AQSER
Automorphic q-series and their application
| Coordinatore | UNIVERSITAET ZU KOELN
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Germany [DE] |
| Totale costo | 1˙240˙500 € |
| EC contributo | 1˙240˙500 € |
| Programma | FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | ERC-2013-StG |
| Funding Scheme | ERC-SG |
| Anno di inizio | 2014 |
| Periodo (anno-mese-giorno) | 2014-01-01 - 2018-12-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITAET ZU KOELN
Organization address
address: ALBERTUS MAGNUS PLATZ contact info |
DE (KOELN) | hostInstitution | 1˙240˙500.00 |
| 2 |
UNIVERSITAET ZU KOELN
Organization address
address: ALBERTUS MAGNUS PLATZ contact info |
DE (KOELN) | hostInstitution | 1˙240˙500.00 |
Mappa
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Obiettivo del progetto (Objective)
'This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.'