Marcolli, Matilde and Panangaden, Jane (2020) Quantum Statistical Mechanics and the Boundary of Modular Curves. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210825-184601111
![]() |
PDF (14 Sep 2021)
- Submitted Version
See Usage Policy. 414kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20210825-184601111
Abstract
The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as part of a family of noncommutative spaces associated to different continued fractions algorithms, endowed with the structure of a quantum statistical mechanical system. Two special cases of this family of quantum systems can be interpreted as a boundary of the system associated to the Shimura variety of GL₂ and an analog for SL₂. The structure of KMS states for this family of systems is discussed. In the geometric cases, the ground states evaluated on boundary arithmetic elements are given by pairings of cusp forms and limiting modular symbols.
Item Type: | Report or Paper (Discussion Paper) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Related URLs: |
| ||||||||||
Additional Information: | The first author is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and the Perimeter Institute for Theoretical Physics. | ||||||||||
Funders: |
| ||||||||||
Record Number: | CaltechAUTHORS:20210825-184601111 | ||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210825-184601111 | ||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
ID Code: | 110544 | ||||||||||
Collection: | CaltechAUTHORS | ||||||||||
Deposited By: | George Porter | ||||||||||
Deposited On: | 25 Aug 2021 22:17 | ||||||||||
Last Modified: | 23 Sep 2021 18:38 |
Repository Staff Only: item control page