Summer semester 2025
Organiser: Uwe Bandelow
Research seminar "Mathematical Models of Photonics"
Enrollment to the seminar: Students who want to attend this seminar for the modules P27, P28 and P35.3 should write an email to uwe.bandelow@hu-berlin.de. Please write as subject MathPho, your name, enrollment number, course of study.
I will save the email address and use it to send information regarding the seminar if this is not explicitly objected. You can cancel your enrollment to the seminar via email as well.
Proposed seminars
Tuesday 27.05.2025 15:00 (WIAS Erhardt Schmidt Lecture Room)Prof. Dmitry Turaev (Imperial College London)Thursday 26.06.2025, 16:00
Universality conjecture for Hamiltonians that split a homoclinic tangencyWe discuss the following conjecture: every Hamiltonian systems with 2 degrees of freedom is universal (i.e., approximates all symplectic dynamics possible in a 2-dimensional disc with arbitrarily good precision) if the change of energy unfolds a homoclinic tangency at some energy level.
Thursday 03.07.2025, 16:00
Thursday 10.07.2025, 16:00
Thursday 17.07.2025, 16:00
Monday 21.07.2025, 14:00 (WIAS Erhardt Schmidt Lecture Room)
Prof. Hinke M Osinga (The University of Auckland)Thursday 24.07.2025, 16:00
Phase resetting in a system of coupled Van der Pol oscillators
Joint work with Kyoung Hyun Lee, Neil Broderick and Bernd Krauskopf
Coupled nonlinear oscillators are found in many application contexts; specific examples in photonics are coupled optical cavities and ring resonators. Synchronisation properties of such systems can be probed by studying the response to external perturbations: after relaxation back to the stable oscillation, there is generally a phase shift. Important information can be gained by studying such phase resets as a function of when the perturbation is applied during the oscillation. We present a case study of a prototypical example: two coupled 1:1 phase-locked Van der Pol oscillators. In contrast to single oscillators, this system has a phase space of dimension four. In particular, the basin of attraction of the stable synchronised oscillation has a complicated boundary, and we show how this affects the observed phase resetting in unexpected ways.