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RTG2491 Autumn School
"Spectra of Analysis in Geometry and Physics"
October 6th to 10th, 2025
Registration is open!
SPEAKERS
Nelia Charalambous (University of Cyprus)
Jeffrey Galkowski (University College London)
Frédéric Rochon (Université du Québec à Montréal)
Alexander Strohmaier (Leibniz Universität Hannover)
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REGISTRATION
Financial support for the accommodation costs can be offered for a limited number of participants.If you would like to apply for funding, please select “Yes” below, fill out the fields and send your CV to rtg2491-events@mi.math.uni-goettingen.de before August 26th, 2025
Registration is open! Please register here
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POSTER
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TENTATIVE PROGRAMME
Nelia Charalambous (University of Cyprus)
Title: The spectrum of geometric operators on noncompact manifolds
Abstract: In this course we will give an overview of classical results for the spectrum of geometric operators such as the Laplacian on functions and differential forms and the Dirac operator. We will be considering both the spectrum when the operator is acting on a Hilbert space, but also on Banach spaces. We will be seeing how spectral results are also related to heat kernel estimates.
Jeffrey Galkowski (University College London)
Title: The high energy behavior of Laplace eigenfunctions: applications of geodesic beams
Abstract: We will discuss the high energy behavior of Laplace eigenfunctions. In particular, we focus on their L^\infty norms and various averages. The course will review some basics of semiclassical analysis and give an introduction to how the method of geodesic beams is used to link the behavior of eigenfunctions to the dynamics of the geodesic flow.
Frédéric Rochon (Université du Québec à Montréal)
Title: $L^2$-cohomology of complete hyperKähler metrics
Abstract: Using manifolds with corners, the first lecture will introduce the notion of quasi-fibered boundary (QFB) metrics, a class of complete riemannian metrics of bounded geometry including many examples of hyperKähler metrics, notably quiver varieties and the $L^2$-metric on the (universal cover of the reduced) moduli space of SU(2)-monopoles of magnetic charge k on $\mathbb{R}^3$. The second lecture will present the key basic features of $L^2$-cohomology for these metrics and give a local description of weighted $L^2$-cohomology in terms of a sheaf on an associated stratified space. The third lecture will focus on local computations of weighted $L^2$-cohomology using elementary results of the $b$-calculus of Melrose. Finally, in the last lecture, we will explain how these local computations can be used to compute reduced $L^2$-cohomology when the $L^2$-harmonic forms are known to decay sufficiently fast at infinity.
Alexander Strohmaier (Leibniz Universität Hannover)
Title: Spectral Theory on Spacetimes
Abstract: Modern methods developed for spectral theory on Riemannian manifolds can also be applied to the more general case of stationary spacetimes. Here spectral theory is of relevance in classical general relativity and quantum field theory. In comparison to the Riemannian case there are also some important differences. I will focus on trace-formulae and high frequency asymptotics.
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Poster Session
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TRAVEL AND ACCOMODATION
Here you will find information on how to get to and your stay in Göttingen.Arriving in Göttingen
Closest airports: Frankfurt Main International, Hannover
Göttingen is well connected via fast trains to most major cities in Germany. The travel time from Frankfurt is about 2h and from Hannover less than 1h.
Walking from the train station to the Mathematical Institut takes no more than 20 minutes passing through the town centre. Most hotels are in walking distance from the main building, however there is also a chance of using the buses.
Göttingen is well connected via fast trains to most major cities in Germany. The travel time from Frankfurt is about 2h and from Hannover less than 1h.
Walking from the train station to the Mathematical Institut takes no more than 20 minutes passing through the town centre. Most hotels are in walking distance from the main building, however there is also a chance of using the buses.
Hotels
Here is a list of recommended Hotels in Göttingen:
Leine Hotel
Eden Hotel
Hotel Central
G Hotel
Novostar
Hotel Stadt Hannover
Leine Hotel
Eden Hotel
Hotel Central
G Hotel
Novostar
Hotel Stadt Hannover
Map
Here is a map where you can find bus stops, sightseeing points and other information about Göttingen. The link is set to the Autumn School room, you can move freely within the map.
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