20-21 February 2025,
Utrecht
Microlocal analysis
and spectral theory
a mini-workshop at the interface of PDEs, spectral
theory and mathematical physics
Microlocal analysis and spectral theory are at the heart of numerous on-going developments in mathematical physics, with applications including Quantum Field Theory, General Relativity, inverse problems, spectral geometry and fluid mechanics. This meeting will be an opportunity to explore the connections between different problems and techniques in the broader context of recent advances at the interface of partial differential equations, spectral theory and differential geometry.
Organisers:
A.
Kyaee
M.
Wrochna
Invited speakers
Spyros Alexakis
| University of
Toronto
Gabriele Benedetti
| Vrije Universiteit Amsterdam
Yannick Bonthonneau |
CNRS and Université Sorbonne Paris Nord
Nguyen Viet Dang |
Université de Strasbourg
Andreas Debrouwere |
Vrije Universiteit Brussel
Christian Gaß |
Universität Wien
András Vasy |
Stanford University (and
Springer Chair, Utrecht)
Jian Wang |
IHES, Bures-sur-Yvette
Alden Waters |
Universität Hannover
Registration
Please register before February 19th. Registration is free, but mandatory. Thank you!
Venue
The conference takes place in the center of Utrecht, at Janskerkhof 15A, 3512 BL Utrecht (room 001). It is a 15 minutes walk from Utrecht Centraal train station, which is connected by frequent direct trains from Rotterdam Centraal (37 min.), Amsterdam Schiphol airport (31 min.) and Amsterdam Centraal (26 min.).
Schedule
Thursday, February 20
13:00-13:50 — András Vasy
14:00-14:50 — Alden Waters
break
15:30-16:20 — Andreas
Debrouwere
16:30-17:20 — Gabriele Benedetti
19:00 — conference dinner
Friday, February 21
9:20- 10:30 — Yannick
Bonthonneau
coffee break
11:00-11:50 — Viet Dang Nguyen
lunch
13:30-14:10 — Jian Wang
14:10-14:50 — Christian
Gaß
coffee break
15:10-16:00 — Spyros Alexakis
Titles and abstracts
Spyros Alexakis
: tba
abstract: tba
Gabriele Benedetti
: Rigidity and flexibility of periodic Hamiltonian flows
abstract: An old problem in classical mechanics asks for the existence of periodic flows within specific classes of Hamiltonian systems such as central forces and geodesic flows. While Bertrand showed that only trivial examples of periodic flows among central systems exist (the gravitational and elastic force), Zoll and, later, Guillemin proved that there are many exotic examples among geodesic flows on the two-sphere. Following Guillemin’s microlocal approach, the goal of this talk is to construct magnetic flows (a generalization of geodesic flows in which the particle is subject to a Lorentz force) on the two-torus which are periodic for just one single value of the energy. This is joint work with Luca Asselle and Massimiliano Berti.
Yannick Bonthonneau : tba
abstract: tba
Nguyen Viet Dang : tba
abstract: tba
Andreas Debrouwere : tba
abstract: tba
Christian Gaß : Operator-theoretic approaches to QFT on curved spacetimes
abstract: I will describe two distinct approaches to Quantum Field Theory of a
scalar field on curved spacetimes based on operator-theory: the on-shell
approach based on the Krein space of solutions of the Klein-Gordon
equation and the off-shell approach based on the space of square
integrable functions on the spacetime. The off-shell approach is often
used implicitly to define the Feynman propagator via the path integral.
In well-behaved situations, the so-defined propagator corresponds to a
time-ordered two-point function between two Hadamard states.
After an introduction to the framework, I will apply these methods to
various patches of de Sitter space, where we encounter a particularly
rich structure. Due to the infinite expansion of de Sitter space, this
example is "not well-behaved": the path integral in the off-shell
approach does not yield a propagator with Hadamard type singularities,
i.e., it does not belong to one of the four parametrix classes of
Duistermaat and Hörmander.
András Vasy : tba
abstract: tba
Jian Wang : Topographic scattering of internal waves
abstract: Internal waves are a central topic in oceanography and the theory of rotating fluids. They are gravity waves in density-stratified fluids. In a two-dimensional aquarium, the velocity of linear internal waves can concentrate on certain attractors. Locations of internal wave attractors are related to periodic orbits of homeomorphisms of the circle, given by a nonlinear "chess billiard" dynamical system. This relation provides a surprising "quantum--classical correspondence" in fluid dynamics. In this talk, I will explain connections between homeomorphisms of circles, spectral theory, and internal wave dynamics.
Alden Waters : tba
abstract: tba
