Conclave meeting of the RTG 2491 “Fourier Analysis and Spectral Theory”

Organized by Leó Bénard, Ralf Meyer, Thomas Schick

October, 2nd – October, 5th, 2020

Mathematics Subject Classification (2010): 57N65, 20J05, 20F65, 57R50, 58D27.

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RTG2441 Retreat 2nd to 4th October 2020 Group Picture

Introduction by the Organizers

The RTG 2491 “Fourier Analysis and Spectral Theory” is the home of mathematical research and education of doctoral students. The research focuses around a common methodology: we apply techniques from spectral theory, in particular Fourier analysis and harmonic analysis. We do this in a variety of areas, from number theory to to differential equations and mathematical physics. Mathematical research tends to be quite specialized and sophisticated. As a consequence, it is often not easy to communicate what we are actually working at, and why this is exciting us so much —as typically it does. But it is a matter of fact that the truly exciting progress in most cases arises at the borderline of areas and from the combination of ideas from different fields. This is true for scientific advances in general, and also for the specific area of mathematics, and also in a subfield. If you have a chance to talk to research mathematicians, be it doctoral students or retired professors at the end of their career: often they will tell you that the decisive idea for a proof or a theorem arose from a chance encounter with someone with different background and perspective, or from a presentation in a rather different field. Consequence: we need to be experts in our specialty, but at the same time we need to learn to understand mathematics outside of our direct area of research. And we need to use the opportunities to communicate with others: excite them of our specific subfield, and become excited by what they are doing.

To foster this, we got together in a small hamlet in the hills south of Göttingen, cutting ourselves even off some of the modern communication channels and used the opportunity of intense interaction. As part of this we set ourselves the goal that each of us would explain to a peer his research, but then the non-expert would present this to the world.
The fruit of this you have in your hands: 15 short portraits of a research program; where Alice is explaining us the research agenda of Bob, while Bob describes what Alice is doing. Now the public is invited to read the outcome of the effort and to get engaged in even more discussions. Have fun!


Christian Bernert (written by Léo Bénard)
On the existence of solutions for Diophantine equations

Geoffrey-Desmond Busche (written by Jialong Deng)
On representation theory for Lie algebroids

Jialong Deng (written by Geoffrey-Desmond Busche)
Why you cannot have bulges everywhere

Tom Dove (written by Eske Ewert)
Topological T -duality

Eske Ewert (written by Tom Dove)
Filtered manifolds and non-elliptic operators

Rosa Marchesini (written by Jérémy Mougel)
In search for ideals in the world of Lie algebroids

Jérémy Mougel (written by Rosa Marchesini)
Finding regularity for bound states in the N-body problem

Leonhard Felix René Hochfilzer (written by Thorsten Hertl)
On the Numbers of Solutions of Systems of Homogeneous Forms

Leonid Ryvkin (written by Fabrizio Zanello)
New techniques for the study of singular foliations

Fabrizio Zanello (written by Leonid Ryvkin)
Field theories associated to the Sine-Gordon equation

Thorsten Hertl (written by Leonhard Hochfilzer)
A very complicated L2-invariant

Rok Havlas (written by Zhicheng Han)
Introduction to the circle method

Thorben Kastenholz (written by David Kern)
Representing homology classes as manifolds

David Kern (written by Thorben Kastenholz)
Geometric quantization – What are the physicists doing?

Léo Bénard (written by Christian Bernert)
Low-dimensional topology

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