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Miniworkshop: L2-Spectral Invariants and the Integrated Density of States
Organized by: Jozef Dodziuk (1), Daniel Lenz (2), Thomas Schick (3) and Ivan Veselić (4)
(1) Mathematics Programm, The CUNY Graduate Center, 365 Fifth Ave., NY 10016, NEW YORK, UNITED STATES(2) Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743, JENA, GERMANY
(3) Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3/5, 37073, GÖTTINGEN, GERMANY
(4) Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Strasse 41, D-09126, CHEMNITZ, GERMANY
Both the study of $L^2$-spectral invariants in geometry and the
investigation of the integrated density of states in mathematical physics
have attracted much attention in recent years. While the two topics are
strongly related, the corresponding communities are rather unaware of each
others work and methods. The main aim of this mini-workshop was to bring
together people from both fields and provide a basis for interaction.
Accordingly, the first two days of the conference were spent with survey
talks solicited by the organizers to highlight concepts and methods. There
were 9 such talks with durations between 60 and 90 minutes.
The second half of the conference was devoted to more detailed
investigations. Most participants used the opportunity to present their
current research in the area of the meeting. There were 13 such talks.
The results presented in those talks contained significant contributions
e.g.~to the Atiyah conjecture about integrality of $L^2$-Betti numbers for
a completely new class of groups by Peter Linnell, a mathematically
rigorous derivation using von Neumann traces of
the asymptotics of the specific heat near absolute zero by Mikhael Shubin,
and approximation results for the integrated
density of states in various new contexts.
Altogether the conference was attended by 17 participants.
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