q, parametrizing degree-2 self-maps of P^1 with an n-periodic ramification point. Two long-standing open questions in complex dynamics are: (1) Is G_n is irreducible over Q? (2) Is Per_n connected? We show that if G_n is irreducible over Q, then Per_n is irreducible over C, and is therefore connected. In order to do this, we find a Q-rational smooth point on a projective completion of Per_n — this Q-rational smooth point represents a special degeneration of degree-2 self-maps, and as such has a tropical interpretation.

Dienstag, 11.02.2025: Good families

Anton Deitmar

Donnerstag, 13.02.2025: The mathematics of locality in many-body quantum systems

Dr. Andrew Lucas (UC Boulder, USA)

In relativity, nothing can travel faster than the speed of light. But there are often emergent speed limits, such as the speed of sound, that limit practical information transfer. In quantum many-body lattice models, the existence of this emergent speed limit was first proved by Lieb and Robinson in 1972. Over 50 years later, their result has formed the backbone of very important results in mathematical physics. I will present a modern perspective on the Lieb-Robinson Theorem and present a selection of its applications, such as: constraining the time to prepare entangled states, the simulatability of quantum physics on classical computers, and the decay of the false vacuum in metastable quantum states.